WEBVTT 00:00:00.150 --> 00:00:02.550 The following content is provided under a Creative 00:00:02.550 --> 00:00:04.090 Commons license. 00:00:04.090 --> 00:00:06.390 Your support will help MIT OpenCourseWare 00:00:06.390 --> 00:00:10.780 continue to offer high quality educational resources for free. 00:00:10.780 --> 00:00:13.380 To make a donation or view additional materials 00:00:13.380 --> 00:00:17.340 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:17.340 --> 00:00:18.510 at ocw.mit.edu. 00:00:22.190 --> 00:00:24.250 WILL MA: OK, guys, I guess I'll get started. 00:00:24.250 --> 00:00:26.190 So I guess one quick announcement 00:00:26.190 --> 00:00:31.259 is, so I guess everyone has taken a look at the prizes. 00:00:31.259 --> 00:00:32.759 If you can take a look at the prizes 00:00:32.759 --> 00:00:34.980 and, especially, if you're near the top 00:00:34.980 --> 00:00:36.900 and expect yourself to be getting some prizes. 00:00:36.900 --> 00:00:39.090 So we haven't announced the final ordering yet, 00:00:39.090 --> 00:00:40.980 because it'll also depend on the homework 00:00:40.980 --> 00:00:43.580 and then we'll decide how much. 00:00:43.580 --> 00:00:45.211 It'll mostly just be number of points, 00:00:45.211 --> 00:00:46.710 but we might give a bit of weighting 00:00:46.710 --> 00:00:50.400 to people who have like a high points per game or something. 00:00:50.400 --> 00:00:53.040 But if you think you have a decent chance of getting 00:00:53.040 --> 00:00:54.920 prizes, it'd be good if you looked them 00:00:54.920 --> 00:00:58.680 over for when you research who this Mike McDonald guy is, how 00:00:58.680 --> 00:01:00.030 much is his coaching worth-- 00:01:00.030 --> 00:01:02.940 you can do that beforehand so that people don't take forever 00:01:02.940 --> 00:01:06.550 deciding which prize you want on Friday. 00:01:06.550 --> 00:01:08.966 OK, so I'm going to get started then. 00:01:08.966 --> 00:01:11.340 So this is going to be the last class I'm going to teach. 00:01:11.340 --> 00:01:15.030 So the final class, on Friday, is 00:01:15.030 --> 00:01:18.480 going to be guess-lectured by Bill Chen. 00:01:18.480 --> 00:01:22.420 So I want to go through an in-depth combinatorial hand 00:01:22.420 --> 00:01:24.390 analysis of a cash-game hand-- 00:01:24.390 --> 00:01:27.872 go very in depth on a hand where you have deep stacks, 00:01:27.872 --> 00:01:30.330 and there's a lot of action, and there's a lot of deduction 00:01:30.330 --> 00:01:31.830 that can take place. 00:01:31.830 --> 00:01:36.000 And then I'll finish with some general poker stuff 00:01:36.000 --> 00:01:39.420 and answer any questions you guys might have about the poker 00:01:39.420 --> 00:01:42.710 economy, how certain things work, the history of poker-- 00:01:42.710 --> 00:01:44.830 I'm happy to answer whatever questions. 00:01:44.830 --> 00:01:48.270 OK, so first, I'll do something more technical and more 00:01:48.270 --> 00:01:49.500 practical to the game. 00:01:49.500 --> 00:01:52.950 So an in-depth combinatorial hand analysis in cash games. 00:01:52.950 --> 00:01:54.810 So I'm going to look at the following hand. 00:01:54.810 --> 00:01:56.580 And the board is visible? 00:01:56.580 --> 00:01:57.240 It's good? 00:01:57.240 --> 00:01:58.760 OK. 00:01:58.760 --> 00:01:59.760 So this is a cash game. 00:01:59.760 --> 00:02:01.218 This is no longer a tournament now. 00:02:01.218 --> 00:02:03.690 And everybody has 100 big blinds. 00:02:03.690 --> 00:02:07.630 So the blinds are $1 and $2, and everyone starts with $200. 00:02:07.630 --> 00:02:09.509 So it's 100 big blinds. 00:02:09.509 --> 00:02:12.000 The cutoff opens near six, and we have eight-seven 00:02:12.000 --> 00:02:13.410 suited on the button. 00:02:13.410 --> 00:02:15.690 And when it's this deep stacked-- 00:02:15.690 --> 00:02:17.130 so in a tournament, this might not 00:02:17.130 --> 00:02:19.860 be a good situation to call, because it just puts 00:02:19.860 --> 00:02:21.580 a lot of risk on you to bust. 00:02:21.580 --> 00:02:24.210 And also, you're not really that deep stacked. 00:02:24.210 --> 00:02:26.280 But here, with 100 big blinds, we 00:02:26.280 --> 00:02:29.400 can really realize a lot of our implied odds 00:02:29.400 --> 00:02:31.047 given that we're both in position, 00:02:31.047 --> 00:02:32.755 and we have a hand that plays very well-- 00:02:32.755 --> 00:02:35.730 a suited connector-- that can make straights and flushes. 00:02:35.730 --> 00:02:40.100 So we decide to call, and the big blind also calls. 00:02:40.100 --> 00:02:44.660 OK, so the flop is 10, eight, six with a club, 00:02:44.660 --> 00:02:48.850 and the cutoff continuation bet's 14. 00:02:48.850 --> 00:02:50.940 So one thing I'll talk about first 00:02:50.940 --> 00:02:53.520 is, continuation bet sizing. 00:02:53.520 --> 00:02:56.100 So I said a bit about this, but I 00:02:56.100 --> 00:02:57.900 wanted to talk a bit more about bet sizing. 00:02:57.900 --> 00:02:59.942 And this is really just a review of what I've 00:02:59.942 --> 00:03:01.150 been talking about all class. 00:03:01.150 --> 00:03:04.770 It's the same principles when deciding your flop and turn bet 00:03:04.770 --> 00:03:05.460 sizing. 00:03:05.460 --> 00:03:07.890 So you don't want to bet so small that your opponent has 00:03:07.890 --> 00:03:10.110 the odds to call with anything, but you 00:03:10.110 --> 00:03:12.720 don't want to bet so big that you are risking a lot of chips 00:03:12.720 --> 00:03:13.890 when you're bluffing. 00:03:13.890 --> 00:03:17.420 And also, if your raise size commits your entire stack 00:03:17.420 --> 00:03:21.960 anyway, like if you're roughly, let's say, betting 40% or more 00:03:21.960 --> 00:03:24.540 of your remaining chips, then you might as well go all-in 00:03:24.540 --> 00:03:26.940 if it's the flop or the turn because you probably 00:03:26.940 --> 00:03:28.782 aren't going to fold. 00:03:28.782 --> 00:03:30.240 Given that your hand is good enough 00:03:30.240 --> 00:03:32.040 to put in 40% of your chips, you probably 00:03:32.040 --> 00:03:34.110 have enough equity that you're OK 00:03:34.110 --> 00:03:37.494 putting in 100% of your chips. 00:03:37.494 --> 00:03:39.660 Remember that raising your bet gives them the option 00:03:39.660 --> 00:03:41.460 to reraise, so that's always an incentive 00:03:41.460 --> 00:03:44.580 against raising a flop bet. 00:03:44.580 --> 00:03:46.400 The sizing should be bigger on dry boards 00:03:46.400 --> 00:03:47.730 and smaller on dry boards. 00:03:47.730 --> 00:03:48.840 We talked about this. 00:03:48.840 --> 00:03:49.420 And you want to bet? 00:03:49.420 --> 00:03:51.336 Bet a bit bigger when they're out of position. 00:03:51.336 --> 00:03:53.790 So he's kind of out of position here against us, 00:03:53.790 --> 00:03:56.670 and he bets 14 into 19, which is a reasonably big bet, 00:03:56.670 --> 00:03:57.960 but I think it's fine. 00:03:57.960 --> 00:04:00.390 So with our hand here, eight-seven of clubs, 00:04:00.390 --> 00:04:02.940 I think we definitely don't want to be folding. 00:04:02.940 --> 00:04:04.860 So let's talk about the differences 00:04:04.860 --> 00:04:07.410 between raising and calling. 00:04:07.410 --> 00:04:12.910 So we decide to call, and so what's the analysis? 00:04:12.910 --> 00:04:15.250 So we're definitely not folding. 00:04:15.250 --> 00:04:16.860 Raising, I think, is a bit suicidal 00:04:16.860 --> 00:04:20.010 when we have a medium-strength hand that can play well 00:04:20.010 --> 00:04:21.810 in position on a lot of turns. 00:04:21.810 --> 00:04:24.030 And we have a backdoor flush draw; 00:04:24.030 --> 00:04:25.980 and our straight draw's very legitimate 00:04:25.980 --> 00:04:27.960 when there is no flush draw out there. 00:04:27.960 --> 00:04:30.080 So we decide to just call. 00:04:30.080 --> 00:04:32.700 We have to be a bit worried about a big blind check-raise, 00:04:32.700 --> 00:04:34.410 but I think it's OK. 00:04:34.410 --> 00:04:36.780 It's not that big of a deal, especially when there's 00:04:36.780 --> 00:04:37.930 no flush draw. 00:04:37.930 --> 00:04:41.100 So the big blind folds. 00:04:41.100 --> 00:04:46.880 And on the turn is the queen of clubs, and he bets 30. 00:04:46.880 --> 00:04:50.850 OK, so this is sort of a tougher decision now than the flop, 00:04:50.850 --> 00:04:51.840 I'd say. 00:04:51.840 --> 00:04:53.850 So let's analyze this. 00:04:53.850 --> 00:04:58.000 So he bets 30 into 47, we've got 180 behind, 00:04:58.000 --> 00:04:59.730 which is about four times the pot, 00:04:59.730 --> 00:05:02.509 and we've got a pretty bad hand right now, 00:05:02.509 --> 00:05:04.050 but we still have a pair, and we have 00:05:04.050 --> 00:05:06.570 lots of chances to hit a straight, or hit a flush, 00:05:06.570 --> 00:05:08.980 or hit three of a kind or hit two pairs. 00:05:08.980 --> 00:05:12.379 So tons of outs-- tons of river cards that help us. 00:05:12.379 --> 00:05:13.920 And so what are the benefits of each? 00:05:13.920 --> 00:05:16.770 OK, so I think it's fairly clear we're 00:05:16.770 --> 00:05:19.330 not going to fold here with this much equity. 00:05:19.330 --> 00:05:22.534 So what are the benefits of calling? 00:05:22.534 --> 00:05:24.450 Well, we get to see the river for sure, right? 00:05:24.450 --> 00:05:27.300 If the river's a club, then we don't 00:05:27.300 --> 00:05:29.557 want to fold in situations and not 00:05:29.557 --> 00:05:31.890 see the river when it could be a club, which is the best 00:05:31.890 --> 00:05:34.364 card for us, essentially. 00:05:34.364 --> 00:05:36.030 Yeah, so we really want to see the river 00:05:36.030 --> 00:05:39.960 because if we raise, then maybe they could reraise all-in, 00:05:39.960 --> 00:05:41.910 and then we would have to fold. 00:05:41.910 --> 00:05:44.210 So that's one clear benefit. 00:05:44.210 --> 00:05:46.730 And another sort of benefit is, we already 00:05:46.730 --> 00:05:48.120 have a pair to start with. 00:05:48.120 --> 00:05:50.637 So we don't really need to bluff to win a hand. 00:05:50.637 --> 00:05:52.970 So this is something I've been talking about a lot, too. 00:05:55.710 --> 00:05:58.950 If you don't need to raise to win the hand because you 00:05:58.950 --> 00:06:01.020 already have a pair, then there's 00:06:01.020 --> 00:06:02.579 a lot more incentive to call. 00:06:02.579 --> 00:06:04.120 So what are some benefits of raising? 00:06:04.120 --> 00:06:07.130 Well, if you get him to fold something like pocket jacks-- 00:06:07.130 --> 00:06:09.060 if we think he might have like pocket jacks-- 00:06:09.060 --> 00:06:12.570 it can definitely get him to fold some better hands. 00:06:12.570 --> 00:06:15.510 And we can bet the river and win a bigger pot when we hit. 00:06:15.510 --> 00:06:18.630 And we can also maybe make some bigger bluffs when we miss. 00:06:18.630 --> 00:06:22.140 So we'll go through a more detailed analysis in a bit, 00:06:22.140 --> 00:06:25.560 but I like calling in this situation. 00:06:25.560 --> 00:06:27.960 I think with a draw that has no showdown 00:06:27.960 --> 00:06:31.500 value, like say I had nine-five of clubs instead of eight-seven 00:06:31.500 --> 00:06:33.350 of clubs, which has a pair, I think 00:06:33.350 --> 00:06:35.970 I would raise for two reasons. 00:06:35.970 --> 00:06:40.110 One is, I would need to bluff the river anyway 00:06:40.110 --> 00:06:41.200 if I miss the river. 00:06:41.200 --> 00:06:43.710 So if I raise now, I just give myself a chance 00:06:43.710 --> 00:06:45.300 to win the pot right now. 00:06:45.300 --> 00:06:49.680 And another benefit of raising is that I can-- 00:06:49.680 --> 00:06:52.320 I'm not that unhappy if he goes all-in 00:06:52.320 --> 00:06:58.110 because my jaw is less strong than eight-seven of clubs is. 00:06:58.110 --> 00:07:00.604 OK, and then maybe with a hand like ace-jack of clubs, 00:07:00.604 --> 00:07:02.520 I would raise just because we can maybe get it 00:07:02.520 --> 00:07:05.568 in against weaker flush draws. 00:07:05.568 --> 00:07:08.520 OK, so yeah, this is a general principle 00:07:08.520 --> 00:07:11.550 that I haven't really talked about for playing on flops 00:07:11.550 --> 00:07:14.280 and turns. 00:07:14.280 --> 00:07:16.126 And this sort of goes along with most 00:07:16.126 --> 00:07:18.000 of the stuff we've talked about in this class 00:07:18.000 --> 00:07:21.180 but, in general, when you have like the stone-cold nuts 00:07:21.180 --> 00:07:24.364 and when you have weaker draws, you 00:07:24.364 --> 00:07:27.030 want to be the one-- you want to be betting and raising in a way 00:07:27.030 --> 00:07:30.286 such that your opponent gets the last bet in. 00:07:30.286 --> 00:07:33.750 So one person is always going to go all-in first, right? 00:07:33.750 --> 00:07:36.420 If you're raising each other or betting and raising, 00:07:36.420 --> 00:07:38.400 one person is going to go on first, 00:07:38.400 --> 00:07:39.930 and the other person, basically, has 00:07:39.930 --> 00:07:43.200 to decide whether to call or fold and play for your stack. 00:07:43.200 --> 00:07:45.690 So if you have the stone-cold nuts, 00:07:45.690 --> 00:07:49.801 then you want to be the person having your opponent go all-in 00:07:49.801 --> 00:07:50.300 first. 00:07:50.300 --> 00:07:51.900 Because obviously, you have a very easy decision. 00:07:51.900 --> 00:07:53.570 You just call and you're going to win. 00:07:53.570 --> 00:07:56.250 On the other hand, if you have like a weaker draw, 00:07:56.250 --> 00:07:57.961 which is, essentially, your bluff-- 00:07:57.961 --> 00:07:59.460 because we don't want to be bluffing 00:07:59.460 --> 00:08:00.510 with absolutely nothing. 00:08:00.510 --> 00:08:01.926 We want to be bluffing, basically, 00:08:01.926 --> 00:08:03.480 with our weaker draws. 00:08:03.480 --> 00:08:05.740 That's also an easy decision because if, let's say, 00:08:05.740 --> 00:08:07.410 we have a gutshot straight draw. 00:08:07.410 --> 00:08:09.420 So we have four outs only. 00:08:09.420 --> 00:08:11.664 We're not that sad if our opponent goes all-in 00:08:11.664 --> 00:08:13.080 on the flop or all-in on the turn. 00:08:13.080 --> 00:08:14.070 We just fold. 00:08:14.070 --> 00:08:17.640 We have an easy decision; whereas if we 00:08:17.640 --> 00:08:19.615 have a more vulnerable good hand-- like you 00:08:19.615 --> 00:08:22.780 have top pair with a medium kicker, then 00:08:22.780 --> 00:08:23.890 it's a tough decision. 00:08:27.180 --> 00:08:29.430 If our opponent goes all-in, we have a tough decision. 00:08:29.430 --> 00:08:30.590 We're not sure what to do. 00:08:30.590 --> 00:08:32.419 And same if we have a stronger draw-- like 00:08:32.419 --> 00:08:35.010 say we have a flush draw, and we have nine outs, 00:08:35.010 --> 00:08:36.990 and then our opponent goes all-in on the flop, 00:08:36.990 --> 00:08:40.500 and we have like 1.61 odds to call or something. 00:08:40.500 --> 00:08:42.270 It's a difficult decision. 00:08:42.270 --> 00:08:45.052 And so in these hands, you definitely 00:08:45.052 --> 00:08:46.510 want to-- you generally want to bet 00:08:46.510 --> 00:08:49.410 and raise in a way that allows you to get the last bet in. 00:08:49.410 --> 00:08:52.070 Because with a stronger draw, your opponent 00:08:52.070 --> 00:08:53.280 gets to make a decision. 00:08:53.280 --> 00:08:56.187 But even if they have the nuts, you still have nine outs. 00:08:56.187 --> 00:08:57.770 And with a more vulnerable good hand-- 00:08:57.770 --> 00:08:59.353 I mean, if your opponent has the nuts, 00:08:59.353 --> 00:09:01.230 I guess you're kind of dead, but you're 00:09:01.230 --> 00:09:03.270 sort of protecting the times you go all-in 00:09:03.270 --> 00:09:04.740 with your stronger draws. 00:09:04.740 --> 00:09:07.710 So following that principle, I decide to just call here 00:09:07.710 --> 00:09:11.760 because if I raise, then I have to make a decision when he goes 00:09:11.760 --> 00:09:12.750 all-in-- 00:09:12.750 --> 00:09:15.930 whether to call with my medium-strength hand and pretty 00:09:15.930 --> 00:09:17.491 good draw. 00:09:17.491 --> 00:09:21.130 OK, so we call, and the river's an ace of spades. 00:09:21.130 --> 00:09:26.500 So we completely miss, and our opponent checks to us. 00:09:26.500 --> 00:09:28.640 So we decide to bluff the river for 70. 00:09:28.640 --> 00:09:31.380 And this is sort of the main decision I want to analyze, 00:09:31.380 --> 00:09:34.700 and it's going to be quite a complicated decision. 00:09:34.700 --> 00:09:36.970 So let's do some quick analysis. 00:09:36.970 --> 00:09:39.400 So yes, we do have some chances of winning 00:09:39.400 --> 00:09:40.449 with our pair of eights. 00:09:40.449 --> 00:09:42.490 So maybe you can make a case that there's no need 00:09:42.490 --> 00:09:44.440 to bluff because we do have a pair, 00:09:44.440 --> 00:09:46.600 but there's a lot of reasons to bluff. 00:09:46.600 --> 00:09:49.870 So one is, there's a lot of higher cards on the board now. 00:09:49.870 --> 00:09:52.710 The pair of eights-- they looked pretty good on the flop, 00:09:52.710 --> 00:09:56.230 but now it's a lot worse after a queen turn and an ace river. 00:09:56.230 --> 00:09:58.750 So we can get him to fold a queen. 00:09:58.750 --> 00:10:01.090 He can have a queen, and he could very willingly 00:10:01.090 --> 00:10:03.580 be able to fold it. 00:10:03.580 --> 00:10:05.660 Also, the pot is big. 00:10:05.660 --> 00:10:07.420 They bet the flop and the turn, and we 00:10:07.420 --> 00:10:08.720 called the flop and the turn. 00:10:08.720 --> 00:10:12.250 So both ranges are just very strong because so much money 00:10:12.250 --> 00:10:13.340 has already gone in. 00:10:13.340 --> 00:10:16.690 So a pair of eights is not so good. 00:10:16.690 --> 00:10:18.970 If you knew that he had two random cards, sure, 00:10:18.970 --> 00:10:21.340 a pair of eights will win a decent percent of the time. 00:10:21.340 --> 00:10:23.298 But when you know you're up against a hand that 00:10:23.298 --> 00:10:26.020 was willing to bet the flop and bet the turn, 00:10:26.020 --> 00:10:28.780 it's less likely the pair of eights is good. 00:10:28.780 --> 00:10:31.390 And then, the ace is always a scary card. 00:10:31.390 --> 00:10:33.430 And another advantage of bluffing is-- 00:10:33.430 --> 00:10:35.390 this is why position is so great-- 00:10:35.390 --> 00:10:37.930 especially when it's deep stacked in a cash game. 00:10:37.930 --> 00:10:41.610 We're in position, and we know that he checked the river. 00:10:41.610 --> 00:10:43.480 So maybe he's trapping with like king-jack, 00:10:43.480 --> 00:10:46.537 but it's more likely than not that it's a sign of weakness 00:10:46.537 --> 00:10:47.620 that he checked the river. 00:10:47.620 --> 00:10:52.760 So we could try to bluff him off his hand. 00:10:52.760 --> 00:10:54.779 OK, so what about river bet sizing? 00:10:54.779 --> 00:10:56.570 So okay, so one thing is whether the bluff. 00:10:56.570 --> 00:10:58.640 Two, is if you bluff, how much do you bet? 00:10:58.640 --> 00:11:02.277 So I decided to bet 70 into 107. 00:11:02.277 --> 00:11:04.360 And so what are the things to consider when you're 00:11:04.360 --> 00:11:06.680 deciding your river bet sizing? 00:11:06.680 --> 00:11:09.410 So one is, there's no more cards to come on the river. 00:11:09.410 --> 00:11:11.984 So in some sense, there's less of a worry 00:11:11.984 --> 00:11:13.900 to betting really, really small, because there 00:11:13.900 --> 00:11:17.000 is no such thing as letting your opponent see a draw. 00:11:17.000 --> 00:11:19.040 But it still has a disadvantage. 00:11:19.040 --> 00:11:21.860 Like if your opponent checks to you and you bet small, 00:11:21.860 --> 00:11:24.144 it still does give them the option to check-raise. 00:11:24.144 --> 00:11:26.060 So that is one thing you worry about if you're 00:11:26.060 --> 00:11:27.800 trying to bet really small. 00:11:27.800 --> 00:11:29.690 And another thing is, you should bet big 00:11:29.690 --> 00:11:31.520 if your hand is polarized. 00:11:31.520 --> 00:11:34.730 By polarized I mean, you either have the stone-cold nuts 00:11:34.730 --> 00:11:35.630 or you have a bluff. 00:11:38.240 --> 00:11:41.470 Basically, if you bet small and your range is polarized, 00:11:41.470 --> 00:11:44.420 your opponent can just call with a very wide range of hands 00:11:44.420 --> 00:11:45.980 because their odds are too good. 00:11:45.980 --> 00:11:49.490 By betting big, you give your opponent worst odds to call, 00:11:49.490 --> 00:11:54.230 and since you have a stone-cold bluff some percent of the time, 00:11:54.230 --> 00:11:56.670 you don't want your opponent to have the odds to call 00:11:56.670 --> 00:11:59.670 with like third pair. 00:11:59.670 --> 00:12:02.640 OK so, it doesn't matter what they 00:12:02.640 --> 00:12:04.710 did, because our decision is betting 70. 00:12:04.710 --> 00:12:06.530 OK, so now what I sort of want to do 00:12:06.530 --> 00:12:08.420 is, a lot happened this hand, right? 00:12:08.420 --> 00:12:12.180 We know they raised the preflop, bet flop, bet turn, 00:12:12.180 --> 00:12:13.310 checked river. 00:12:13.310 --> 00:12:16.620 So in some sense, we have a ton of information. 00:12:16.620 --> 00:12:19.280 So in the tournaments that you play, maybe a hand like this 00:12:19.280 --> 00:12:21.210 doesn't show up that often because often it's 00:12:21.210 --> 00:12:24.980 just an all-in preflop, and you can't really deduce that much 00:12:24.980 --> 00:12:26.210 about your opponent's hand. 00:12:26.210 --> 00:12:29.640 It's just like, he has the top 30% of hands or something. 00:12:29.640 --> 00:12:32.240 But here, we can actually do a lot of deduction. 00:12:32.240 --> 00:12:36.290 So let's replay the hand from our opponent's perspective 00:12:36.290 --> 00:12:39.780 and sort of exploitatively put them on a range. 00:12:39.780 --> 00:12:42.000 So let's go put ourselves in our opponent's shoes 00:12:42.000 --> 00:12:44.580 and consider all the actions they did. 00:12:44.580 --> 00:12:47.220 So I'm going to use exploitative analysis here. 00:12:47.220 --> 00:12:49.190 So there are some flaws with this. 00:12:49.190 --> 00:12:51.740 We are sort of arrogantly assuming 00:12:51.740 --> 00:12:53.570 we're one step ahead of our opponent-- 00:12:53.570 --> 00:12:56.030 we can build a mathematical model for our opponent. 00:12:56.030 --> 00:12:58.100 But still, this is a useful exercise even 00:12:58.100 --> 00:12:59.900 though, yes, there are flaws. 00:12:59.900 --> 00:13:01.580 Maybe he's one step ahead of us. 00:13:01.580 --> 00:13:03.680 Maybe there's flaws in our probabilistic model. 00:13:03.680 --> 00:13:06.380 But let's just assume for the sake of the exercise 00:13:06.380 --> 00:13:08.120 that we can do this pretty well. 00:13:08.120 --> 00:13:13.460 OK, so first of all, preflop, what's our opponent's range? 00:13:13.460 --> 00:13:16.340 Let's just say, roughly, he's opening from the cutoff. 00:13:16.340 --> 00:13:18.680 Let's say he's opening about 30% of hands. 00:13:18.680 --> 00:13:21.440 I think that's about reasonable for like an average player, 00:13:21.440 --> 00:13:23.990 and I think it's consistent with the guidelines 00:13:23.990 --> 00:13:25.270 I gave in the first lecture. 00:13:25.270 --> 00:13:29.840 So this includes any pair, any suited ace, any two Broadway 00:13:29.840 --> 00:13:32.010 cards, which are cards 10 and higher. 00:13:32.010 --> 00:13:35.390 It includes suited hands as bad as five-three suited. 00:13:35.390 --> 00:13:37.580 This is maybe one difference between cash games 00:13:37.580 --> 00:13:40.370 and tournaments, where five-three suited 00:13:40.370 --> 00:13:43.460 is a pretty bad hand in tournaments when it's so short; 00:13:43.460 --> 00:13:45.860 but when it's 100 big blinds deep, 00:13:45.860 --> 00:13:47.930 a hand like five-three suited is a lot better 00:13:47.930 --> 00:13:50.980 than a hand like 10-8 offsuit. 00:13:50.980 --> 00:13:52.730 So yeah, so it includes five-three suited, 00:13:52.730 --> 00:13:55.940 but not like nine-eight off or like king-seven off, 00:13:55.940 --> 00:13:59.840 which are just terrible hands when it's 100 big blinds deep. 00:13:59.840 --> 00:14:03.360 So OK, so what's our opponent's range here? 00:14:03.360 --> 00:14:05.410 So they decided to continuation the bet. 00:14:05.410 --> 00:14:09.200 They continuation bet into the flop against two players 00:14:09.200 --> 00:14:12.020 after the big blind check. 00:14:12.020 --> 00:14:14.510 So what can we put him on? 00:14:14.510 --> 00:14:16.850 OK, so this is a complicated analysis, 00:14:16.850 --> 00:14:19.070 and you can't really do this during the game itself, 00:14:19.070 --> 00:14:21.620 but it's very useful to do it after the hand. 00:14:21.620 --> 00:14:23.570 So let's review the factors of why 00:14:23.570 --> 00:14:26.060 a player would continuation bet and then consider 00:14:26.060 --> 00:14:29.390 why he continuation bets. 00:14:29.390 --> 00:14:32.200 OK, so this is also sort of a review 00:14:32.200 --> 00:14:33.440 class since the last class. 00:14:33.440 --> 00:14:35.777 So what are the incentives for continuation betting? 00:14:35.777 --> 00:14:37.610 Well, your hand is good enough that it beats 00:14:37.610 --> 00:14:38.776 most of their calling hands. 00:14:38.776 --> 00:14:42.839 So you're betting for value or your showdown value is poor, 00:14:42.839 --> 00:14:43.880 but you have some equity. 00:14:43.880 --> 00:14:44.780 You have some backdoor equity. 00:14:44.780 --> 00:14:46.490 You have some overcards or draws, 00:14:46.490 --> 00:14:48.860 and you're, essentially, bluffing. 00:14:48.860 --> 00:14:51.560 Another incentive is, you're out of position like he is, 00:14:51.560 --> 00:14:53.660 and it's not like he can see a free turn 00:14:53.660 --> 00:14:57.380 card by checking because I can still bet if he checks. 00:14:57.380 --> 00:15:01.490 So you want to bet-- few opponents, you want to bet. 00:15:01.490 --> 00:15:03.990 Incentives against continuation betting-- 00:15:03.990 --> 00:15:06.710 one is, your hand is so dominant that you 00:15:06.710 --> 00:15:09.210 need to give him a turn card to hope that he improves. 00:15:09.210 --> 00:15:10.310 So this is like the trap-- 00:15:10.310 --> 00:15:12.137 the slow play. 00:15:12.137 --> 00:15:14.470 You have decent showdown value, but not amazing showdown 00:15:14.470 --> 00:15:17.096 value-- so like, middle pair. 00:15:17.096 --> 00:15:18.470 You don't want a continuation bet 00:15:18.470 --> 00:15:21.590 if you have like zero equity on a reasonably dry board 00:15:21.590 --> 00:15:24.050 like this one. 00:15:24.050 --> 00:15:26.236 And there's too many people for you to fold out 00:15:26.236 --> 00:15:28.610 or-- like you're in position, and you can see a free turn 00:15:28.610 --> 00:15:29.380 by checking. 00:15:29.380 --> 00:15:31.400 So there's a lot of things but, still, 00:15:31.400 --> 00:15:33.330 let's look at the situation again keeping 00:15:33.330 --> 00:15:34.580 some of those factors in mind. 00:15:34.580 --> 00:15:38.544 He continuation bet into 10, eight, six rainbow, which 00:15:38.544 --> 00:15:39.710 means three different suits. 00:15:44.430 --> 00:15:49.857 OK, so actually, before I show this slide, 00:15:49.857 --> 00:15:51.440 I'm going to use the annotate feature, 00:15:51.440 --> 00:15:56.010 and we'll try to write on here what hands we 00:15:56.010 --> 00:15:56.820 think he can have. 00:15:56.820 --> 00:15:58.440 So this is going to take a while, 00:15:58.440 --> 00:16:01.140 but I plan on spending the next 20, 25 00:16:01.140 --> 00:16:02.470 minutes discussing this hand. 00:16:02.470 --> 00:16:05.360 OK, so does someone want to say a hand that you 00:16:05.360 --> 00:16:07.667 think is in this range at this point in the hand? 00:16:07.667 --> 00:16:10.000 Pretend we don't know what he's going to do on the turn. 00:16:10.000 --> 00:16:12.030 Yeah, just at this point in the hand, 00:16:12.030 --> 00:16:15.750 can someone tell me a hand you think is in his range? 00:16:15.750 --> 00:16:16.366 Yeah? 00:16:16.366 --> 00:16:17.674 AUDIENCE: Ace-jack. 00:16:17.674 --> 00:16:19.350 WILL MA: OK, yeah, ace/jack. 00:16:19.350 --> 00:16:21.442 OK, I think that's reasonable. 00:16:21.442 --> 00:16:22.900 It's actually, I think, a bit weak. 00:16:22.900 --> 00:16:27.870 But let's say like ace/jack suited with a backdoor flush 00:16:27.870 --> 00:16:28.440 draw. 00:16:28.440 --> 00:16:29.981 OK, I'll write down ace-jack for now. 00:16:29.981 --> 00:16:31.984 OK, so someone go and tell me another hand. 00:16:31.984 --> 00:16:32.484 Yeah? 00:16:32.484 --> 00:16:33.609 AUDIENCE: [INAUDIBLE] pair. 00:16:33.609 --> 00:16:35.540 Maybe 9-10, 10-jack suited? 00:16:35.540 --> 00:16:36.640 Ace-10? 00:16:36.640 --> 00:16:39.750 WILL MA: OK, ace-10-- 00:16:39.750 --> 00:16:43.470 sure, jack-10-- 10-9-- 00:16:43.470 --> 00:16:45.000 OK. 00:16:45.000 --> 00:16:48.697 Someone want to tell me another type of hand maybe? 00:16:48.697 --> 00:16:49.196 Yeah? 00:16:49.196 --> 00:16:50.680 AUDIENCE: [INAUDIBLE] pocket jacks? 00:16:50.680 --> 00:16:50.990 WILL MA: OK, good. 00:16:50.990 --> 00:16:51.795 Pocket jacks, yeah. 00:16:51.795 --> 00:16:53.520 So that's a clear value hand. 00:16:57.320 --> 00:16:59.480 Someone want to tell me another type of hand? 00:16:59.480 --> 00:17:01.130 AUDIENCE: What about queen-jack? 00:17:01.130 --> 00:17:01.590 WILL MA: Queen-jack. 00:17:01.590 --> 00:17:02.350 OK, that's a good idea. 00:17:02.350 --> 00:17:03.350 Yeah, that's a good one. 00:17:03.350 --> 00:17:06.420 So Queen-jack I think is one of the best draws-- 00:17:06.420 --> 00:17:10.225 not the best draw-- what is the best draw, would you say? 00:17:10.225 --> 00:17:12.909 AUDIENCE: Queen-jack of clubs? 00:17:12.909 --> 00:17:15.450 WILL MA: Queen-jack of clubs, yeah, but queen of clubs only-- 00:17:15.450 --> 00:17:17.207 it's not the best straight draw, right? 00:17:17.207 --> 00:17:17.790 Yeah, what's-- 00:17:17.790 --> 00:17:19.000 AUDIENCE: Jack-nine. 00:17:19.000 --> 00:17:20.041 WILL MA: Yeah, jack-nine. 00:17:20.041 --> 00:17:22.589 Jack-nine or queen-nine. 00:17:22.589 --> 00:17:24.165 I wrote some hands here. 00:17:24.165 --> 00:17:28.440 OK, jack-nine, or queen-nine, or like five-seven. 00:17:28.440 --> 00:17:29.600 OK. 00:17:29.600 --> 00:17:31.230 AUDIENCE: One pair of sixes. 00:17:31.230 --> 00:17:31.940 Is it possible? 00:17:31.940 --> 00:17:32.920 WILL MA: Pocket sixes? 00:17:32.920 --> 00:17:33.150 AUDIENCE: Yeah. 00:17:33.150 --> 00:17:33.990 WILL MA: Yeah, yeah, OK, that's good. 00:17:33.990 --> 00:17:35.220 So I'll write that down. 00:17:35.220 --> 00:17:37.257 So pocket sixes, good. 00:17:37.257 --> 00:17:39.090 OK, here's a question, what do you guys want 00:17:39.090 --> 00:17:45.840 to put him on if he has a really, really good hand? 00:17:45.840 --> 00:17:47.280 So this is open ended. 00:17:47.280 --> 00:17:48.780 I didn't come with a [INAUDIBLE].. 00:17:48.780 --> 00:17:52.080 You guys want to assume that he checks with pocket 10s 00:17:52.080 --> 00:17:54.540 and like nine-seven-- basically the absolute best 00:17:54.540 --> 00:17:56.520 hands on this board to trap us? 00:17:56.520 --> 00:17:58.277 Or do you want to assume that he bets? 00:18:01.801 --> 00:18:02.300 Yeah? 00:18:02.300 --> 00:18:03.924 AUDIENCE: I think if he has nine-seven, 00:18:03.924 --> 00:18:06.260 he'd probably bet because someone might get a better 00:18:06.260 --> 00:18:07.386 straight if he doesn't bet. 00:18:07.386 --> 00:18:09.426 WILL MA: OK, yeah that's a reasonable assumption. 00:18:09.426 --> 00:18:12.140 I think it can go either way with nine-seven and like pocket 00:18:12.140 --> 00:18:13.040 10s-- 00:18:13.040 --> 00:18:14.450 depending on our opponent. 00:18:14.450 --> 00:18:16.125 Pocket sixes, I think, is a clear bet, 00:18:16.125 --> 00:18:17.270 whereas pocket 10s is not. 00:18:17.270 --> 00:18:19.790 Because pocket 10s-- you're taking away so many 00:18:19.790 --> 00:18:22.050 of the top hands from your opponents, 00:18:22.050 --> 00:18:25.950 whereas pocket sixes just gets so much value when you bet. 00:18:25.950 --> 00:18:29.180 OK, so roughly speaking, I sort of categorized 00:18:29.180 --> 00:18:31.950 all the hands he could have into five categories. 00:18:31.950 --> 00:18:33.695 So the first-- the top is hands that 00:18:33.695 --> 00:18:36.500 are so good that he checks to trap or check-raise. 00:18:36.500 --> 00:18:38.090 The second category is like the hands 00:18:38.090 --> 00:18:40.420 that are good but not that good-- he value bets. 00:18:40.420 --> 00:18:42.010 Then it's like medium-strength hands 00:18:42.010 --> 00:18:45.389 that he checks to check-call. 00:18:45.389 --> 00:18:47.430 So this doesn't agree with exactly what we wrote, 00:18:47.430 --> 00:18:48.013 but that's OK. 00:18:48.013 --> 00:18:49.910 But this is just roughly-- 00:18:49.910 --> 00:18:53.031 and then the next category is hands that he bluffs. 00:18:53.031 --> 00:18:55.530 And then the last category is hands that he just check-folds 00:18:55.530 --> 00:18:56.738 because they have no equity-- 00:18:56.738 --> 00:18:59.240 like pocket threes, where he would just give up the hand. 00:18:59.240 --> 00:19:02.631 So we basically crossed off these three categories 00:19:02.631 --> 00:19:04.130 because with these three categories, 00:19:04.130 --> 00:19:07.940 he would check, whereas the top one, he's checking to trap; 00:19:07.940 --> 00:19:10.070 the second one, he's checking for a showdown; 00:19:10.070 --> 00:19:11.927 and the last one, he's checking to give up. 00:19:11.927 --> 00:19:13.760 And then the two types of hands he's betting 00:19:13.760 --> 00:19:19.760 are, essentially, value bets and like draws or bluffs. 00:19:19.760 --> 00:19:22.420 OK, so now let's consider the situation on the turn. 00:19:25.850 --> 00:19:29.390 OK, so once again, let's consider his incentives first 00:19:29.390 --> 00:19:31.521 for betting again on the turn. 00:19:31.521 --> 00:19:33.020 Sorry if this is a bit hard to read. 00:19:33.020 --> 00:19:41.320 Maybe I should do it on notepad so that the annotate 00:19:41.320 --> 00:19:42.000 isn't annoying. 00:19:45.280 --> 00:19:46.670 Sorry, just give me a sec. 00:19:56.918 --> 00:20:00.030 OK, so what are the incentives for betting again on the turn? 00:20:00.030 --> 00:20:02.280 So one is, you bet a good hand for value on the flop, 00:20:02.280 --> 00:20:04.680 and your hand is still good on the turn. 00:20:04.680 --> 00:20:06.320 So you're getting for more value. 00:20:06.320 --> 00:20:08.730 Two is, you bluffed a speculative hand on the flop 00:20:08.730 --> 00:20:10.380 and now you either hit the turn-- 00:20:10.380 --> 00:20:13.260 like the queen helped you-- so like if you had jack-nine 00:20:13.260 --> 00:20:16.080 or you improved your draw-- 00:20:16.080 --> 00:20:18.990 or like an overcard to the board came, which was the case, 00:20:18.990 --> 00:20:22.350 and maybe you thought bluffing the turn could be good. 00:20:22.350 --> 00:20:25.020 So OK, so he bet the turn. 00:20:25.020 --> 00:20:27.210 OK, so let's maybe put the hands we think 00:20:27.210 --> 00:20:29.670 he could have into PokerStove. 00:20:29.670 --> 00:20:32.280 So yeah, I think that's the easiest way to do it. 00:20:32.280 --> 00:20:33.480 OK, so let's do this. 00:20:36.830 --> 00:20:38.570 OK, so roughly speaking-- 00:20:38.570 --> 00:20:39.580 can everyone see this? 00:20:39.580 --> 00:20:42.070 This is easy enough to see, right? 00:20:42.070 --> 00:20:44.080 OK, so let's do this. 00:20:44.080 --> 00:20:44.840 So bear with me. 00:20:44.840 --> 00:20:47.700 This is a meticulous exercise. 00:20:47.700 --> 00:20:51.780 OK, so let's say preflop, 30%-- 00:20:51.780 --> 00:20:53.480 OK, this is about reasonable. 00:20:53.480 --> 00:20:55.720 Actually, let me give him a few more pairs. 00:20:55.720 --> 00:20:57.910 I'll take away ace-six off. 00:20:57.910 --> 00:21:01.560 Let's say he goes suited connectors down 00:21:01.560 --> 00:21:04.935 to five-four suited, suited one gappers down 00:21:04.935 --> 00:21:08.820 to five-three suited-- suited two gappers. 00:21:08.820 --> 00:21:11.700 So suited two gappers means suited cards 00:21:11.700 --> 00:21:14.650 that are three apart, essentially. 00:21:14.650 --> 00:21:17.760 Yeah, you have like eight-five suited, something like this. 00:21:20.437 --> 00:21:22.020 Something like this is fine, probably, 00:21:22.020 --> 00:21:23.760 but let's say he plays 10-6 suited. 00:21:23.760 --> 00:21:25.390 OK, something like this-- 00:21:25.390 --> 00:21:28.476 maybe take away some of the worst offsuit hands. 00:21:28.476 --> 00:21:29.600 OK, so something like this. 00:21:29.600 --> 00:21:30.180 OK, good. 00:21:30.180 --> 00:21:31.530 So on the flop, what happened? 00:21:31.530 --> 00:21:34.770 On the flop-- we said, OK, so let's eliminate hands. 00:21:34.770 --> 00:21:35.835 What can we eliminate? 00:21:35.835 --> 00:21:38.795 So this is his entire range of possibilities, preflop. 00:21:38.795 --> 00:21:40.950 OK, so on the flop, we're going to eliminate 00:21:40.950 --> 00:21:45.150 pocket twos, threes, fours, and fives because he just gives up. 00:21:45.150 --> 00:21:46.620 Pocket sevens and nines we're going 00:21:46.620 --> 00:21:49.920 to eliminate because we're going to assume he checks. 00:21:49.920 --> 00:21:55.375 Five-three is bad enough we can assume he gives up. 00:21:55.375 --> 00:22:03.060 Let me just display the flop so that we can see. 00:22:03.060 --> 00:22:05.190 OK, so what else? 00:22:05.190 --> 00:22:07.229 OK, so let's go through everything. 00:22:07.229 --> 00:22:08.520 I'll deal with this a bit fast. 00:22:11.210 --> 00:22:12.977 OK, let's say all the middle pairs-- 00:22:12.977 --> 00:22:13.810 he's going to check. 00:22:13.810 --> 00:22:16.810 So I'm going to remove most of the hands with an eight 00:22:16.810 --> 00:22:17.310 in them-- 00:22:20.160 --> 00:22:22.410 yeah, so ace-eight, king-eight, queen-eight, jack, OK, 00:22:22.410 --> 00:22:23.493 so 10-8 he's going to bet. 00:22:23.493 --> 00:22:25.790 AUDIENCE: You do that just because you have an eight? 00:22:25.790 --> 00:22:26.730 AUDIENCE: Pretty much. 00:22:26.730 --> 00:22:29.850 WILL MA: Yeah, so we will take that into account. 00:22:29.850 --> 00:22:31.942 But he could still have an eight, right? 00:22:31.942 --> 00:22:32.900 But yeah, you're right. 00:22:32.900 --> 00:22:35.210 It is less likely, and we will take it into account 00:22:35.210 --> 00:22:37.100 at the very end. 00:22:37.100 --> 00:22:38.540 So ace-five, let's assume-- 00:22:38.540 --> 00:22:40.970 let's assume a lot of these offsuit aces, 00:22:40.970 --> 00:22:45.680 he gives up because even with overcards but with no backdoor 00:22:45.680 --> 00:22:51.300 flush draw on a dry board, I think is kind of scary. 00:22:51.300 --> 00:22:53.845 OK, so let's say something like this on the flop-- 00:22:53.845 --> 00:22:55.670 eight-five, let's eliminate that. 00:22:55.670 --> 00:22:57.636 Eight-seven, I think he'll check. 00:22:57.636 --> 00:22:59.510 So nine-seven, we're going to assume he bets. 00:22:59.510 --> 00:23:01.195 Let's assume he checks pocket 10s. 00:23:01.195 --> 00:23:02.570 Let's assumes he also checks some 00:23:02.570 --> 00:23:10.090 of the weaker 10s-- like jack-10, 00:23:10.090 --> 00:23:12.510 let's suppose he checks. 00:23:12.510 --> 00:23:14.375 Maybe 10-9, he checks as well. 00:23:14.375 --> 00:23:15.105 10-7, he checks. 00:23:18.600 --> 00:23:21.977 OK, nine-eight he checks. 00:23:21.977 --> 00:23:23.060 OK, am I missing anything? 00:23:23.060 --> 00:23:25.330 Did someone see something you disagree with? 00:23:25.330 --> 00:23:26.640 King-queen off, king-jack off-- 00:23:26.640 --> 00:23:28.320 I think those are too weak, too-- 00:23:28.320 --> 00:23:30.890 that end of this board-- 00:23:30.890 --> 00:23:34.675 queen-nine, king-nine suited, ace-nine down here. 00:23:34.675 --> 00:23:37.570 OK, I think this is roughly-- 00:23:37.570 --> 00:23:39.475 it'll get easier on the turn, basically. 00:23:39.475 --> 00:23:43.452 OK, So let's say this is what he's going to have on the flop. 00:23:43.452 --> 00:23:44.910 Actually, some of these weaker aces 00:23:44.910 --> 00:23:46.160 probably should be eliminated. 00:23:46.160 --> 00:23:49.350 OK, let's eliminate everything down to ace-five and below. 00:23:49.350 --> 00:23:50.920 Ace-seven and ace-nine we'll keep in 00:23:50.920 --> 00:23:52.211 because he has a straight draw. 00:23:55.580 --> 00:23:58.440 OK, so on the turn, he bets again. 00:23:58.440 --> 00:24:01.172 So did someone want to suggest a hand that maybe we 00:24:01.172 --> 00:24:02.880 should eliminate because he bet the turn? 00:24:05.750 --> 00:24:06.250 Yeah? 00:24:06.250 --> 00:24:07.750 AUDIENCE: Only weak 10s, I guess? 00:24:07.750 --> 00:24:08.310 WILL MA: OK, good. 00:24:08.310 --> 00:24:09.976 Yeah, I think that's a very good answer. 00:24:09.976 --> 00:24:12.940 So let's get rid of ace-10 and king-10 because those 00:24:12.940 --> 00:24:15.460 are no longer good hands-- or they're no longer, I think, 00:24:15.460 --> 00:24:18.120 hands that you want to really continue betting for value, 00:24:18.120 --> 00:24:18.630 right? 00:24:18.630 --> 00:24:20.950 Queen-10 is good because you hit two pair. 00:24:20.950 --> 00:24:25.210 OK, is there another hand that's of a similar category? 00:24:25.210 --> 00:24:28.420 So I guess pocket jacks is of a similar category, right? 00:24:28.420 --> 00:24:32.350 It's not as good as it once was. 00:24:32.350 --> 00:24:34.507 OK, so what are some other hands maybe you 00:24:34.507 --> 00:24:35.590 don't want to bluff with-- 00:24:35.590 --> 00:24:37.048 you don't want to bet with anymore? 00:24:44.802 --> 00:24:46.260 Are there any hands you think maybe 00:24:46.260 --> 00:24:48.220 he would just give up because-- 00:24:48.220 --> 00:24:50.476 AUDIENCE: The six-five. 00:24:50.476 --> 00:24:52.265 WILL MA: Yeah, I think that's reasonable. 00:24:55.920 --> 00:24:57.300 Most of these, we can assume he's 00:24:57.300 --> 00:25:01.770 going to give up on the queen, like five-four, especially. 00:25:01.770 --> 00:25:03.819 So on the flop, he didn't even have a great hand. 00:25:03.819 --> 00:25:05.110 It was just drawing to a seven. 00:25:05.110 --> 00:25:07.050 But now, it's sort of worse. 00:25:07.050 --> 00:25:08.730 So yeah, let's get rid of five-four. 00:25:11.384 --> 00:25:13.050 Do you think they would continue betting 00:25:13.050 --> 00:25:17.300 like nine-six or seven-six? 00:25:17.300 --> 00:25:19.800 Yeah, even seven-five is a pretty bad-- 00:25:19.800 --> 00:25:22.970 is a lot worse after the queen because seven-five 00:25:22.970 --> 00:25:25.150 was like drawing to a nine. 00:25:25.150 --> 00:25:27.780 But now, when the queen comes, the nine 00:25:27.780 --> 00:25:30.960 is not a good card because you still lose to a jack. 00:25:30.960 --> 00:25:33.110 So maybe we can get rid of that one. 00:25:33.110 --> 00:25:35.370 Do you think they definitely continue 00:25:35.370 --> 00:25:37.660 betting with ace-king, ace-queen, ace-jack in all 00:25:37.660 --> 00:25:38.160 those? 00:25:42.880 --> 00:25:43.824 Yeah? 00:25:43.824 --> 00:25:45.564 AUDIENCE: Maybe if they had ace-queen, 00:25:45.564 --> 00:25:48.554 they would keep it [INAUDIBLE] pretend to [INAUDIBLE].. 00:25:48.554 --> 00:25:50.470 WILL MA: Yeah, so ace-queen, I think, is good. 00:25:50.470 --> 00:25:52.735 All right, so I think this is [INAUDIBLE] good. 00:25:52.735 --> 00:25:54.145 Ace-nine-- some of these hands, I 00:25:54.145 --> 00:25:56.020 think they would probably stop bluffing with. 00:25:56.020 --> 00:25:59.360 Like I think jack-seven suited is pretty-- 00:25:59.360 --> 00:26:03.410 maybe some of the sixes also, I think, it's hard to-- 00:26:03.410 --> 00:26:05.100 even like ace-seven suited, I think 00:26:05.100 --> 00:26:06.470 it's hard to continue bluffing. 00:26:06.470 --> 00:26:07.886 Because as we see, there's already 00:26:07.886 --> 00:26:10.370 enough hands with draws, right? 00:26:10.370 --> 00:26:13.340 There are already a lot of bluffs here like king-jack, 00:26:13.340 --> 00:26:15.010 ace-king-- 00:26:15.010 --> 00:26:17.590 I guess like queen-nine, nine-six, 00:26:17.590 --> 00:26:20.000 some of these-- so yeah, maybe he'll bluff with these, 00:26:20.000 --> 00:26:22.890 but OK, let's get rid of these. 00:26:22.890 --> 00:26:27.900 OK, so we've sort of cut down his range a bit. 00:26:27.900 --> 00:26:31.070 So now it's a river situation, and he checks. 00:26:31.070 --> 00:26:32.190 So what does this mean? 00:26:32.190 --> 00:26:34.610 Well, it seems improbable that their opponent 00:26:34.610 --> 00:26:36.740 would be trying to trap us with this check 00:26:36.740 --> 00:26:40.170 because he's already been showing plenty of aggression. 00:26:40.170 --> 00:26:42.020 So it's hard for him to pretend he suddenly 00:26:42.020 --> 00:26:44.265 has a bad hand by checking. 00:26:44.265 --> 00:26:46.100 And with the pot already so big, he 00:26:46.100 --> 00:26:49.280 can get a large percent of our remaining stack into the pot 00:26:49.280 --> 00:26:51.680 just by betting instead of check-raising. 00:26:51.680 --> 00:26:56.680 So it seems like it's less likely he's checking as a trap. 00:26:56.680 --> 00:26:59.110 And also, the ace is sort of a better card 00:26:59.110 --> 00:27:01.130 for his range than ours because he's 00:27:01.130 --> 00:27:03.560 the one who's been betting, so having draws, 00:27:03.560 --> 00:27:05.390 having overcards like aces-- 00:27:05.390 --> 00:27:10.760 and for us, we're much less likely than him to have an ace. 00:27:10.760 --> 00:27:12.500 So if it's a better card for his range, 00:27:12.500 --> 00:27:15.500 he should be betting both for value and with his bluffs. 00:27:15.500 --> 00:27:17.780 So that being said, so let's suppose 00:27:17.780 --> 00:27:20.480 we assume it's sort of unlikely he 00:27:20.480 --> 00:27:23.000 has a really, really good hand, but he could so easily 00:27:23.000 --> 00:27:27.350 have a hand that beats ours and calls our potential bluff. 00:27:27.350 --> 00:27:31.370 So OK, so now let's go back to PokerStove and eliminate 00:27:31.370 --> 00:27:32.120 some more hands. 00:27:32.120 --> 00:27:34.140 OK, so what are some hands we can eliminate 00:27:34.140 --> 00:27:35.680 after he checks the river? 00:27:35.680 --> 00:27:36.797 AUDIENCE: Aces. 00:27:36.797 --> 00:27:37.630 WILL MA: Aces, yeah. 00:27:37.630 --> 00:27:38.890 I think that's a good one. 00:27:38.890 --> 00:27:42.197 I think aces, pretty clearly, he'll bet again on the river. 00:27:42.197 --> 00:27:43.030 What's another hand? 00:27:43.030 --> 00:27:44.260 AUDIENCE: King-jack. 00:27:44.260 --> 00:27:46.080 WILL MA: Yeah, king-jack I think he might. 00:27:46.080 --> 00:27:47.630 OK, so let's eliminate all other good hands 00:27:47.630 --> 00:27:49.270 that we think he's going to continuation bet, right? 00:27:49.270 --> 00:27:51.170 I think with any straight, I think 00:27:51.170 --> 00:27:52.930 it's reasonable to assume they're just 00:27:52.930 --> 00:27:53.846 going to keep betting. 00:27:53.846 --> 00:27:55.850 Like nine-seven-- even though it's nowhere near 00:27:55.850 --> 00:27:59.020 the monster it was on the flop, it still 00:27:59.020 --> 00:28:00.890 only loses to jack-nine and king-jack. 00:28:00.890 --> 00:28:03.470 So let's get rid of that one. 00:28:03.470 --> 00:28:05.650 AUDIENCE: Certainly like ace-queen-- 00:28:05.650 --> 00:28:06.280 all those. 00:28:09.290 --> 00:28:12.650 WILL MA: Yeah, I think most strong two pairs I think, 00:28:12.650 --> 00:28:14.210 definitely, he'll keep betting. 00:28:14.210 --> 00:28:15.750 So let's get rid of that. 00:28:15.750 --> 00:28:17.300 Let's get rid of ace-queen. 00:28:17.300 --> 00:28:20.140 Let's get rid of queen-queen. 00:28:20.140 --> 00:28:21.370 Let's get rid of queen-10. 00:28:21.370 --> 00:28:24.530 I think queen-10 is good enough. 00:28:24.530 --> 00:28:27.130 Ace-eight-- let's get rid of that one-- 00:28:27.130 --> 00:28:28.225 yeah, that's good enough. 00:28:28.225 --> 00:28:30.350 Pocket eights, pocket sixes I think is good enough. 00:28:33.020 --> 00:28:33.710 OK, good. 00:28:33.710 --> 00:28:36.650 So OK, we've got some hands here-- 00:28:36.650 --> 00:28:38.600 basically, all the good hands we removed-- 00:28:38.600 --> 00:28:41.050 all the really good hands that he bets again. 00:28:41.050 --> 00:28:42.500 What do you guys think about 10-8? 00:28:42.500 --> 00:28:45.150 I guess it doesn't matter too much. 00:28:45.150 --> 00:28:47.870 Let's assume he checks 10-8 because by this river, 00:28:47.870 --> 00:28:50.600 10-8 is no longer the powerhouse it was. 00:28:50.600 --> 00:28:52.190 Oh, I've got to get rid of jack-nine. 00:28:52.190 --> 00:28:55.580 OK, what are some other hands you think we can eliminate? 00:28:55.580 --> 00:28:57.830 So there there's actually another category of hands 00:28:57.830 --> 00:28:59.580 we could, potentially, eliminate here. 00:29:02.110 --> 00:29:02.610 Yeah? 00:29:02.610 --> 00:29:06.786 AUDIENCE: He would probably bet an ace. 00:29:06.786 --> 00:29:11.292 WILL MA: Well an ace isn't that good of a hand. 00:29:11.292 --> 00:29:13.000 So this is one problem with this analysis 00:29:13.000 --> 00:29:15.284 is, it is very subject to debate what 00:29:15.284 --> 00:29:16.450 we think about our opponent. 00:29:16.450 --> 00:29:19.480 But for the sake of this exercise, I'd say-- 00:29:19.480 --> 00:29:20.920 I mean also I think in practice-- 00:29:20.920 --> 00:29:23.895 I think it's not clear that you should value bet an ace here. 00:29:23.895 --> 00:29:25.353 Because there's just a lot of stuff 00:29:25.353 --> 00:29:27.850 that beats you-- a lot of straights, a lot of two pairs. 00:29:27.850 --> 00:29:29.558 I think that even if you have a ace-king, 00:29:29.558 --> 00:29:31.600 you shouldn't really be confident enough 00:29:31.600 --> 00:29:32.700 in your hand to bet. 00:29:32.700 --> 00:29:34.990 Like maybe ace-king is marginal but definitely 00:29:34.990 --> 00:29:38.160 not like ace-seven. 00:29:38.160 --> 00:29:39.510 Yeah? 00:29:39.510 --> 00:29:41.990 AUDIENCE: Bluff bets-- so like weak hands, maybe six-four. 00:29:41.990 --> 00:29:42.906 WILL MA: Great, great. 00:29:42.906 --> 00:29:45.100 Yeah, exactly, so that's what I wanted to hear. 00:29:45.100 --> 00:29:47.900 So we can also eliminate some of his really weak hands. 00:29:47.900 --> 00:29:48.590 This is crucial. 00:29:48.590 --> 00:29:50.030 This is an easy thing to miss. 00:29:50.030 --> 00:29:52.170 We can probably assume he's not going 00:29:52.170 --> 00:29:55.975 to have king-seven because the ace is a reasonable card 00:29:55.975 --> 00:29:57.061 to bluff. 00:29:57.061 --> 00:29:59.060 It's not great-- it's not like the ace of clubs, 00:29:59.060 --> 00:30:00.976 which would be a better card for him to bluff, 00:30:00.976 --> 00:30:02.180 but if he's got nothing-- 00:30:02.180 --> 00:30:04.160 like if he just completely missed-- 00:30:04.160 --> 00:30:05.790 probably-- I mean, let's assume you 00:30:05.790 --> 00:30:07.722 know these guys are pretty good players. 00:30:07.722 --> 00:30:08.930 He's probably going to bluff. 00:30:08.930 --> 00:30:12.560 So let's assume he at least has a pair. 00:30:12.560 --> 00:30:15.380 He has some showdown value, because if he had zero showdown 00:30:15.380 --> 00:30:16.610 value, he would have bluffed. 00:30:16.610 --> 00:30:21.930 So let's get rid of king-seven, let's get rid of king-nine. 00:30:21.930 --> 00:30:26.870 Six-five six-four-- I think, definitely, he 00:30:26.870 --> 00:30:28.790 should be bluffing, but maybe some players 00:30:28.790 --> 00:30:30.530 will see a pair of sixes and say, oh I 00:30:30.530 --> 00:30:31.850 have enough showdown value. 00:30:31.850 --> 00:30:33.933 So let's get rid of one of them but not the other. 00:30:33.933 --> 00:30:35.100 Maybe that's reasonable. 00:30:35.100 --> 00:30:36.667 So let's get rid of two. 00:30:36.667 --> 00:30:38.250 So let's get of six-four and seven-six 00:30:38.250 --> 00:30:39.990 but keep in six-five and nine-six. 00:30:42.790 --> 00:30:48.050 OK, so we leave ourselves with these. 00:30:48.050 --> 00:30:50.450 OK, so this seems about reasonable, I think. 00:30:55.630 --> 00:30:59.419 Let's eliminate ace-seven. 00:30:59.419 --> 00:31:01.460 I think we should have eliminated it on the turn. 00:31:01.460 --> 00:31:04.126 Maybe like ace-seven of clubs we can-- oh no, ace-seven of clubs 00:31:04.126 --> 00:31:07.680 he can't have because we have the seven of clubs. 00:31:07.680 --> 00:31:10.280 I think any other ace-seven other than the ace-seven 00:31:10.280 --> 00:31:13.640 of clubs is kind of bad to bet on the turn because the seven 00:31:13.640 --> 00:31:16.710 isn't really that good of a card to-- 00:31:16.710 --> 00:31:18.050 isn't that good of a draw. 00:31:18.050 --> 00:31:20.870 So let's get rid of ace-seven. 00:31:20.870 --> 00:31:22.400 So let's just suppose it's this. 00:31:22.400 --> 00:31:26.260 OK, so that was a lot of work. 00:31:26.260 --> 00:31:30.410 OK, so now roughly speaking, we can 00:31:30.410 --> 00:31:33.800 conclude his range on the river is something like this. 00:31:33.800 --> 00:31:35.540 So let's assume that he's going to call 00:31:35.540 --> 00:31:37.430 with top pair or better. 00:31:37.430 --> 00:31:39.590 Once again, this is a pretty strong assumption, 00:31:39.590 --> 00:31:41.694 but let's suppose this is the way 00:31:41.694 --> 00:31:42.860 we think he's going to play. 00:31:42.860 --> 00:31:45.680 He's going to call if he has an ace or better 00:31:45.680 --> 00:31:47.690 and fold other ones. 00:31:47.690 --> 00:31:52.310 So we're risking 70 to win 100. 00:31:52.310 --> 00:31:54.394 So let's do an exact calculation now 00:31:54.394 --> 00:31:56.060 of how many combinations of these hands. 00:31:58.820 --> 00:31:59.820 I'll do this on Notepad. 00:32:04.870 --> 00:32:07.955 OK, let me pull up the board. 00:32:18.840 --> 00:32:22.340 OK, hopefully, people can see this. 00:32:22.340 --> 00:32:24.445 So when I said combinatorial hand analysis, 00:32:24.445 --> 00:32:25.820 I mean we're going to, basically, 00:32:25.820 --> 00:32:27.170 count the combinations. 00:32:27.170 --> 00:32:29.180 And like you pointed out, this is-- 00:32:29.180 --> 00:32:31.860 oh crap, did I accidentally get rid of that? 00:32:31.860 --> 00:32:33.820 Oh, that's not good. 00:32:33.820 --> 00:32:36.050 OK, let me quickly put it back. 00:32:36.050 --> 00:32:40.450 So OK, we had kings left, ace-king, ace-jack, ace-nine, 00:32:40.450 --> 00:32:48.920 king-queen, queen-jack, queen-nine, what else? 00:32:48.920 --> 00:32:55.130 10-8, 10-6, eight-six-- we had some sixes, right? 00:32:55.130 --> 00:33:01.232 Seven-six, six-five-- and is there something 00:33:01.232 --> 00:33:01.940 else I'm missing? 00:33:01.940 --> 00:33:06.560 Does anyone remember if there's something 00:33:06.560 --> 00:33:09.604 I'm forgetting to check off? 00:33:09.604 --> 00:33:11.020 I knocked queen-nine off, I guess. 00:33:11.020 --> 00:33:11.880 I think this about right. 00:33:11.880 --> 00:33:13.660 Maybe I'm missing like one or two things. 00:33:20.865 --> 00:33:21.740 No one sees anything? 00:33:21.740 --> 00:33:26.020 I think this is approximately what we had, right? 00:33:26.020 --> 00:33:29.780 OK, hopefully I didn't miss enough 00:33:29.780 --> 00:33:31.280 that it drastically changes. 00:33:31.280 --> 00:33:32.700 It shouldn't. 00:33:32.700 --> 00:33:34.240 OK, so let's count the combinations. 00:33:34.240 --> 00:33:38.420 Because you can look at the square on the PokerStove and-- 00:33:38.420 --> 00:33:40.190 let me clear this annotation-- sorry, 00:33:40.190 --> 00:33:41.900 I should've done that a while ago. 00:33:41.900 --> 00:33:46.490 OK, so you can see the yellow hands on the square 00:33:46.490 --> 00:33:49.740 and roughly see how many hands of each type. 00:33:49.740 --> 00:33:54.210 There's, essentially, three types of hands he could have. 00:33:54.210 --> 00:33:59.030 There's hands that call, there's hands that beat us and call, 00:33:59.030 --> 00:34:01.730 there's hands that beat us and fold, 00:34:01.730 --> 00:34:06.470 and there's hands that we beat and fold. 00:34:06.470 --> 00:34:08.929 But the thing is, if you just look at these yellow squares, 00:34:08.929 --> 00:34:11.929 it won't give you the right probabilities because we 00:34:11.929 --> 00:34:13.489 have certain cards in our hand. 00:34:13.489 --> 00:34:15.550 And also, because of the specific ways 00:34:15.550 --> 00:34:17.449 suited combinations work, there's 00:34:17.449 --> 00:34:19.181 different combinations of each hand. 00:34:19.181 --> 00:34:20.389 So OK, let's go through this. 00:34:20.389 --> 00:34:24.580 So how many combinations of ace-king suited are there 00:34:24.580 --> 00:34:27.030 that-- so we assume he had a backdoor flush draw 00:34:27.030 --> 00:34:29.270 on the flop, but-- 00:34:29.270 --> 00:34:33.892 so how many combinations of ace-king suited are possible? 00:34:33.892 --> 00:34:35.850 Don't worry about the backdoor flush draw part. 00:34:35.850 --> 00:34:37.308 It doesn't matter for this example. 00:34:37.308 --> 00:34:39.949 So how many combinations of ace-king suited, Will? 00:34:39.949 --> 00:34:40.973 Three. 00:34:40.973 --> 00:34:42.139 Because it has to be suited. 00:34:42.139 --> 00:34:44.389 And it can't be spades because the ace of spades 00:34:44.389 --> 00:34:45.409 is on the board. 00:34:45.409 --> 00:34:48.090 So it's three combinations. 00:34:48.090 --> 00:34:50.268 OK, ace-jack suited? 00:34:50.268 --> 00:34:51.139 AUDIENCE: Three. 00:34:51.139 --> 00:34:52.560 WILL MA: Three, OK, good. 00:34:52.560 --> 00:34:55.424 Ace-nine suited? 00:34:55.424 --> 00:34:56.408 AUDIENCE: Three. 00:34:56.408 --> 00:34:57.139 WILL MA: Three. 00:34:57.139 --> 00:34:59.800 OK, good. 00:34:59.800 --> 00:35:01.585 All right, pocket kings? 00:35:01.585 --> 00:35:03.440 AUDIENCE: About six? 00:35:03.440 --> 00:35:05.240 WILL MA: Right, so pocket kings is six. 00:35:05.240 --> 00:35:07.281 Because there's no kings; we don't see any kings, 00:35:07.281 --> 00:35:09.240 and there's no such thing as suitedness. 00:35:09.240 --> 00:35:11.530 So yeah, so one thing you realize in this-- 00:35:11.530 --> 00:35:14.159 oh, so pocket kings we're assuming he's going to fold-- 00:35:14.159 --> 00:35:15.950 one thing you will realize in this exercise 00:35:15.950 --> 00:35:18.020 is, you've got to put a lot of weight 00:35:18.020 --> 00:35:20.120 on the offsuit hands instead of the suited hands. 00:35:20.120 --> 00:35:23.600 Because the offsuit hands, combinatorially, have way more 00:35:23.600 --> 00:35:26.030 possibilities-- essentially three times as many 00:35:26.030 --> 00:35:28.190 possibilities-- as the suited hands. 00:35:28.190 --> 00:35:31.040 So like this queen-jack offsuit in here 00:35:31.040 --> 00:35:33.110 has a huge weight in our calculation. 00:35:33.110 --> 00:35:35.090 That's by far his most likely hand. 00:35:35.090 --> 00:35:38.600 Because it's the only offsuit hand we're putting him on. 00:35:38.600 --> 00:35:40.480 Yeah, it's the only offsuit-- 00:35:40.480 --> 00:35:43.250 is it really only the offsuit hand that he could have? 00:35:43.250 --> 00:35:45.200 I guess according to our analysis, 00:35:45.200 --> 00:35:46.835 we're assuming the only offsuit hand he 00:35:46.835 --> 00:35:48.230 could have is queen-jack off. 00:35:48.230 --> 00:35:50.438 So how many combinations of queen-jack off are there? 00:35:54.379 --> 00:35:54.920 AUDIENCE: 12. 00:35:54.920 --> 00:35:56.680 AUDIENCE: 12. 00:35:56.680 --> 00:35:59.530 WILL MA: OK, so let's just say queen-jack in total. 00:35:59.530 --> 00:36:01.685 Queen-jack suited plus offsuit is 12. 00:36:01.685 --> 00:36:04.540 Because we see a queen, so there's four jacks, 00:36:04.540 --> 00:36:06.135 three queens, three times four is 12. 00:36:06.135 --> 00:36:07.510 It could be suited or not suited. 00:36:07.510 --> 00:36:09.092 So OK, that counts for both of those. 00:36:09.092 --> 00:36:10.300 What about king-queen suited? 00:36:13.102 --> 00:36:14.510 AUDIENCE: Three as well? 00:36:14.510 --> 00:36:17.660 WILL MA: So it's three as well, but I'm going to put it as two 00:36:17.660 --> 00:36:20.900 because I can assume if he had king-queen of spades, 00:36:20.900 --> 00:36:24.619 which has no flush dras-- like no runner-runner flush draw 00:36:24.619 --> 00:36:25.160 on the flop-- 00:36:25.160 --> 00:36:26.870 I'm going to assume that he would have folded king-queen 00:36:26.870 --> 00:36:27.786 of spades on the flop. 00:36:27.786 --> 00:36:31.390 So I'm going to give it two. 00:36:31.390 --> 00:36:33.140 OK, so which ones haven't we done? 00:36:33.140 --> 00:36:37.350 Queen-nine suited, how many combinations? 00:36:37.350 --> 00:36:38.460 Three? 00:36:38.460 --> 00:36:39.630 AUDIENCE: Yes. 00:36:39.630 --> 00:36:44.820 WILL MA: OK, 10-8 suited, these get five. 00:36:44.820 --> 00:36:46.920 So the reason why 10-8 is suited is 00:36:46.920 --> 00:36:49.680 because we're assuming he doesn't raise 10-8 offsuit 00:36:49.680 --> 00:36:51.040 preflop from that position. 00:36:51.040 --> 00:36:53.770 So that's why 10-8 has to be suited. 00:36:53.770 --> 00:36:56.220 So how many combinations of 10-8 suited? 00:36:56.220 --> 00:36:57.000 Two. 00:36:57.000 --> 00:36:59.310 OK, how many combinations of 10-6 suited? 00:36:59.310 --> 00:37:00.750 AUDIENCE: Two as well. 00:37:00.750 --> 00:37:01.350 WILL MA: Two. 00:37:01.350 --> 00:37:04.962 How many combinations of eight-six suited? 00:37:04.962 --> 00:37:05.830 AUDIENCE: One? 00:37:05.830 --> 00:37:06.590 WILL MA: One, yes. 00:37:06.590 --> 00:37:07.089 OK. 00:37:12.200 --> 00:37:13.570 I miscategorized this one. 00:37:13.570 --> 00:37:16.550 So queen-nine is in this category that he's folding. 00:37:16.550 --> 00:37:20.000 These are all the hands that call our bluff and beat us. 00:37:20.000 --> 00:37:22.160 And so the last category is the hands 00:37:22.160 --> 00:37:24.860 that we can actually beat if we check it down. 00:37:24.860 --> 00:37:25.910 So it's very small. 00:37:25.910 --> 00:37:30.150 It's just seven-six and six-five suited. 00:37:30.150 --> 00:37:33.134 OK, so seven-six suited, how many combinations? 00:37:33.134 --> 00:37:34.090 AUDIENCE: Two? 00:37:34.090 --> 00:37:34.970 WILL MA: Two. 00:37:34.970 --> 00:37:37.760 Six-five suited, three? 00:37:37.760 --> 00:37:40.107 OK. 00:37:40.107 --> 00:37:40.940 Did I miss anything? 00:37:40.940 --> 00:37:42.710 I think this is it, right? 00:37:42.710 --> 00:37:45.440 OK, so basically we have to tally it up. 00:37:45.440 --> 00:37:46.955 So here, there's 14. 00:37:50.320 --> 00:37:52.500 Here, there's 23. 00:37:52.500 --> 00:37:53.470 And here, there's five. 00:37:56.870 --> 00:38:03.547 OK so now that we've done this calculation, 00:38:03.547 --> 00:38:05.130 we need to, basically, run the numbers 00:38:05.130 --> 00:38:06.450 with these calculations. 00:38:06.450 --> 00:38:10.354 So essentially, roughly speaking, 00:38:10.354 --> 00:38:12.270 they're going to fold more than half the time. 00:38:17.709 --> 00:38:19.500 So the numbers-- I think this will actually 00:38:19.500 --> 00:38:21.030 come out close because with the way 00:38:21.030 --> 00:38:23.860 we did this specific calculation, 00:38:23.860 --> 00:38:26.220 I think we gave him a lot of combinations of hands 00:38:26.220 --> 00:38:28.050 that we can actually check and beat. 00:38:28.050 --> 00:38:30.540 But I think this is still-- this will still definitely 00:38:30.540 --> 00:38:31.620 call for a bluff. 00:38:31.620 --> 00:38:32.489 But it close. 00:38:32.489 --> 00:38:34.530 If you've done the homework, the homework sort of 00:38:34.530 --> 00:38:35.640 addresses this, right? 00:38:39.700 --> 00:38:42.210 It's not just the probability he's calling our bluff, 00:38:42.210 --> 00:38:44.400 it's the probability he's calling 00:38:44.400 --> 00:38:48.020 our bluff versus the probability we win the hand by checking. 00:38:48.020 --> 00:38:51.975 And the probability we win the hand by checking is roughly 5 00:38:51.975 --> 00:38:54.500 out of 42-- 00:38:54.500 --> 00:38:58.320 so which is pretty small, and he folds more than half the time. 00:38:58.320 --> 00:38:59.730 So if you run the numbers, you'll 00:38:59.730 --> 00:39:03.390 see that bluffing is overwhelmingly profitable. 00:39:03.390 --> 00:39:07.280 And I think this is a good example 00:39:07.280 --> 00:39:09.670 of why this combinatorial analysis is good-- 00:39:09.670 --> 00:39:12.450 is because if you look at PokerStove 00:39:12.450 --> 00:39:15.880 and you look at this, you might actually think 00:39:15.880 --> 00:39:19.150 bluffing is bad because you look at most of the hands-- 00:39:19.150 --> 00:39:22.120 ace-king, ace-jack, ace-nine, 10-8, 10-6, 8-6-- 00:39:22.120 --> 00:39:25.680 it's hands that call us and beat us, 00:39:25.680 --> 00:39:28.080 but when you do this combinatorial analysis, 00:39:28.080 --> 00:39:31.460 you'll realize there's way more combinations of queen-jack 00:39:31.460 --> 00:39:33.270 than there are eight-six. 00:39:33.270 --> 00:39:35.460 So looking at this itself isn't quite enough 00:39:35.460 --> 00:39:38.070 because this doesn't weight the probabilities of each one 00:39:38.070 --> 00:39:40.460 correctly. 00:39:40.460 --> 00:39:43.410 So this is a good exercise to do, I think. 00:39:43.410 --> 00:39:45.750 Even though we made a lot of assumptions in our model, 00:39:45.750 --> 00:39:50.040 but it's a very good exercise to do after the fact 00:39:50.040 --> 00:39:52.740 to sort of just analyze what are the different-- all 00:39:52.740 --> 00:39:55.035 the different possibilities. 00:39:55.035 --> 00:39:57.250 OK, so I'm going to take a quick break here. 00:39:57.250 --> 00:39:59.640 And then for the last half of the class, 00:39:59.640 --> 00:40:03.180 I'm going to just talk about some general poker topics. 00:40:03.180 --> 00:40:04.110 So no math. 00:40:04.110 --> 00:40:05.880 No poker hands. 00:40:05.880 --> 00:40:08.200 But just some general stuff about poker and some ending 00:40:08.200 --> 00:40:10.590 remarks since this is the last time 00:40:10.590 --> 00:40:12.914 I'm teaching since Bill Chen is coming next time. 00:40:12.914 --> 00:40:15.330 If you want to, during the break, think about any question 00:40:15.330 --> 00:40:17.560 you might want to ask me about poker in general-- 00:40:17.560 --> 00:40:19.890 or specific-- and-- 00:40:19.890 --> 00:40:22.287 yeah-- so we'll take like a 10-minute break. 00:40:22.287 --> 00:40:23.745 Make sure you hand in the homework. 00:40:26.280 --> 00:40:28.770 All right, so I'm going to wrap up 00:40:28.770 --> 00:40:32.130 with some general thoughts about poker and poker in general. 00:40:32.130 --> 00:40:35.190 So one question that I get asked a lot 00:40:35.190 --> 00:40:37.320 is, it's called the Moneymaker effect. 00:40:37.320 --> 00:40:39.540 So what happened-- and this is sort of a big catalyst 00:40:39.540 --> 00:40:41.010 for poker becoming really popular-- 00:40:41.010 --> 00:40:44.450 was, I think in 2003, Chris Moneymaker, 00:40:44.450 --> 00:40:45.630 that's actually his name-- 00:40:45.630 --> 00:40:48.480 Moneymaker is his last name-- 00:40:48.480 --> 00:40:51.650 he spent like $1 playing in this satellite on PokerStars, 00:40:51.650 --> 00:40:54.179 won a seat to the World Series of Poker main event, 00:40:54.179 --> 00:40:56.220 and then went there, and then won the whole thing 00:40:56.220 --> 00:40:58.460 for like $2.5 million. 00:40:58.460 --> 00:41:00.136 It was a beautiful Cinderella story, 00:41:00.136 --> 00:41:01.260 and then people heard this. 00:41:01.260 --> 00:41:02.730 And also, they made it seem like, you know, 00:41:02.730 --> 00:41:04.520 it's not like the lottery where you've got to get really, 00:41:04.520 --> 00:41:05.686 really lucky to become rich. 00:41:05.686 --> 00:41:07.730 It's literally, this guy's really smart. 00:41:07.730 --> 00:41:10.420 He can read people, and it's all skill. 00:41:10.420 --> 00:41:11.280 And he did this. 00:41:11.280 --> 00:41:13.890 And it's sort of like, anyone can become a poker star just 00:41:13.890 --> 00:41:16.380 like Chris Moneymaker. 00:41:16.380 --> 00:41:19.510 And this was a huge driving force 00:41:19.510 --> 00:41:22.360 in the popularity of poker. 00:41:22.360 --> 00:41:25.260 So a question that I wondered myself is, 00:41:25.260 --> 00:41:27.305 how could there actually be so much money? 00:41:27.305 --> 00:41:29.430 Because someone has to be losing this money for you 00:41:29.430 --> 00:41:31.370 to be winning this money, right? 00:41:31.370 --> 00:41:34.770 So where is the money coming from? 00:41:34.770 --> 00:41:37.940 Can anyone smart and motivated succeed in poker? 00:41:37.940 --> 00:41:40.650 Et cetera. 00:41:40.650 --> 00:41:43.581 OK, so what's unique about poker? 00:41:43.581 --> 00:41:45.330 Why can't you make this much money playing 00:41:45.330 --> 00:41:47.280 like chess or something? 00:41:47.280 --> 00:41:50.110 Why can't you make this much money playing hockey? 00:41:50.110 --> 00:41:51.630 So what's unique about poker? 00:41:51.630 --> 00:41:53.470 So I guess four unique aspects that allows 00:41:53.470 --> 00:41:54.720 for there to be so much money. 00:41:54.720 --> 00:41:56.740 So I'm going to talk about them individually. 00:41:56.740 --> 00:42:00.205 One is, I think everyone is overconfident, myself included. 00:42:00.205 --> 00:42:04.050 Two is, gambling self-control-- aspects of that. 00:42:04.050 --> 00:42:06.570 Three is, it's a very fast-evolving game. 00:42:06.570 --> 00:42:08.760 And four is, what I sort of started the class-- 00:42:08.760 --> 00:42:12.650 the very first class I talked about being credit card 00:42:12.650 --> 00:42:14.750 roulette-- not being results-oriented. 00:42:14.750 --> 00:42:15.990 And I think that's very hard. 00:42:15.990 --> 00:42:19.770 So I'll go through each one of them separately. 00:42:19.770 --> 00:42:22.100 So yeah, one is this huge overconfidence thing, 00:42:22.100 --> 00:42:23.100 which is very prevalent. 00:42:23.100 --> 00:42:26.910 So it's normal, in general, for people to be overconfident. 00:42:26.910 --> 00:42:30.150 I don't know how many of you have seen the experiment where 00:42:30.150 --> 00:42:33.090 it's like, you know, write down your 95% confidence 00:42:33.090 --> 00:42:35.000 intervals for all these things. 00:42:35.000 --> 00:42:37.380 So if they're actually 95% confidence intervals 00:42:37.380 --> 00:42:39.180 and they're correctly calibrated, 00:42:39.180 --> 00:42:41.790 then actually 19 out of 20 of your intervals 00:42:41.790 --> 00:42:43.530 should contain the real thing. 00:42:43.530 --> 00:42:45.270 But like you do this for a normal person, 00:42:45.270 --> 00:42:48.990 it'll be like, 30% of their things actually lie neutral. 00:42:48.990 --> 00:42:52.640 So they're just drastically overconfident. 00:42:52.640 --> 00:42:55.530 And so yeah, it's normal to be overconfident, but especially 00:42:55.530 --> 00:42:56.586 in poker. 00:42:56.586 --> 00:42:57.960 I think poker is among the things 00:42:57.960 --> 00:43:00.210 I know where it's easiest to overestimate 00:43:00.210 --> 00:43:02.000 your own abilities. 00:43:02.000 --> 00:43:04.110 Does someone want to suggest any others? 00:43:04.110 --> 00:43:06.209 Is there something else you think where like, 00:43:06.209 --> 00:43:08.000 everyone thinks they're good at this thing? 00:43:12.200 --> 00:43:17.480 So I can think of two examples that I think are sort of true. 00:43:17.480 --> 00:43:21.335 Raise your hand if you think you're a below medium driver. 00:43:23.932 --> 00:43:26.015 No, but some people actually are willing to do it. 00:43:26.015 --> 00:43:28.400 Because I very rarely talk to someone who admitted 00:43:28.400 --> 00:43:29.677 to being bad at driving. 00:43:29.677 --> 00:43:31.760 Everyone I've ever asked about their driving skill 00:43:31.760 --> 00:43:34.490 thinks they're really good at driving a car, myself included. 00:43:34.490 --> 00:43:37.577 I definitely don't think I'm a below medium driver. 00:43:37.577 --> 00:43:38.660 Another thing is teaching. 00:43:38.660 --> 00:43:41.360 I've also barely talked to someone 00:43:41.360 --> 00:43:44.090 who thinks they're worse than medium at teaching. 00:43:47.032 --> 00:43:48.490 I guess maybe Professor [INAUDIBLE] 00:43:48.490 --> 00:43:49.840 can speak about this. 00:43:54.900 --> 00:43:57.820 Most things someone will admit to being bad at this, 00:43:57.820 --> 00:44:02.340 but poker is similar to these two examples I thought of-- 00:44:02.340 --> 00:44:03.560 driving, teaching, sort of. 00:44:03.560 --> 00:44:06.120 Where it's just very easy to think you're really good at it, 00:44:06.120 --> 00:44:09.270 and it's hard to admit to yourself that you're not 00:44:09.270 --> 00:44:10.270 good at it. 00:44:10.270 --> 00:44:13.770 Yeah, so one saying in poker is, if you can't spot the fish 00:44:13.770 --> 00:44:17.190 at the table-- the fish is like the losing player that everyone 00:44:17.190 --> 00:44:18.530 is trying to win money from-- 00:44:18.530 --> 00:44:20.520 then you are the fish. 00:44:20.520 --> 00:44:23.210 This is sort of a popular saying. 00:44:23.210 --> 00:44:26.355 So why is overconfidence so common in poker? 00:44:29.480 --> 00:44:30.720 It's like a mental battle. 00:44:30.720 --> 00:44:33.330 Your mentally battling against your opponent. 00:44:33.330 --> 00:44:34.110 Is he bluffing? 00:44:34.110 --> 00:44:34.950 Is he not? 00:44:34.950 --> 00:44:36.900 And it's just easy to always assume-- 00:44:36.900 --> 00:44:40.409 which I do throughout a lot of this class, right? 00:44:40.409 --> 00:44:41.700 I talk about exploitative play. 00:44:41.700 --> 00:44:43.670 I'm building a model for our opponent 00:44:43.670 --> 00:44:47.070 and assuming that they behave as a probabilistic machine 00:44:47.070 --> 00:44:48.330 according to my model. 00:44:48.330 --> 00:44:50.250 I'm assuming that I'm ahead of my opponent. 00:44:50.250 --> 00:44:52.032 I'm assuming I'm better. 00:44:52.032 --> 00:44:54.150 There's also a lot of selective memory, I think. 00:44:54.150 --> 00:44:56.100 It's easy to remember your bad beats-- 00:44:56.100 --> 00:44:59.590 the time they hit a king on the river and beat your aces-- 00:44:59.590 --> 00:45:02.730 and it's easy to forget the times you got really lucky 00:45:02.730 --> 00:45:04.170 on the river and beat them. 00:45:04.170 --> 00:45:08.250 So selective memory, I think, is a big aspect. 00:45:08.250 --> 00:45:11.410 I think lack of clear benchmarks is a big aspect as well. 00:45:11.410 --> 00:45:13.740 So it's not like running 100 meters. 00:45:13.740 --> 00:45:16.300 No one who takes 30 seconds to run 100 meters 00:45:16.300 --> 00:45:19.410 is going to think, oh, I can compete in the Olympics, right? 00:45:19.410 --> 00:45:20.410 Because it's very clear. 00:45:20.410 --> 00:45:23.210 There's a very clear benchmark how fast you need to be. 00:45:23.210 --> 00:45:26.700 But in poker, even if you don't win tournaments, 00:45:26.700 --> 00:45:28.800 it's easy to complain about luck. 00:45:28.800 --> 00:45:30.780 And there's different types of tournaments. 00:45:30.780 --> 00:45:33.570 And it's easy to like bend the benchmarks in a way 00:45:33.570 --> 00:45:36.910 to convince yourself that you're better than you are. 00:45:36.910 --> 00:45:39.690 It's easy to hit a lucky streak and consider it all skill, 00:45:39.690 --> 00:45:42.150 and you can blame all your losing streaks on luck. 00:45:42.150 --> 00:45:43.740 So those are some reasons I think. 00:45:43.740 --> 00:45:46.020 I think poker is just a very well-designed game 00:45:46.020 --> 00:45:48.030 for this purpose and to, basically, 00:45:48.030 --> 00:45:50.730 tricking and deceiving people into overestimating 00:45:50.730 --> 00:45:53.880 their own ability. 00:45:53.880 --> 00:45:56.460 And another aspect of it is, and this 00:45:56.460 --> 00:45:58.720 is what's really tough poker, I think, is, 00:45:58.720 --> 00:46:01.240 even though it's so easy to be overconfident, 00:46:01.240 --> 00:46:03.780 and it's such a flaw to be overconfident, it's also, 00:46:03.780 --> 00:46:04.950 in some sense, necessary. 00:46:04.950 --> 00:46:06.750 You know, if you're not confident, 00:46:06.750 --> 00:46:08.190 how can you take risks? 00:46:08.190 --> 00:46:11.000 Poker-- you're gambling, essentially, 00:46:11.000 --> 00:46:13.200 and you have to do risky things. 00:46:13.200 --> 00:46:16.650 And if you're not confident, how can you do risky things, right? 00:46:16.650 --> 00:46:20.460 And also, if you're trying to mentally read your opponent, 00:46:20.460 --> 00:46:21.960 if you're constantly remind yourself 00:46:21.960 --> 00:46:24.720 that you're dumber than you think you are, then how can 00:46:24.720 --> 00:46:28.980 you actually think that you can outread your opponent? 00:46:28.980 --> 00:46:30.750 And I talked about this results-oriented. 00:46:30.750 --> 00:46:32.310 You need to be confident to trust 00:46:32.310 --> 00:46:35.310 that you made a good decision even though your result was 00:46:35.310 --> 00:46:37.600 you lost $10,000 on the day. 00:46:37.600 --> 00:46:41.820 So confidence is also necessary, but it's also so easy 00:46:41.820 --> 00:46:42.860 to be overconfident. 00:46:42.860 --> 00:46:46.470 So this balance of being exactly the right confidence 00:46:46.470 --> 00:46:50.010 is something that I think even like professional poker 00:46:50.010 --> 00:46:53.464 players strive to try to strike the balance between every day. 00:46:53.464 --> 00:46:54.630 And I think it's very tough. 00:46:54.630 --> 00:46:55.980 And it's something I struggle with a lot, 00:46:55.980 --> 00:46:58.485 too, to try to figure out when I'm being overconfident 00:46:58.485 --> 00:47:02.470 and when I'm being underconfident. 00:47:02.470 --> 00:47:05.580 So I think one good mentality-- so back to this driving thing 00:47:05.580 --> 00:47:09.300 is, I think it's a good mentality-- you know, 00:47:09.300 --> 00:47:10.800 if you play poker and you enjoy it. 00:47:10.800 --> 00:47:11.950 I think it's a great game. 00:47:11.950 --> 00:47:14.340 It's a beautiful mathematical game and a fun game 00:47:14.340 --> 00:47:17.010 to play with friends if you're just 00:47:17.010 --> 00:47:19.350 are willing to admit, you know, I play in this home game 00:47:19.350 --> 00:47:20.150 every Friday night. 00:47:20.150 --> 00:47:23.190 I'm probably a below average player. 00:47:23.190 --> 00:47:25.744 I probably lose, on average, $10 every time I play. 00:47:25.744 --> 00:47:26.910 I think that's totally fine. 00:47:26.910 --> 00:47:28.368 It's just like spending your Friday 00:47:28.368 --> 00:47:29.760 night going to see a movie. 00:47:29.760 --> 00:47:33.990 You pay $10 and you're happy to take $10 out of your wallet 00:47:33.990 --> 00:47:37.590 and not see it again, right? 00:47:37.590 --> 00:47:40.740 I think it would be a healthy mentality for more people 00:47:40.740 --> 00:47:43.579 to be willing to do this and just admit to themselves, 00:47:43.579 --> 00:47:45.870 yeah, I enjoy playing poker, and I lose a bit of money, 00:47:45.870 --> 00:47:47.470 but you know, I have fun doing it. 00:47:47.470 --> 00:47:49.410 And it's the same as seeing a movie 00:47:49.410 --> 00:47:52.640 but, in reality, I think this isn't the case. 00:47:52.640 --> 00:47:56.280 Even at these friendly Friday night games for low stakes, 00:47:56.280 --> 00:47:58.260 probably, if you ask all the people there, 00:47:58.260 --> 00:48:00.060 do you think you're beating your friends? 00:48:00.060 --> 00:48:01.350 Everyone's going to say yes. 00:48:01.350 --> 00:48:05.250 Everyone's not saying, oh, I'm going there, essentially, 00:48:05.250 --> 00:48:07.410 paying $10 to play poker with my friends. 00:48:07.410 --> 00:48:10.020 Everyone's saying, I'm winning a bit of money or whatever, 00:48:10.020 --> 00:48:10.520 right? 00:48:10.520 --> 00:48:16.440 So I think that's an important mentality to try to have that. 00:48:16.440 --> 00:48:18.645 And I think it's fine. 00:48:18.645 --> 00:48:22.320 You don't have to be the best at everything, right? 00:48:22.320 --> 00:48:25.306 So one story I like to tell is, so David Einhorn-- 00:48:25.306 --> 00:48:26.305 he's like a billionaire. 00:48:26.305 --> 00:48:29.460 I think he founded Greenlight Capital or something. 00:48:29.460 --> 00:48:33.340 And he actually won $4 million in a $1 million 00:48:33.340 --> 00:48:37.170 buy-in poker tournament and donated it all to charity. 00:48:37.170 --> 00:48:39.240 And after the fact-- 00:48:39.240 --> 00:48:41.520 he's always like a super smart guy-- 00:48:41.520 --> 00:48:43.860 so he played a $1 million buy-in tournament. 00:48:43.860 --> 00:48:46.850 So everyone else playing this tournament is like a poker 00:48:46.850 --> 00:48:48.990 professional-- the best in the world-- 00:48:48.990 --> 00:48:52.400 and he's just like this rich billionaire who 00:48:52.400 --> 00:48:53.960 doesn't really-- like he wasn't bad, 00:48:53.960 --> 00:48:56.750 but he just started playing poker. 00:48:56.750 --> 00:48:59.730 Like, he's a smart guy, and he got coaching to play it, 00:48:59.730 --> 00:49:02.930 but he was the clear loser in the tournament. 00:49:02.930 --> 00:49:03.930 And he just admitted it. 00:49:03.930 --> 00:49:05.638 He just said you know, I'm a billionaire. 00:49:05.638 --> 00:49:07.250 I'm happy to spend a million dollars 00:49:07.250 --> 00:49:08.330 playing this tournament. 00:49:08.330 --> 00:49:12.077 I understand I'm probably expecting to lose like $200,000 00:49:12.077 --> 00:49:14.410 or whatever playing this tournament with all these guys, 00:49:14.410 --> 00:49:15.330 but I'm fine with it. 00:49:15.330 --> 00:49:17.514 I got a million dollars, who cares, right? 00:49:17.514 --> 00:49:18.680 And he was just very honest. 00:49:18.680 --> 00:49:21.070 And even after he actually won $4 million, 00:49:21.070 --> 00:49:22.820 he didn't come first, he came like third-- 00:49:22.820 --> 00:49:26.010 he just admitted, you know, he said like, I was very lucky. 00:49:26.010 --> 00:49:28.670 I came in expecting to just lose this $1 million 00:49:28.670 --> 00:49:30.584 that I don't care about, and then 00:49:30.584 --> 00:49:32.750 he just donated all his winnings to charity, anyway. 00:49:32.750 --> 00:49:35.150 But I wish more people were like him. 00:49:35.150 --> 00:49:37.040 I think that's a very good mentality 00:49:37.040 --> 00:49:39.800 to have to just admit that you're playing poker for fun, 00:49:39.800 --> 00:49:43.060 and that's totally fine. 00:49:43.060 --> 00:49:45.060 OK, so the second thing I want to talk about 00:49:45.060 --> 00:49:47.870 is gambling self-control. 00:49:47.870 --> 00:49:51.290 So I think this can also be the downfall 00:49:51.290 --> 00:49:53.990 of a lot of smart and motivated people trying 00:49:53.990 --> 00:49:54.870 to get into poker. 00:49:58.102 --> 00:49:59.810 So these are some things that can happen. 00:49:59.810 --> 00:50:01.730 So after getting unlucky in the previous hand, 00:50:01.730 --> 00:50:04.200 you play the next hand poorly because you're upset. 00:50:04.200 --> 00:50:07.460 You're tilted, as poker player say. 00:50:07.460 --> 00:50:10.179 Or playing when you're tired just to get unstuck. 00:50:10.179 --> 00:50:12.470 I've definitely done this many times before in my poker 00:50:12.470 --> 00:50:13.460 career. 00:50:13.460 --> 00:50:15.470 If I lost money, especially when I 00:50:15.470 --> 00:50:18.290 feel like I'd gotten unlucky playing against someone 00:50:18.290 --> 00:50:20.060 who I'm better than and just like, 00:50:20.060 --> 00:50:22.150 I've lost money because I got unlucky, 00:50:22.150 --> 00:50:26.240 I won't stop playing until I get unstuck, which is like, 00:50:26.240 --> 00:50:29.270 win back the money I lost until I'm in the black, essentially. 00:50:29.270 --> 00:50:32.922 And it's terrible because even if I'm a bit better, 00:50:32.922 --> 00:50:34.630 if I'm playing with this mentality trying 00:50:34.630 --> 00:50:36.900 to get unstuck, I'm just going to be making 00:50:36.900 --> 00:50:40.020 below average decisions, and it's just not a good thing 00:50:40.020 --> 00:50:42.330 to do. 00:50:42.330 --> 00:50:44.640 And also from the other side, it can be 00:50:44.640 --> 00:50:46.370 hard to rationalize gambling. 00:50:46.370 --> 00:50:48.830 So it's hard to stop yourself from gambling too much, 00:50:48.830 --> 00:50:52.520 but it's also sometimes hard to rationalize that, you know, 00:50:52.520 --> 00:50:54.830 gambling-- there is a lot of stigma around gambling. 00:50:54.830 --> 00:50:57.740 You have to convince yourself that, I 00:50:57.740 --> 00:50:59.172 shouldn't be too scared. 00:50:59.172 --> 00:51:01.130 I'm playing this game that involves-- you know, 00:51:01.130 --> 00:51:02.150 you can call it gambling-- 00:51:02.150 --> 00:51:03.890 I'm playing this game with a lot of luck. 00:51:03.890 --> 00:51:05.914 And you've got to convince yourself that, this 00:51:05.914 --> 00:51:07.080 is what I'm fine with doing. 00:51:07.080 --> 00:51:08.240 It's like a lottery. 00:51:08.240 --> 00:51:10.280 And you've got to sometimes make decisions 00:51:10.280 --> 00:51:11.540 under pressure as well. 00:51:11.540 --> 00:51:13.456 And you've just got to rationalize to yourself 00:51:13.456 --> 00:51:15.389 that, yeah, there's a lot of luck in this, 00:51:15.389 --> 00:51:16.930 but this is the game I chose to play. 00:51:21.020 --> 00:51:22.595 The third thing is-- 00:51:22.595 --> 00:51:26.450 so fast evolution, I think, is another big aspect 00:51:26.450 --> 00:51:31.550 of how there was so much money in Texas hold 'em for so long. 00:51:31.550 --> 00:51:34.490 So it was a relatively new game, also 00:51:34.490 --> 00:51:36.020 with a lot of hidden depth. 00:51:36.020 --> 00:51:38.060 So something like this can never happen 00:51:38.060 --> 00:51:40.440 in chess, where chess has been studied 00:51:40.440 --> 00:51:42.620 for hundreds, thousands of years, 00:51:42.620 --> 00:51:44.600 and it's not like a new game. 00:51:44.600 --> 00:51:47.450 And even though the best player today is still better than 00:51:47.450 --> 00:51:50.610 the best player 20 years ago, it's not like the game is 00:51:50.610 --> 00:51:55.110 evolving super fast, whereas hold 'em was like a new game-- 00:51:55.110 --> 00:51:57.110 a relatively new game at the time. 00:51:57.110 --> 00:51:59.960 And just-- there was so much hidden depth, 00:51:59.960 --> 00:52:03.409 and the best players just kept improving so fast that-- 00:52:03.409 --> 00:52:05.450 so like you say, like the best player in the year 00:52:05.450 --> 00:52:09.380 2000 would be like a terrible player by 2004. 00:52:09.380 --> 00:52:12.640 And like the best player in 2004 would be a bad player 00:52:12.640 --> 00:52:13.910 by 2008, et cetera. 00:52:13.910 --> 00:52:16.580 So it's just, even if you're on top of the game 00:52:16.580 --> 00:52:18.680 right now, if you stop studying, you're 00:52:18.680 --> 00:52:21.560 going to be nowhere near the top of the game in like a year. 00:52:21.560 --> 00:52:23.010 So it was just so fast. 00:52:23.010 --> 00:52:25.640 Can anyone else think of other examples of things 00:52:25.640 --> 00:52:28.106 that are kind of like this? 00:52:28.106 --> 00:52:32.420 AUDIENCE: CrossFit was-- well, if you get like-- 00:52:32.420 --> 00:52:37.280 the winner of the 2009-2010 games wouldn't even compete. 00:52:37.280 --> 00:52:38.370 WILL MA: Oh, wow. 00:52:38.370 --> 00:52:39.430 OK I didn't know that. 00:52:39.430 --> 00:52:40.400 That's cool. 00:52:40.400 --> 00:52:43.574 I didn't know CrossFit was that good, yeah. 00:52:43.574 --> 00:52:46.730 That's pretty crazy. 00:52:46.730 --> 00:52:49.910 There's one other thing I can sort of think of. 00:52:49.910 --> 00:52:53.000 How many you guys have done math contests as a kid? 00:52:53.000 --> 00:52:56.384 I think those, to my knowledge, have gotten a lot harder, 00:52:56.384 --> 00:52:57.800 just in terms of how good you need 00:52:57.800 --> 00:53:00.560 to be to say, be on the United States national team 00:53:00.560 --> 00:53:04.060 is way harder now than it was, say, 30 years ago from what 00:53:04.060 --> 00:53:06.485 I've heard. 00:53:06.485 --> 00:53:08.500 But yeah, so this aspect of Texas hold 00:53:08.500 --> 00:53:10.730 'em-- so this was also a huge driving factor. 00:53:10.730 --> 00:53:14.570 Because it would be easy to tell yourself, 00:53:14.570 --> 00:53:16.920 I was the best player in the world four years ago. 00:53:16.920 --> 00:53:20.400 I could obviously sit down at this $1/$2 game and make money, 00:53:20.400 --> 00:53:20.900 right? 00:53:20.900 --> 00:53:22.670 And the answer would often be, no. 00:53:22.670 --> 00:53:26.600 So this was another reason why there was a lot of money in it. 00:53:26.600 --> 00:53:29.630 Because it's easy to just remember 00:53:29.630 --> 00:53:31.490 that you were the best a year ago and just 00:53:31.490 --> 00:53:36.760 forget that the tides are rising so fast. 00:53:36.760 --> 00:53:39.800 So that being said, so I wanted to also take this opportunity 00:53:39.800 --> 00:53:41.574 to suggest some further readings for-- 00:53:41.574 --> 00:53:42.740 I know I've been asked this. 00:53:42.740 --> 00:53:43.000 Yeah? 00:53:43.000 --> 00:53:44.270 AUDIENCE: So why is that? 00:53:44.270 --> 00:53:45.670 Based on your understanding? 00:53:45.670 --> 00:53:49.790 I think because of your strategies-- 00:53:49.790 --> 00:53:51.266 you have to improve your strategy? 00:53:51.266 --> 00:53:52.640 WILL MA: Yeah, yeah, I also think 00:53:52.640 --> 00:53:54.930 there was a lot of hidden depth. 00:53:54.930 --> 00:53:59.040 So I mean, I think with any new thing, this will be the case. 00:53:59.040 --> 00:54:01.940 But I think in poker, there were many times 00:54:01.940 --> 00:54:05.930 where the consensus amongst the top players was that they 00:54:05.930 --> 00:54:08.065 were close to solving the game. 00:54:08.065 --> 00:54:09.440 And then a year later, they would 00:54:09.440 --> 00:54:13.607 realize they missed completely viable strategies that 00:54:13.607 --> 00:54:15.440 completely messed up all their calculations, 00:54:15.440 --> 00:54:17.220 and they had to start over. 00:54:17.220 --> 00:54:19.700 So I think that was big. 00:54:19.700 --> 00:54:22.184 It's easy to think that you've solved the game 00:54:22.184 --> 00:54:23.600 and then suddenly realize, oh, I'm 00:54:23.600 --> 00:54:25.955 nowhere near solving the game because I forgot about all 00:54:25.955 --> 00:54:28.108 of these different strategies. 00:54:30.680 --> 00:54:33.762 This might be sort of true with a lot of-- 00:54:33.762 --> 00:54:34.970 I'm trying to think, I mean-- 00:54:34.970 --> 00:54:36.950 the biggest thing is, it's a new thing. 00:54:36.950 --> 00:54:38.990 Like it's hard for this to happen like-- 00:54:38.990 --> 00:54:41.330 I think in most sports that people 00:54:41.330 --> 00:54:43.910 have done for a long time, people get gradually better, 00:54:43.910 --> 00:54:44.600 right? 00:54:44.600 --> 00:54:46.574 You look at like, the 100-meter sprint. 00:54:46.574 --> 00:54:48.740 It's like, yeah, the world record is getting broken, 00:54:48.740 --> 00:54:50.960 but it's not like it's going to go from 10 seconds 00:54:50.960 --> 00:54:52.260 to five seconds. 00:54:52.260 --> 00:54:57.860 It'll go from 10 seconds to 9.99 seconds or something like that. 00:54:57.860 --> 00:55:02.504 So I think just the fact that it's new is a big aspect. 00:55:02.504 --> 00:55:05.630 But yeah, Texas hold 'em would be the equivalent to the world 00:55:05.630 --> 00:55:08.090 record in the 100 meters being 10 seconds then 00:55:08.090 --> 00:55:09.670 like five seconds a year later, then 00:55:09.670 --> 00:55:14.270 like two seconds like two years later, it was just insane. 00:55:14.270 --> 00:55:16.790 OK, so that being said, so some people have asked me, 00:55:16.790 --> 00:55:20.840 if I want to continue learning about poker and reading poker, 00:55:20.840 --> 00:55:21.950 what should I do? 00:55:21.950 --> 00:55:25.455 So that being said, I think the best resources, by far, 00:55:25.455 --> 00:55:27.280 are online. 00:55:27.280 --> 00:55:29.030 A lot of people have asked me about books, 00:55:29.030 --> 00:55:33.560 and I will recommend some books, but I think books, basically, 00:55:33.560 --> 00:55:35.190 blew out of date way too fast. 00:55:35.190 --> 00:55:38.540 So I think, in general, the best resources are online. 00:55:38.540 --> 00:55:42.530 So cardrunners.com is a website where, basically, poker pros 00:55:42.530 --> 00:55:46.752 can make videos of themselves while playing and talking. 00:55:46.752 --> 00:55:48.460 You do have to pay to get a subscription. 00:55:48.460 --> 00:55:52.970 OK, so this is a bit of a biased advice, just a warning, 00:55:52.970 --> 00:55:54.810 because I'm a pro at CardRunners, 00:55:54.810 --> 00:55:58.050 but, I mean, amongst like 50, 60 other pros. 00:55:58.050 --> 00:55:59.930 They also donated some free memberships 00:55:59.930 --> 00:56:02.570 to students in the class if you guys looked at the prizes. 00:56:02.570 --> 00:56:06.770 So you can get some free memberships to CardRunners. 00:56:06.770 --> 00:56:10.040 A good free resource is Two Plus Two forums. 00:56:10.040 --> 00:56:13.130 I think there's a lot of garbage on those forums nowadays 00:56:13.130 --> 00:56:16.310 but, still, most of the best poker players in the world 00:56:16.310 --> 00:56:19.785 still do use those forums and posts on those forums-- so 00:56:19.785 --> 00:56:20.410 twoplustwo.com. 00:56:20.410 --> 00:56:23.950 There is a lot of garbage and banter, 00:56:23.950 --> 00:56:25.750 but if you are just trying to improve, 00:56:25.750 --> 00:56:27.250 there is good content on there. 00:56:27.250 --> 00:56:30.490 You just have to find it. 00:56:30.490 --> 00:56:32.960 So this is a new thing, but on Twitch streams-- 00:56:32.960 --> 00:56:36.370 so Twitch is a website you can go on to watch, 00:56:36.370 --> 00:56:39.970 essentially, poker pros play in real time. 00:56:39.970 --> 00:56:42.820 They share their screens and talk through their hands. 00:56:42.820 --> 00:56:44.620 It's a pretty good free resource. 00:56:44.620 --> 00:56:47.080 It's sometimes more entertaining than educational, 00:56:47.080 --> 00:56:48.730 but I think it's quite good. 00:56:48.730 --> 00:56:51.520 And they would do like a 10-minute delay 00:56:51.520 --> 00:56:54.820 so that you can't watch them and you know what cards they have. 00:56:54.820 --> 00:56:57.010 In case anyone was considering trying 00:56:57.010 --> 00:57:00.340 to do that to get an advantage. 00:57:00.340 --> 00:57:02.530 So these are some online resources, 00:57:02.530 --> 00:57:05.260 and I will suggest some books, although I 00:57:05.260 --> 00:57:09.010 do think most of these books, I think, are reasonably outdated. 00:57:09.010 --> 00:57:11.475 But I do think they're very-- in my opinion, 00:57:11.475 --> 00:57:12.850 out of the books I've read, these 00:57:12.850 --> 00:57:14.590 are the best-written books. 00:57:14.590 --> 00:57:17.320 And even if they're a bit outdated, 00:57:17.320 --> 00:57:19.480 I think the theory and the way they're written 00:57:19.480 --> 00:57:22.000 is very good and also somewhat entertaining 00:57:22.000 --> 00:57:24.820 and sort of gives you an idea on the history of poker 00:57:24.820 --> 00:57:27.869 and the evolution of the game. 00:57:27.869 --> 00:57:29.410 So my favorite book is the first one. 00:57:29.410 --> 00:57:31.200 It's called, Small Stakes Hold 'em. 00:57:31.200 --> 00:57:35.260 It's by Ed Miller, who's a MIT graduate; David Sklansky; 00:57:35.260 --> 00:57:36.790 and Mason Malmuth. 00:57:36.790 --> 00:57:38.420 So this is actually limit hold 'em, 00:57:38.420 --> 00:57:40.970 which is, in some sense, a solved game nowadays, 00:57:40.970 --> 00:57:43.000 and no one plays limit hold 'em anymore. 00:57:43.000 --> 00:57:46.630 So limit hold 'em is where you can't bet any amount. 00:57:46.630 --> 00:57:50.770 You have to bet a very specific size. 00:57:50.770 --> 00:57:52.796 But I think this is one of the classic books. 00:57:52.796 --> 00:57:54.670 So this is one of the classic books in poker. 00:57:54.670 --> 00:57:57.037 It's very well written and written by mathematicians. 00:57:57.037 --> 00:57:59.245 And it just goes through the basic concepts of poker, 00:57:59.245 --> 00:58:01.828 I think, very, very well, even though it's for limit hold 'em. 00:58:01.828 --> 00:58:02.710 And it's a good read. 00:58:05.830 --> 00:58:09.100 Yeah, it might even be a collector's item nowadays. 00:58:09.100 --> 00:58:11.620 So one story I'd like to tell about this book is-- 00:58:11.620 --> 00:58:14.410 so my good friend, Mike McDonald, he was-- 00:58:14.410 --> 00:58:18.540 so he's the guy who got me into poker. 00:58:18.540 --> 00:58:20.800 He's probably read this book, he says like-- 00:58:20.800 --> 00:58:22.960 maybe like 20 times. 00:58:22.960 --> 00:58:25.764 And then he's also a guy who doesn't really like reading. 00:58:25.764 --> 00:58:27.430 So I think there was a point in his life 00:58:27.430 --> 00:58:31.390 where he's read less than 20 different books in his life 00:58:31.390 --> 00:58:34.990 but then this specific book more than 20 times. 00:58:34.990 --> 00:58:37.330 So it's a very good book. 00:58:37.330 --> 00:58:39.520 Harrington on Hold 'em is on tournaments. 00:58:39.520 --> 00:58:40.420 It's outdated. 00:58:40.420 --> 00:58:42.070 It's really, really badly outdated, 00:58:42.070 --> 00:58:44.390 but I still think it's very well written and has 00:58:44.390 --> 00:58:45.352 some good concepts. 00:58:45.352 --> 00:58:46.810 That's how I first started learning 00:58:46.810 --> 00:58:50.830 to play tournaments is Harrington on Hold 'em 1 and 2. 00:58:50.830 --> 00:58:53.620 Kill Phil/ Kill Everyone I think is pretty good, 00:58:53.620 --> 00:58:54.620 pretty up to date-- 00:58:54.620 --> 00:58:56.400 it's decent, I think. 00:58:56.400 --> 00:58:57.970 Every Hand Revealed is-- 00:58:57.970 --> 00:58:59.770 Gus Hansen's a very famous poker player 00:58:59.770 --> 00:59:02.620 who's been around forever. 00:59:02.620 --> 00:59:05.920 So it's a book where he goes through every hand he played 00:59:05.920 --> 00:59:07.384 in this tournament that he won. 00:59:07.384 --> 00:59:09.550 And I think it's more entertaining than educational, 00:59:09.550 --> 00:59:12.340 but he's definitely a really good player. 00:59:12.340 --> 00:59:14.050 Mathematics of Poker by Bill Chen. 00:59:14.050 --> 00:59:17.240 It's not that practical-- don't tell Bill this when he comes 00:59:17.240 --> 00:59:18.880 Friday-- 00:59:18.880 --> 00:59:22.030 it's theoretically very interesting if you like math-- 00:59:22.030 --> 00:59:23.380 if you like game theory. 00:59:23.380 --> 00:59:25.340 It's theoretically very interesting. 00:59:25.340 --> 00:59:28.890 Building a Bankroll is a recent book that-- 00:59:28.890 --> 00:59:30.870 this year, he didn't have any leftovers 00:59:30.870 --> 00:59:33.140 to donate to our class but, in the past, 00:59:33.140 --> 00:59:36.070 he's supported our class and donated 00:59:36.070 --> 00:59:37.250 a lot of copies of the book. 00:59:37.250 --> 00:59:42.007 And I think it's pretty up to date, and it's for cash games, 00:59:42.007 --> 00:59:43.090 so I think it's very good. 00:59:47.290 --> 00:59:50.110 OK, so back to the four things about poker that I think 00:59:50.110 --> 00:59:52.450 makes it unique. 00:59:52.450 --> 00:59:57.790 So the fourth point is this idea of not being results-oriented. 00:59:57.790 --> 00:59:59.760 So yeah, so we talked about this a lot 00:59:59.760 --> 01:00:04.090 in the first class already-- this decision mentality, where 01:00:04.090 --> 01:00:06.610 you need to care about the decision you made, 01:00:06.610 --> 01:00:08.080 not the result you got. 01:00:08.080 --> 01:00:11.020 And I think this actually is a barrier 01:00:11.020 --> 01:00:14.210 to a lot of smart and motivated people getting 01:00:14.210 --> 01:00:18.910 into poker because it's almost antithetical. 01:00:18.910 --> 01:00:21.810 If you're a smart and motivated person, you're used to like-- 01:00:21.810 --> 01:00:25.180 you study hard, and then you get a good result on your tests, 01:00:25.180 --> 01:00:27.090 right? 01:00:27.090 --> 01:00:29.711 If you get a failing grade in your test, 01:00:29.711 --> 01:00:31.960 you're never going to be able to go up to your parents 01:00:31.960 --> 01:00:34.145 and be like, oh, I make good decisions, 01:00:34.145 --> 01:00:36.520 but I just got really unlucky and failed the test, right? 01:00:36.520 --> 01:00:37.769 No one's going to believe you. 01:00:40.720 --> 01:00:43.360 In poker, this can happen all the time. 01:00:43.360 --> 01:00:48.514 So it is a bit antithetical to sort of being motivated. 01:00:48.514 --> 01:00:50.180 One thing poker players like to laugh at 01:00:50.180 --> 01:00:54.190 is, I don't know if you put the word, results-oriented 01:00:54.190 --> 01:00:56.650 on your resume? 01:00:56.650 --> 01:00:59.080 I've seen seminars that teach you to become 01:00:59.080 --> 01:01:01.630 "results-oriented," and advertising this as being 01:01:01.630 --> 01:01:03.070 a great thing. 01:01:03.070 --> 01:01:04.630 You achieve results. 01:01:04.630 --> 01:01:07.870 You work hard, make decisions, and you achieve results. 01:01:07.870 --> 01:01:09.670 But we always laugh at this. 01:01:09.670 --> 01:01:11.140 Because results-oriented is always 01:01:11.140 --> 01:01:12.910 a negative term in poker. 01:01:12.910 --> 01:01:16.060 If a poker player says someone is results-oriented, 01:01:16.060 --> 01:01:17.960 they don't respect them very much. 01:01:17.960 --> 01:01:20.510 But I've seen resume's where people say, 01:01:20.510 --> 01:01:22.300 I'm very results-oriented. 01:01:28.340 --> 01:01:31.820 So a related thing is, it's easy to underestimate 01:01:31.820 --> 01:01:33.620 the variance in poker. 01:01:33.620 --> 01:01:36.860 And this is a big aspect, too, that goes on 01:01:36.860 --> 01:01:39.080 with being results-oriented. 01:01:39.080 --> 01:01:42.560 So this statistical experiment involving making up 01:01:42.560 --> 01:01:44.390 sequences of coin flips-- 01:01:44.390 --> 01:01:47.350 I've heard of this where a professor would 01:01:47.350 --> 01:01:50.910 ask students to make up a sequence of 200 coin flips. 01:01:50.910 --> 01:01:53.160 Can we get half the class to do this? 01:01:53.160 --> 01:01:57.220 And then can we get the other half to actually flip 200 coins 01:01:57.220 --> 01:01:59.470 and write down like heads, tails, heads, heads, heads, 01:01:59.470 --> 01:02:01.130 tails? 01:02:01.130 --> 01:02:04.190 And he could tell with like 100% certainty 01:02:04.190 --> 01:02:06.830 which ones are made up and which ones were real. 01:02:06.830 --> 01:02:08.750 And the way he did this is basically 01:02:08.750 --> 01:02:11.050 looking at which of the-- 01:02:11.050 --> 01:02:13.280 what's the longest sequence of heads in a row 01:02:13.280 --> 01:02:14.660 or tails in a row? 01:02:14.660 --> 01:02:18.050 And basically, in reality, if you flipped 200 coins-- 01:02:18.050 --> 01:02:19.490 I forget the exact numbers, but I 01:02:19.490 --> 01:02:22.280 think it's something like, you're like 99% 01:02:22.280 --> 01:02:25.760 to get at least like six or seven of the same thing 01:02:25.760 --> 01:02:28.790 in a row, whereas in all the made-up ones 01:02:28.790 --> 01:02:30.990 that people would be like, oh if there was heads 01:02:30.990 --> 01:02:33.290 seven times in a row, that can't be random, right? 01:02:33.290 --> 01:02:36.870 So we can't put seven hands in a row. 01:02:36.870 --> 01:02:40.730 So I think it's known that it's easy to underestimate 01:02:40.730 --> 01:02:43.190 how long you can get unlucky looking for. 01:02:43.190 --> 01:02:45.950 Like it's easy to think, I've been unlucky the last three 01:02:45.950 --> 01:02:48.730 times; that means I must deserve to get lucky now. 01:02:48.730 --> 01:02:51.890 But this is not true, mathematically. 01:02:51.890 --> 01:02:55.510 And it's just very easy to underestimate 01:02:55.510 --> 01:02:58.820 variance and underestimate how likely it 01:02:58.820 --> 01:03:01.340 is that you're just actually going to lose 10 coin 01:03:01.340 --> 01:03:02.360 flips in a row in poker. 01:03:02.360 --> 01:03:06.410 It's going to happen to you, and you're going to get tilted. 01:03:06.410 --> 01:03:08.940 And it's very important to control tilt. 01:03:08.940 --> 01:03:11.120 And yeah, pretty much every poker player 01:03:11.120 --> 01:03:14.270 thinks they're unluckier than mathematically possible. 01:03:14.270 --> 01:03:17.390 I've definitely felt like this in many parts of my career. 01:03:17.390 --> 01:03:19.940 I still feel like this sometimes now. 01:03:19.940 --> 01:03:22.160 It's very easy to get this feeling where you just, 01:03:22.160 --> 01:03:23.490 how can it be possible? 01:03:23.490 --> 01:03:25.710 How could I actually lose 20 coin flips in a row? 01:03:25.710 --> 01:03:27.750 Well, it can happen. 01:03:27.750 --> 01:03:32.174 And one of my poker players that I was talking to, John Cannon, 01:03:32.174 --> 01:03:34.340 he plays a lot of online poker, and this is actually 01:03:34.340 --> 01:03:36.450 a picture of his desk. 01:03:36.450 --> 01:03:39.500 He, basically, was so angry I think he smashed his mouse 01:03:39.500 --> 01:03:41.260 and made a big hole in his desk. 01:03:41.260 --> 01:03:43.670 So it can really frustrate you. 01:03:48.440 --> 01:03:49.955 And I hate to say this, but I think 01:03:49.955 --> 01:03:53.400 even if you're working very hard, you 01:03:53.400 --> 01:03:55.696 do need some lucky big scores along the way, 01:03:55.696 --> 01:03:57.320 especially at the start to get into it, 01:03:57.320 --> 01:03:59.840 even if you're very smart and working in the right way. 01:03:59.840 --> 01:04:02.587 And this is also antithetical and smart. 01:04:02.587 --> 01:04:04.670 Antithetical to smart and motivated people, right? 01:04:04.670 --> 01:04:08.030 Because we want to believe that if you work hard 01:04:08.030 --> 01:04:10.400 and you're smart, then you'll make it for sure. 01:04:10.400 --> 01:04:13.580 But I wouldn't say this is true in poker. 01:04:13.580 --> 01:04:15.830 I mean, I think I'm willing to admit that I think 01:04:15.830 --> 01:04:18.140 I was very lucky at the start. 01:04:18.140 --> 01:04:20.120 I had some big scores at the start that 01:04:20.120 --> 01:04:21.950 really drove my interest in the game 01:04:21.950 --> 01:04:25.280 and really propelled me into professional poker. 01:04:25.280 --> 01:04:28.510 And I think there probably, in a parallel universe, 01:04:28.510 --> 01:04:31.670 could be another copy of me that did the exact same things 01:04:31.670 --> 01:04:34.160 and just didn't get as lucky as I did at the start 01:04:34.160 --> 01:04:36.240 and just never got into poker. 01:04:36.240 --> 01:04:39.940 So this fact that you do still need to get lucky, 01:04:39.940 --> 01:04:42.440 even if you make all the right decisions [INAUDIBLE] make it 01:04:42.440 --> 01:04:42.939 is-- 01:04:42.939 --> 01:04:47.424 It's sort of a tough thing to swallow. 01:04:47.424 --> 01:04:48.840 This is sort of a different story, 01:04:48.840 --> 01:04:52.700 but I'd like to argue that that's sort of true in life, 01:04:52.700 --> 01:04:54.260 too-- 01:04:54.260 --> 01:04:56.930 the fact that being smart and working hard 01:04:56.930 --> 01:05:00.950 doesn't guarantee success by any means. 01:05:00.950 --> 01:05:05.720 So although that's a negative thing for poker, 01:05:05.720 --> 01:05:08.930 I'd like to end with what I call, "the joy of making 01:05:08.930 --> 01:05:10.670 good decisions." 01:05:10.670 --> 01:05:13.310 So even though not everyone makes it in poker, 01:05:13.310 --> 01:05:16.400 but poker players-- 01:05:16.400 --> 01:05:18.864 we like to talk about sort of, you're not really there. 01:05:18.864 --> 01:05:21.530 You shouldn't be trying to think about making money or whatever. 01:05:21.530 --> 01:05:23.960 You're sort of just there to enjoy the game, 01:05:23.960 --> 01:05:26.480 and have an honest opinion on your ability, 01:05:26.480 --> 01:05:29.031 and calibrate your confidence. 01:05:29.031 --> 01:05:31.280 I've told the Bill Gates/Doyle Brunson story but yeah, 01:05:31.280 --> 01:05:34.280 basically, Bill Gates, I think, was a pretty good poker 01:05:34.280 --> 01:05:36.970 player for quite a while. 01:05:36.970 --> 01:05:37.970 And he would make money. 01:05:37.970 --> 01:05:42.892 And clearly, it was not his best way to make money. 01:05:42.892 --> 01:05:45.350 He could probably just go to his company and make like $500 01:05:45.350 --> 01:05:48.480 a second or something like that. 01:05:48.480 --> 01:05:50.720 But when asked about it, Bill Gates would just say, 01:05:50.720 --> 01:05:53.000 I love making good decisions. 01:05:53.000 --> 01:05:55.420 I love thinking about this game and making decisions. 01:05:55.420 --> 01:05:58.040 And even though, clearly, the money means nothing to me, 01:05:58.040 --> 01:06:01.070 it's still important to me, as a personal goal, 01:06:01.070 --> 01:06:03.170 to succeed at this game and make money, 01:06:03.170 --> 01:06:05.460 even though it doesn't mean anything. 01:06:05.460 --> 01:06:07.910 So it's about this joy of making good decisions. 01:06:07.910 --> 01:06:10.670 And I think part of the reason Bill Gates was 01:06:10.670 --> 01:06:13.381 able to be quite good was because the money meant nothing 01:06:13.381 --> 01:06:13.880 to him. 01:06:13.880 --> 01:06:15.504 He didn't really care about his results 01:06:15.504 --> 01:06:17.240 and how much he made or lost, clearly. 01:06:17.240 --> 01:06:21.720 He just focused on making the best decisions. 01:06:21.720 --> 01:06:26.030 And so it is true that there's a decent amount of luck in poker 01:06:26.030 --> 01:06:30.790 but, yes, I would argue, life is luck, and you only live once-- 01:06:30.790 --> 01:06:32.630 there's all these sayings but, overall, 01:06:32.630 --> 01:06:35.720 the thing to keep in mind is, like Jennifer Shahade talked 01:06:35.720 --> 01:06:38.220 about this with the "Goldilocks" video-- 01:06:38.220 --> 01:06:41.170 so you want to think of your life and/or your poker career 01:06:41.170 --> 01:06:44.840 or whatever as one long session where you're just trying 01:06:44.840 --> 01:06:46.530 to make the best decisions. 01:06:46.530 --> 01:06:49.040 And even if you don't get the best results today, 01:06:49.040 --> 01:06:52.010 hope that you get better results throughout the course 01:06:52.010 --> 01:06:54.280 of your life. 01:06:54.280 --> 01:06:57.380 So yeah, that's the end of what I wanted 01:06:57.380 --> 01:07:00.590 to say about the general poker and what 01:07:00.590 --> 01:07:02.180 I hope you take away from this class 01:07:02.180 --> 01:07:06.860 from a non-mathematical, non-poker point of view. 01:07:06.860 --> 01:07:09.410 I guess there is a bit of time for questions. 01:07:09.410 --> 01:07:11.600 There's a lot of things I didn't talk about, 01:07:11.600 --> 01:07:16.050 but I'm happy to answer questions about. 01:07:16.050 --> 01:07:20.070 Yeah, I'm happy to answer any questions, now. 01:07:20.070 --> 01:07:22.082 Yeah? 01:07:22.082 --> 01:07:25.730 AUDIENCE: Now that there are no longer any class tournaments, 01:07:25.730 --> 01:07:28.710 where can I go to play to get better and improve? 01:07:32.740 --> 01:07:34.640 WILL MA: So there's an MIT poker club, 01:07:34.640 --> 01:07:37.000 and they run tournaments on PokerStars 01:07:37.000 --> 01:07:40.550 similar to the way the class works. 01:07:40.550 --> 01:07:42.920 The way you can get into the poker club 01:07:42.920 --> 01:07:46.250 is so [INAUDIBLE] is part of it. 01:07:46.250 --> 01:07:48.200 She's like one of the execs. 01:07:48.200 --> 01:07:49.550 Maybe you should ask her. 01:07:49.550 --> 01:07:50.300 Send her an email. 01:07:50.300 --> 01:07:51.487 I can ask her. 01:07:51.487 --> 01:07:53.570 I'll ask her, and I'll send something to the class 01:07:53.570 --> 01:07:55.570 if you guys are interested in continuing playing 01:07:55.570 --> 01:07:57.820 poker on PokerStars and-- 01:07:57.820 --> 01:08:01.310 yeah, so there's the MIT Poker Club. 01:08:01.310 --> 01:08:03.590 And I know in the past, sometimes 01:08:03.590 --> 01:08:06.860 the classes continued playing tournaments 01:08:06.860 --> 01:08:08.362 after the class is over. 01:08:08.362 --> 01:08:10.820 We would have like a tournament every Saturday or something 01:08:10.820 --> 01:08:13.150 for people to play, but I don't know if-- 01:08:13.150 --> 01:08:14.278 they didn't last very long. 01:08:14.278 --> 01:08:16.069 I think people quickly lost interest in it. 01:08:16.069 --> 01:08:18.020 But yeah, I think just the poker club. 01:08:18.020 --> 01:08:21.350 Actually, Martin, you're in the Poker Club, right? 01:08:21.350 --> 01:08:23.789 So maybe you can something to answer that question. 01:08:23.789 --> 01:08:26.957 AUDIENCE: So sometimes we have [INAUDIBLE] games where people 01:08:26.957 --> 01:08:29.840 can play like $0.25, $0.50 [INAUDIBLE].. 01:08:29.840 --> 01:08:34.880 So there's like a million you can get on. 01:08:34.880 --> 01:08:36.580 WILL MA: OK, I'll find some information 01:08:36.580 --> 01:08:37.930 from [INAUDIBLE] and Martin. 01:08:37.930 --> 01:08:39.100 I'll send something to the class, 01:08:39.100 --> 01:08:40.641 and I'll give you guys some pointers. 01:08:43.404 --> 01:08:44.779 AUDIENCE: How do you, personally, 01:08:44.779 --> 01:08:46.583 deal with downswing? 01:08:49.910 --> 01:08:51.950 WILL MA: Yeah, so definitely, I've 01:08:51.950 --> 01:08:54.340 gone through bad downswings and times 01:08:54.340 --> 01:08:56.620 where I really hated the game. 01:08:56.620 --> 01:08:58.390 I think I mostly just took a break. 01:08:58.390 --> 01:09:01.060 So yeah, I mostly just took a break. 01:09:04.660 --> 01:09:08.894 My first couple of downswings when I was first starting, 01:09:08.894 --> 01:09:10.810 I just took a break from the game for a while, 01:09:10.810 --> 01:09:13.720 like a month or something, and then came back. 01:09:13.720 --> 01:09:14.859 That's sort of what I did. 01:09:14.859 --> 01:09:19.454 Nowadays, I'd say like the last four years, I've been-- 01:09:19.454 --> 01:09:21.370 I'd like to think I was fairly good at dealing 01:09:21.370 --> 01:09:22.300 with downswings. 01:09:22.300 --> 01:09:24.580 I sort of went through enough downswings 01:09:24.580 --> 01:09:27.689 where I kind of was able to just keep it together through it 01:09:27.689 --> 01:09:28.439 for the most part. 01:09:28.439 --> 01:09:30.290 Like maybe I'd play slightly less, 01:09:30.290 --> 01:09:32.158 but I wouldn't quit altogether. 01:09:36.062 --> 01:09:39.405 AUDIENCE: So for small cash games online, what kind of edge 01:09:39.405 --> 01:09:40.864 do you think you have? 01:09:40.864 --> 01:09:41.700 WILL MA: For small? 01:09:41.700 --> 01:09:43.283 AUDIENCE: And then what kind of edge-- 01:09:43.283 --> 01:09:46.050 what is your like, borderline edge where it suddenly wouldn't 01:09:46.050 --> 01:09:47.472 become worth it anymore? 01:09:47.472 --> 01:09:52.390 WILL MA: Oh, so how much edge do I think I have? 01:09:52.390 --> 01:09:55.751 So in online cash games-- 01:09:55.751 --> 01:09:58.000 the thing is, I don't really specialize in cash games, 01:09:58.000 --> 01:10:00.320 so I never really play them. 01:10:00.320 --> 01:10:02.230 So I'd say it's probably very little. 01:10:02.230 --> 01:10:04.420 I mean, I'm sure I can find low enough stakes where 01:10:04.420 --> 01:10:05.770 I'll have a significant edge-- 01:10:05.770 --> 01:10:07.394 AUDIENCE: Or even in tournaments, then? 01:10:07.394 --> 01:10:08.990 Online small stakes tournaments? 01:10:08.990 --> 01:10:14.290 WILL MA: Yeah, yeah, so in tournaments, I'd 01:10:14.290 --> 01:10:19.960 say there's still a decent edge, and I'll play it for-- 01:10:19.960 --> 01:10:22.855 but mostly, I'd I'll play poker, mostly, for fun nowadays. 01:10:25.810 --> 01:10:30.850 I rarely force myself to do it for making money, I'd say. 01:10:30.850 --> 01:10:32.380 Most of the time I'm playing, I'm 01:10:32.380 --> 01:10:33.838 still trying to make good decisions 01:10:33.838 --> 01:10:35.950 because I enjoy doing that, but I'm not really 01:10:35.950 --> 01:10:40.126 doing it for the power degree or whatever. 01:10:40.126 --> 01:10:42.815 AUDIENCE: So what about maybe the best cash-game player 01:10:42.815 --> 01:10:45.863 in the world, how much would they make in about $0.25/$0.50 01:10:45.863 --> 01:10:46.362 online? 01:10:46.362 --> 01:10:50.620 WILL MA: Oh, $0.25/$0.50 online? 01:10:50.620 --> 01:10:53.230 So I don't have a great sense of this, but let me think. 01:10:55.910 --> 01:11:00.190 So the thing is, the players who are sort of considered the top 01:11:00.190 --> 01:11:03.400 players in the world who play like very high stakes-- 01:11:03.400 --> 01:11:06.820 like nosebleeds stakes with like $100/$200 big blinds 01:11:06.820 --> 01:11:07.950 or something-- 01:11:07.950 --> 01:11:10.090 it's sort of, the variance is so high 01:11:10.090 --> 01:11:12.290 that it's not really accepted who's 01:11:12.290 --> 01:11:14.590 the best because if it was accepted, you know, 01:11:14.590 --> 01:11:18.650 someone had a win rate over someone else, 01:11:18.650 --> 01:11:21.250 then the guy who was worse just wouldn't be playing. 01:11:21.250 --> 01:11:22.840 So the only reason those games run 01:11:22.840 --> 01:11:24.880 is because they all think they have a win rate. 01:11:24.880 --> 01:11:27.250 So it's hard for me to say the number 01:11:27.250 --> 01:11:28.870 because I'm not going to know better 01:11:28.870 --> 01:11:31.312 than what they're true win rates are against each other. 01:11:31.312 --> 01:11:33.520 And they're all going to tell me something different, 01:11:33.520 --> 01:11:36.430 because they all think they're beating the other guys. 01:11:36.430 --> 01:11:38.460 As far as how much a really top player 01:11:38.460 --> 01:11:42.457 can win at a low-stakes game, it's still 01:11:42.457 --> 01:11:43.720 going to be very significant. 01:11:43.720 --> 01:11:50.830 I think making something maybe like, five or six big blinds 01:11:50.830 --> 01:11:53.344 per 100. 01:11:53.344 --> 01:11:55.260 Yeah, five or six big blinds per 100, I think, 01:11:55.260 --> 01:11:57.550 is maybe doable at a reasonably low stakes-- 01:11:57.550 --> 01:11:59.230 if you're like one of the very best. 01:12:02.740 --> 01:12:03.570 It's quite a lot. 01:12:03.570 --> 01:12:04.510 It's quite generous. 01:12:04.510 --> 01:12:08.180 But let's say every 100 hands you make five big blinds. 01:12:08.180 --> 01:12:14.650 So let's say you play $0.25/$0.50, 01:12:14.650 --> 01:12:15.730 five big blinds is $250. 01:12:15.730 --> 01:12:17.610 You make that every 100 hands. 01:12:17.610 --> 01:12:22.660 If you play six tables, you can get in about 100 hands 01:12:22.660 --> 01:12:24.650 per hour, 120 hands per hour. 01:12:24.650 --> 01:12:27.040 So that's 600 hands per hour. 01:12:29.680 --> 01:12:32.680 So it's six times $250; so it's like $15. 01:12:32.680 --> 01:12:35.580 So it's not a lot, but I mean those guys can play stakes way 01:12:35.580 --> 01:12:38.950 higher than $0.25/$0.50 and still have a slightly smaller 01:12:38.950 --> 01:12:40.040 edge. 01:12:40.040 --> 01:12:46.480 So if you imagine they play 250/$5. 01:12:46.480 --> 01:12:49.739 Then suddenly, you multiply, then that'll give me about $10. 01:12:49.739 --> 01:12:52.030 I mean you would be decreasing it because they probably 01:12:52.030 --> 01:12:53.990 wouldn't make five big blinds per hour-- 01:12:53.990 --> 01:12:57.482 five big blinds per 100. 01:12:57.482 --> 01:12:59.690 But I think those numbers are ballpark correct, yeah. 01:13:04.650 --> 01:13:05.642 All right, yeah? 01:13:05.642 --> 01:13:08.122 AUDIENCE: What's a good for playing at a casino, 01:13:08.122 --> 01:13:09.479 like exploiting people? 01:13:09.479 --> 01:13:11.770 WILL MA: What's a good strategy for playing at a casino 01:13:11.770 --> 01:13:12.686 and exploiting people? 01:13:19.270 --> 01:13:22.560 One general thing that's going to do is, you go there-- 01:13:22.560 --> 01:13:27.250 you sleep at night, and you go there at like 7:00 AM and play 01:13:27.250 --> 01:13:30.003 against people who have been tilted and angry for-- 01:13:30.003 --> 01:13:30.950 [LAUGHTER] 01:13:30.950 --> 01:13:33.360 And you just woke up at 7 AM in the morning. 01:13:33.360 --> 01:13:36.730 And you're in such a good mood, and they're all in a bad mood, 01:13:36.730 --> 01:13:39.310 and you can win a lot of money. 01:13:39.310 --> 01:13:42.700 In terms of specific strategy, I think 01:13:42.700 --> 01:13:44.650 it depends a lot on the player. 01:13:44.650 --> 01:13:48.130 I think, in general, playing tight is pretty good. 01:13:48.130 --> 01:13:49.660 At least I'd say I consider myself, 01:13:49.660 --> 01:13:51.340 in general, a tight player, and I 01:13:51.340 --> 01:13:54.160 think a decent amount of money can 01:13:54.160 --> 01:13:56.470 be made at casinos against recreational players 01:13:56.470 --> 01:13:58.990 just by them getting bored. 01:13:58.990 --> 01:14:01.950 Like at a nine-headed table, you're only paying the blinds-- 01:14:01.950 --> 01:14:04.570 1 and 1/2 blinds every nine hands. 01:14:04.570 --> 01:14:06.220 You can easily get away with only 01:14:06.220 --> 01:14:09.380 playing like pocket nines plus, ace-queen plus. 01:14:09.380 --> 01:14:13.104 I mean, that's extreme, but they'll probably still call you 01:14:13.104 --> 01:14:14.020 because they're bored. 01:14:14.020 --> 01:14:16.080 They're not going to think like, this guy's-- 01:14:16.080 --> 01:14:17.390 I'm going to just fold-- 01:14:17.390 --> 01:14:19.120 so one disadvantage of that strategy 01:14:19.120 --> 01:14:20.680 is, they're just always going to fold to you. 01:14:20.680 --> 01:14:22.805 But in practice, I don't think that's what happens. 01:14:22.805 --> 01:14:26.650 So I think, in general, playing tight 01:14:26.650 --> 01:14:29.660 will always be a pretty good strategy at casinos 01:14:29.660 --> 01:14:33.525 against recreational players. 01:14:33.525 --> 01:14:35.004 AUDIENCE: Yeah? 01:14:35.004 --> 01:14:39.400 Do you have any advice for avoiding 01:14:39.400 --> 01:14:46.160 this pitfall of thinking you're good and you're not actually? 01:14:46.160 --> 01:14:48.790 WILL MA: Not really, because I think it's happened to me 01:14:48.790 --> 01:14:50.140 a lot of times. 01:14:54.490 --> 01:14:59.055 Yeah, I think it really is hard to judge, especially 01:14:59.055 --> 01:14:59.680 in tournaments. 01:14:59.680 --> 01:15:01.450 In cash games, it's slightly easier 01:15:01.450 --> 01:15:04.630 to judge because you can just look at your data points, 01:15:04.630 --> 01:15:06.580 and it'll converge faster. 01:15:06.580 --> 01:15:09.220 In tournaments, the variance is so high you can't really 01:15:09.220 --> 01:15:10.654 use your tournament results. 01:15:10.654 --> 01:15:12.820 I think the most important thing, for me personally, 01:15:12.820 --> 01:15:17.050 was just talking to players and having very honest friends who 01:15:17.050 --> 01:15:20.110 would tell me if they thought I was worse than someone else 01:15:20.110 --> 01:15:21.570 and tell them not to play them. 01:15:21.570 --> 01:15:23.320 And I think that's probably the thing that 01:15:23.320 --> 01:15:26.410 benefited me the most-- just being able to talk to players 01:15:26.410 --> 01:15:29.320 better than me or at a similar level to me 01:15:29.320 --> 01:15:33.070 and just getting their opinion from them talking to me. 01:15:33.070 --> 01:15:36.170 If they think I'm not good enough, I want them to tell me. 01:15:36.170 --> 01:15:39.940 And I think that's one of the most important things is just 01:15:39.940 --> 01:15:44.714 getting good feedback from your friends and honest feedback. 01:15:44.714 --> 01:15:45.540 Yeah? 01:15:45.540 --> 01:15:48.760 AUDIENCE: Since we can't play online here, 01:15:48.760 --> 01:15:51.937 and we can't do it at the casino like every weekend-- 01:15:51.937 --> 01:15:54.270 so we can't play for money-- what's some good motivation 01:15:54.270 --> 01:15:57.817 to keep the Saturday game? 01:15:57.817 --> 01:15:59.650 Is this like poker mentality, and these kids 01:15:59.650 --> 01:16:02.100 will have development in whatever they 01:16:02.100 --> 01:16:04.330 like [INAUDIBLE] jobs? 01:16:04.330 --> 01:16:06.080 WILL MA: OK, so I'll address a few things. 01:16:06.080 --> 01:16:08.150 So one thing that I didn't really formally announce-- 01:16:08.150 --> 01:16:09.733 but yeah, so one thing you pointed out 01:16:09.733 --> 01:16:11.800 is, playing online poker for money 01:16:11.800 --> 01:16:13.750 is illegal in Massachusetts. 01:16:19.720 --> 01:16:22.210 The police can't come arrest you, 01:16:22.210 --> 01:16:25.135 but the website will take all your money 01:16:25.135 --> 01:16:27.260 if they find out you're playing from Massachusetts. 01:16:27.260 --> 01:16:30.030 But I don't believe it's written in Massachusetts 01:16:30.030 --> 01:16:31.650 law or something. 01:16:31.650 --> 01:16:34.050 To my knowledge, the police can't arrest you. 01:16:34.050 --> 01:16:36.880 But yeah, so the question was, if we can't play online, 01:16:36.880 --> 01:16:38.380 what can we do? 01:16:38.380 --> 01:16:41.600 So I think it is legal in New Jersey and Nevada. 01:16:41.600 --> 01:16:43.640 So you can move to New Jersey or Nevada. 01:16:46.300 --> 01:16:48.770 OK, yeah, so if you don't want to go to the casino 01:16:48.770 --> 01:16:51.506 every weekend, so what else can you do? 01:16:51.506 --> 01:16:53.380 OK, so what's the motivation to keep playing? 01:16:53.380 --> 01:16:55.480 So I think I've tried in this class 01:16:55.480 --> 01:16:58.510 to give examples of where I think 01:16:58.510 --> 01:17:05.410 poker is very useful, just in terms of how poker is related 01:17:05.410 --> 01:17:09.190 to nonpoker stuff, like calibrating your confidence, 01:17:09.190 --> 01:17:11.680 figuring out what your biases are, and stuff like that. 01:17:11.680 --> 01:17:13.170 And I also think it's a fun game. 01:17:13.170 --> 01:17:15.120 It's a very fun game. 01:17:15.120 --> 01:17:16.660 It's mathematically interesting. 01:17:16.660 --> 01:17:20.100 But yeah, I mean, if you don't enjoy playing the game much, 01:17:20.100 --> 01:17:23.100 and sense you can't really make money playing it 01:17:23.100 --> 01:17:25.536 in Massachusetts, yeah, then, if both of those are true, 01:17:25.536 --> 01:17:26.910 then there's not that much reason 01:17:26.910 --> 01:17:28.600 to play it if you don't enjoy it. 01:17:28.600 --> 01:17:30.183 I think that's just the biggest thing. 01:17:30.183 --> 01:17:32.720 If you enjoy it and you enjoy the decision-making, 01:17:32.720 --> 01:17:35.843 I think it's very fun, and it's also very good for you. 01:17:35.843 --> 01:17:37.322 AUDIENCE: Thank you. 01:17:40.280 --> 01:17:43.367 WILL MA: All right, cool. 01:17:43.367 --> 01:17:44.950 Yeah, so if there's no more questions, 01:17:44.950 --> 01:17:50.230 then I guess we'll call it here, and then Friday 01:17:50.230 --> 01:17:51.650 will be the last class. 01:17:51.650 --> 01:17:53.483 There's two more nights of tournaments left. 01:17:53.483 --> 01:17:55.960 And yeah, I'm excited for Friday for Bill's lecture 01:17:55.960 --> 01:17:58.310 and to hand out the prizes.