WEBVTT 00:00:01.550 --> 00:00:03.920 The following content is provided under a Creative 00:00:03.920 --> 00:00:05.310 Commons license. 00:00:05.310 --> 00:00:07.520 Your support will help MIT OpenCourseWare 00:00:07.520 --> 00:00:11.610 continue to offer high quality educational resources for free. 00:00:11.610 --> 00:00:14.180 To make a donation or to view additional materials 00:00:14.180 --> 00:00:18.140 from hundreds of MIT courses, visit MIT OpenCourseWare 00:00:18.140 --> 00:00:19.026 at ocw.mit.edu. 00:00:22.140 --> 00:00:27.390 INSTRUCTOR: So today, we start on project 4, which is, 00:00:27.390 --> 00:00:29.640 as you know, the big project. 00:00:29.640 --> 00:00:35.430 And Helen is going to do a walkthrough of the project, 00:00:35.430 --> 00:00:37.920 and the code, and the organization, 00:00:37.920 --> 00:00:41.400 because this is a pretty big sized project. 00:00:41.400 --> 00:00:44.400 It's got about 4,500 lines of code. 00:00:44.400 --> 00:00:50.460 And it's not code that is kind of like simple code. 00:00:50.460 --> 00:00:53.070 It's all content-bearing code. 00:00:53.070 --> 00:00:57.630 So I think having a bit of an orientation to it, 00:00:57.630 --> 00:00:59.910 more than we give for the other codes that you work, 00:00:59.910 --> 00:01:03.670 on which are pretty small, this will be great. 00:01:03.670 --> 00:01:05.650 So, Helen, take it away. 00:01:05.650 --> 00:01:07.900 HELEN XU: Hi, everyone. 00:01:07.900 --> 00:01:09.445 Can you hear me? 00:01:09.445 --> 00:01:11.820 Awesome, so today we're going to be doing the walkthrough 00:01:11.820 --> 00:01:12.750 for the final project. 00:01:12.750 --> 00:01:16.050 You can look at the code and clone it publicly here. 00:01:16.050 --> 00:01:19.110 And please remember to fill up your team's by 7:00 PM today, 00:01:19.110 --> 00:01:23.380 so we can populate the list and get your repos. 00:01:23.380 --> 00:01:25.530 Yeah, and if there are any issues accessing this, 00:01:25.530 --> 00:01:26.800 just let me know. 00:01:26.800 --> 00:01:30.570 Or put it on Piazza and then we can fix it. 00:01:30.570 --> 00:01:33.270 So we just had a game of Lesierchess. 00:01:33.270 --> 00:01:34.860 But in case you missed it, we'll go 00:01:34.860 --> 00:01:37.630 into more details about what the game actually does. 00:01:37.630 --> 00:01:40.290 So first, we're going to go through the game rules. 00:01:40.290 --> 00:01:42.960 So you saw that there are these pieces. 00:01:42.960 --> 00:01:44.030 There's these triangles. 00:01:44.030 --> 00:01:44.780 And there's kings. 00:01:44.780 --> 00:01:46.440 So the triangles are pawns. 00:01:46.440 --> 00:01:48.320 And the kings, they look like crowns. 00:01:48.320 --> 00:01:49.320 And there are two teams. 00:01:49.320 --> 00:01:52.050 There's orange and lavender, or tangerine and lavender. 00:01:52.050 --> 00:01:55.830 And each side starts out with seven pawns and one king. 00:01:55.830 --> 00:01:57.280 And this is the starting position. 00:01:57.280 --> 00:01:59.280 So you can see like the kings are in the corner. 00:01:59.280 --> 00:02:02.040 And they're just lined up like in the middle. 00:02:02.040 --> 00:02:04.600 And each piece has four orientations. 00:02:04.600 --> 00:02:09.880 So you can see that the pawn is up, down, left, right. 00:02:09.880 --> 00:02:12.510 And then the king is also like that. 00:02:12.510 --> 00:02:18.600 And in general, the game starts with tangerine moving first. 00:02:18.600 --> 00:02:21.090 And then the play alternates between the two players. 00:02:21.090 --> 00:02:23.613 Each piece moves the same, whether it's king or pawn. 00:02:23.613 --> 00:02:24.780 And each turn has two parts. 00:02:24.780 --> 00:02:26.050 So you saw the demo. 00:02:26.050 --> 00:02:27.582 But you move first. 00:02:27.582 --> 00:02:29.790 When you pick one of your pieces, and you move first. 00:02:29.790 --> 00:02:32.850 And then at the end, your King has to fire the laser. 00:02:32.850 --> 00:02:35.280 And the laser reflects off the long edge of the pawn. 00:02:35.280 --> 00:02:38.220 And they'll kill the pawn if it shoots the short edges. 00:02:38.220 --> 00:02:40.470 And one side wins when the king gets shot, 00:02:40.470 --> 00:02:43.800 or when the opposing king gets shot, whether by themselves 00:02:43.800 --> 00:02:47.107 or by your own king. 00:02:47.107 --> 00:02:48.690 And so I talked a little about moving. 00:02:48.690 --> 00:02:51.510 And at the beginning of each turn, the player to move 00:02:51.510 --> 00:02:53.340 chooses a piece to move. 00:02:53.340 --> 00:02:55.475 And you can move your King or any of your pawns. 00:02:55.475 --> 00:02:56.850 And there are two types of moves. 00:02:56.850 --> 00:03:00.210 There's basic moves, and swat moves. 00:03:00.210 --> 00:03:03.720 And basic moves are just, basically, shifts or rotations. 00:03:03.720 --> 00:03:07.990 So in the example, you can rotate 90, 180, or 270 degrees. 00:03:07.990 --> 00:03:10.340 So in the top, row you just rotate. 00:03:10.340 --> 00:03:11.920 This is the example of moving a pawn. 00:03:11.920 --> 00:03:13.290 So you rotate your pawn. 00:03:13.290 --> 00:03:15.390 Or you can move to an empty adjacent square. 00:03:15.390 --> 00:03:16.800 So those are the bottom two rows. 00:03:16.800 --> 00:03:19.300 And there are eight adjacent squares in this example. 00:03:19.300 --> 00:03:20.513 So there are eight shifts. 00:03:20.513 --> 00:03:21.930 But there would be less than eight 00:03:21.930 --> 00:03:26.130 if you were, for example, like at the edge of the board. 00:03:26.130 --> 00:03:29.203 And on a move, you can either shift or rotate. 00:03:29.203 --> 00:03:30.120 But you can't do both. 00:03:32.840 --> 00:03:34.500 There are also these swap loops. 00:03:34.500 --> 00:03:38.668 So if you're adjacent to an opposing piece, 00:03:38.668 --> 00:03:39.710 you can switch with them. 00:03:39.710 --> 00:03:41.543 And then you have to make another basic move 00:03:41.543 --> 00:03:43.190 after that, that is not a swap. 00:03:43.190 --> 00:03:45.518 So, basically, you can either-- 00:03:45.518 --> 00:03:47.060 and it has to be with that same piece 00:03:47.060 --> 00:03:48.200 that you just swapped with. 00:03:48.200 --> 00:03:51.380 So you just either shift or rotate. 00:03:51.380 --> 00:03:52.630 Is everyone good on the rules? 00:03:56.570 --> 00:03:58.040 Just a couple more things. 00:03:58.040 --> 00:03:59.600 So there's this Ko rule, which is 00:03:59.600 --> 00:04:02.240 from Go, which ensures that the game makes progress. 00:04:02.240 --> 00:04:06.258 So it makes a move illegal if it undoes the opponent's most 00:04:06.258 --> 00:04:08.550 recent move by just moving back to where you just were. 00:04:11.223 --> 00:04:12.140 So this is an example. 00:04:12.140 --> 00:04:13.820 Let's say you're tangerine. 00:04:13.820 --> 00:04:16.070 And you swapped with the purple one right next to you. 00:04:16.070 --> 00:04:21.740 And then you shifted left and bottom. 00:04:21.740 --> 00:04:26.360 And so lavender can return by swapping back 00:04:26.360 --> 00:04:29.930 with your orange piece, and shifting again. 00:04:29.930 --> 00:04:32.180 But this is actually, illegal because now 00:04:32.180 --> 00:04:34.880 you just got to your original position. 00:04:34.880 --> 00:04:37.520 So you're not allowed to just keep cycling back and forth. 00:04:41.520 --> 00:04:44.850 And so a draw occurs if there have been 50 moves by each side 00:04:44.850 --> 00:04:47.730 without a pawn being zapped, the same position 00:04:47.730 --> 00:04:49.632 repeats itself by the side on move, 00:04:49.632 --> 00:04:51.090 or the two players agree to a draw. 00:04:56.140 --> 00:04:58.040 So just kind of like in chess, a chess clock 00:04:58.040 --> 00:05:00.457 limits the amount of time the players have to make a move. 00:05:00.457 --> 00:05:02.500 So you can't just keep competing indefinitely. 00:05:02.500 --> 00:05:04.810 When it's your moves, your clock counts down. 00:05:04.810 --> 00:05:07.780 When it's your opponent's moves, your clock stops. 00:05:07.780 --> 00:05:09.097 So it's not counting your time. 00:05:09.097 --> 00:05:10.430 And we used Fisher time control. 00:05:10.430 --> 00:05:12.013 There's a picture of Bobby Fisher, who 00:05:12.013 --> 00:05:15.970 made it, up which used an initial time budget and a time 00:05:15.970 --> 00:05:16.600 increment. 00:05:16.600 --> 00:05:20.212 So in this example, there's fis60 and 0.5, 00:05:20.212 --> 00:05:21.670 which means that, in the beginning, 00:05:21.670 --> 00:05:23.840 each player has 60 seconds. 00:05:23.840 --> 00:05:26.050 And you get to use the 60 seconds however you want. 00:05:26.050 --> 00:05:30.520 And when you end your move, you get 0.5 extra seconds. 00:05:30.520 --> 00:05:34.152 But the 60 and 0.5 could be anything. 00:05:34.152 --> 00:05:35.110 That's just an example. 00:05:38.572 --> 00:05:40.530 So we'll go into an example of how you actually 00:05:40.530 --> 00:05:41.520 play this game. 00:05:41.520 --> 00:05:43.290 For a king to zap the enemy king, 00:05:43.290 --> 00:05:46.020 it risks opening itself to counter-attack. 00:05:46.020 --> 00:05:47.730 So look at this example. 00:05:47.730 --> 00:05:51.370 And how can tangerine zap the lavender pawn in F5, 00:05:51.370 --> 00:05:52.650 by moving one of its pieces? 00:06:03.430 --> 00:06:05.140 AUDIENCE: [INAUDIBLE] 00:06:06.800 --> 00:06:07.550 HELEN XU: Move C4. 00:06:11.410 --> 00:06:13.690 AUDIENCE: Tangerine, that's lavender. 00:06:13.690 --> 00:06:16.440 HELEN XU: You're tangerine in this example. 00:06:16.440 --> 00:06:18.580 And you're trying to zap the one on F5. 00:06:26.060 --> 00:06:27.990 Yep? 00:06:27.990 --> 00:06:33.290 AUDIENCE: You move the tangerine piece at E22 to F1. 00:06:33.290 --> 00:06:34.235 HELEN XU: E2 to F1. 00:06:41.120 --> 00:06:43.500 Oh, sorry, by zap, it means shoot the backside. 00:06:46.290 --> 00:06:49.960 That would shoot the long side. 00:06:49.960 --> 00:06:52.450 Good point. 00:06:52.450 --> 00:06:56.348 Yeah, so you're trying to kill the piece on F5. 00:06:56.348 --> 00:06:59.330 AUDIENCE: [INAUDIBLE] 00:06:59.330 --> 00:07:01.060 HELEN XU: Yeah, exactly. 00:07:01.060 --> 00:07:07.090 So in this, you can move C2 to B1, as you just said. 00:07:07.090 --> 00:07:09.210 And then you draw the path. 00:07:09.210 --> 00:07:14.190 And you can see that you've just killed-- 00:07:14.190 --> 00:07:17.460 or if you're tangerine, you've just killed the piece at F5. 00:07:17.460 --> 00:07:18.930 Now, how can lavender counter? 00:07:18.930 --> 00:07:21.660 By counter, we mean lavender can win 00:07:21.660 --> 00:07:22.860 the game from this position. 00:07:29.210 --> 00:07:30.875 AUDIENCE: Is it A4 to A3? 00:07:35.460 --> 00:07:36.280 HELEN XU: A4 to A3. 00:07:40.680 --> 00:07:42.570 No, I don't think so. 00:07:42.570 --> 00:07:43.706 Yep? 00:07:43.706 --> 00:07:46.580 AUDIENCE: [INAUDIBLE] 00:07:46.580 --> 00:07:48.640 HELEN XU: Sorry, what? 00:07:48.640 --> 00:07:52.135 King, like the orange one? 00:07:52.135 --> 00:07:53.010 Oh, the lavender one. 00:07:57.120 --> 00:07:59.030 You're trying to shoot the orange king. 00:08:02.720 --> 00:08:05.190 Oh, yes, you're right. 00:08:05.190 --> 00:08:08.180 You can, actually. 00:08:08.180 --> 00:08:10.490 Yes, good, that's not the one that we had, 00:08:10.490 --> 00:08:13.080 but apparently there are two ways. 00:08:13.080 --> 00:08:14.540 Good. 00:08:14.540 --> 00:08:16.060 So if you notice you could also-- 00:08:16.060 --> 00:08:17.360 that's another way to get that path. 00:08:17.360 --> 00:08:18.985 But you can also move one of the pawns. 00:08:21.570 --> 00:08:26.830 Cool, so this is just pointing out 00:08:26.830 --> 00:08:29.440 one of the subtleties of the game, which is you 00:08:29.440 --> 00:08:33.309 should watch out for just naively killing 00:08:33.309 --> 00:08:35.559 all the pieces you can, because that might open you up 00:08:35.559 --> 00:08:39.520 to the opponent. 00:08:39.520 --> 00:08:41.159 Yeah? 00:08:41.159 --> 00:08:42.890 AUDIENCE: [INAUDIBLE] 00:08:42.890 --> 00:08:45.233 HELEN XU: Yes, it can be from any direction. 00:08:45.233 --> 00:08:46.900 But the pawns only die if you shoot them 00:08:46.900 --> 00:08:48.570 from not on the long edge. 00:08:48.570 --> 00:08:49.450 Yep? 00:08:49.450 --> 00:08:52.750 AUDIENCE: What if you shoot your own block? 00:08:52.750 --> 00:08:54.550 HELEN XU: By block, you mean your own pawn? 00:08:54.550 --> 00:08:55.120 AUDIENCE: Yeah. 00:08:55.120 --> 00:08:55.995 HELEN XU: You'll die. 00:08:55.995 --> 00:08:57.435 AUDIENCE: Oh. 00:08:57.435 --> 00:08:58.060 HELEN XU: Yeah? 00:09:00.590 --> 00:09:02.238 AUDIENCE: [INAUDIBLE] 00:09:07.000 --> 00:09:09.880 HELEN XU: Yes, but only one piece can be on each square. 00:09:09.880 --> 00:09:13.450 But you can have as many near you. 00:09:13.450 --> 00:09:16.120 But do you have a question? 00:09:16.120 --> 00:09:20.120 AUDIENCE: Can you make it impossible to kill your person? 00:09:20.120 --> 00:09:21.990 HELEN XU: Like your King? 00:09:21.990 --> 00:09:24.510 Like if you barricaded it by pawns. 00:09:24.510 --> 00:09:27.080 But then the opponent can come in and swap with them, 00:09:27.080 --> 00:09:30.990 so it will open your barricade. 00:09:30.990 --> 00:09:33.610 AUDIENCE: Can the purple king shoot upward? 00:09:33.610 --> 00:09:35.018 HELEN XU: If it wanted to. 00:09:35.018 --> 00:09:37.435 But then in this example, it would shoot up off the board, 00:09:37.435 --> 00:09:38.477 and nothing would happen. 00:09:38.477 --> 00:09:39.703 Yeah? 00:09:39.703 --> 00:09:41.620 AUDIENCE: When you kill a pawn, does the laser 00:09:41.620 --> 00:09:44.427 stop at the place where the pawn is or does it 00:09:44.427 --> 00:09:45.260 go through the pawn? 00:09:45.260 --> 00:09:49.110 HELEN XU: No, it just shoots one. 00:09:49.110 --> 00:09:52.445 Good questions. 00:09:52.445 --> 00:09:53.320 Everyone good so far? 00:09:56.550 --> 00:09:57.690 OK, great. 00:09:57.690 --> 00:10:00.330 PROFESSOR: This year, it shoots only one. 00:10:00.330 --> 00:10:03.854 Last year, it kept shooting. 00:10:03.854 --> 00:10:05.967 AUDIENCE: Can the king shoot itself? 00:10:05.967 --> 00:10:06.550 HELEN XU: Yes. 00:10:09.330 --> 00:10:10.788 It should try not to, but it can. 00:10:10.788 --> 00:10:11.830 So you should be careful. 00:10:21.890 --> 00:10:26.150 So moving on-- we use force Fosythe-Edwards Notation, 00:10:26.150 --> 00:10:30.290 which is a representation of a chess position using a string. 00:10:30.290 --> 00:10:33.860 So you can see an example of the starting position. 00:10:33.860 --> 00:10:35.888 And the bottom includes the string 00:10:35.888 --> 00:10:37.430 that describes the starting position. 00:10:40.610 --> 00:10:42.670 If you look at the representation, 00:10:42.670 --> 00:10:45.310 the arrow corresponds to one of the rows. 00:10:45.310 --> 00:10:50.860 And that points to the substring that has a bubble over it. 00:10:50.860 --> 00:10:55.360 So in this row, there is one purple pawn at B3, 00:10:55.360 --> 00:10:59.470 and two orange ones at F3 and G3. 00:10:59.470 --> 00:11:01.170 So this is row three. 00:11:01.170 --> 00:11:04.090 And the slashes separate the rows in the string. 00:11:04.090 --> 00:11:06.190 And the one represents there's an empty space. 00:11:06.190 --> 00:11:07.990 And then there's a pawn facing southeast. 00:11:07.990 --> 00:11:10.690 And then there's three empty spaces, and one facing 00:11:10.690 --> 00:11:13.090 northwest, and then one facing southeast, and then 00:11:13.090 --> 00:11:14.806 an empty space. 00:11:14.806 --> 00:11:16.740 AUDIENCE: [INAUDIBLE] 00:11:16.740 --> 00:11:19.382 HELEN XU: Oh, yeah, it's animated. 00:11:25.990 --> 00:11:26.890 What do you mean? 00:11:30.710 --> 00:11:34.560 Yeah, so at the end of the string, there's also a-- 00:11:34.560 --> 00:11:37.547 it just tells you which side's move it is. 00:11:37.547 --> 00:11:38.880 So this is the opening position. 00:11:38.880 --> 00:11:42.550 But you can use any position in this notation. 00:11:42.550 --> 00:11:44.010 And this is useful for debugging, 00:11:44.010 --> 00:11:46.110 because if you, for example, you're running a bot, 00:11:46.110 --> 00:11:47.527 and it crashes at some position. 00:11:47.527 --> 00:11:49.110 And you can get back to that position. 00:11:49.110 --> 00:11:50.250 You can start up the game and just 00:11:50.250 --> 00:11:52.708 go there without having to make all the moves to get there. 00:11:59.783 --> 00:12:01.450 And this is how you represent the games. 00:12:01.450 --> 00:12:03.760 So each of these is one move. 00:12:03.760 --> 00:12:07.330 And the left column is tangerine. 00:12:07.330 --> 00:12:10.780 And the right column is lavender. 00:12:10.780 --> 00:12:13.090 And an example, you can see E6, E7, 00:12:13.090 --> 00:12:17.340 means they moved a piece from E6 to E7. 00:12:17.340 --> 00:12:22.390 B3L, so you rotated the piece on B3 left. 00:12:22.390 --> 00:12:25.780 There's D5, E4, F5, which means that you swapped. 00:12:25.780 --> 00:12:28.180 So your original piece was on D5. 00:12:28.180 --> 00:12:29.590 You swapped with the one at E4. 00:12:29.590 --> 00:12:33.130 And now you moved that piece to F5. 00:12:33.130 --> 00:12:36.240 So the one that was E4 is now on F5. 00:12:36.240 --> 00:12:39.070 And the opposing piece is now on D5, because you swapped. 00:12:41.900 --> 00:12:43.490 You can swap and then rotate. 00:12:43.490 --> 00:12:46.160 So instead of just having a third square, 00:12:46.160 --> 00:12:48.620 you would just have a rotation. 00:12:48.620 --> 00:12:50.280 And at the end, you could see who won. 00:12:50.280 --> 00:12:53.560 So in this one, lavender one because it's 0-1. 00:12:53.560 --> 00:12:55.393 But 1-0 would mean tangerine wins. 00:12:55.393 --> 00:12:56.810 And half and half would be a draw. 00:12:59.660 --> 00:13:02.450 So you can look at the logs for your games. 00:13:02.450 --> 00:13:03.189 Yes? 00:13:03.189 --> 00:13:05.145 AUDIENCE: [INAUDIBLE] 00:13:07.983 --> 00:13:09.900 HELEN XU: There's a rotate up and rotate down. 00:13:12.545 --> 00:13:15.300 AUDIENCE: [INAUDIBLE] do a U-turn? 00:13:15.300 --> 00:13:16.800 HELEN XU: Oh, is that what U is? 00:13:16.800 --> 00:13:19.405 AUDIENCE: Yeah, U-turn. 00:13:19.405 --> 00:13:21.780 HELEN XU: Oh I, see because there's only three rotations. 00:13:21.780 --> 00:13:24.200 Yes, sorry, so left is 90. 00:13:24.200 --> 00:13:25.320 Then right is 270. 00:13:25.320 --> 00:13:27.680 And U is 180, because you flip it. 00:13:34.420 --> 00:13:36.193 Is everyone good on the notation? 00:13:36.193 --> 00:13:37.860 This is just how you describe the games, 00:13:37.860 --> 00:13:39.318 if you wanted to look at your logs, 00:13:39.318 --> 00:13:40.620 and if there are some issues. 00:13:43.758 --> 00:13:46.050 So you can test your bot with other teams in the class, 00:13:46.050 --> 00:13:48.420 as well as with staff bots on the scrimmage server. 00:13:48.420 --> 00:13:51.900 And we have a reference, which is here, which 00:13:51.900 --> 00:13:53.820 is just the additional release. 00:13:53.820 --> 00:13:56.595 But we will be optimizing our bots while we're 00:13:56.595 --> 00:13:57.470 optimizing your bots. 00:13:57.470 --> 00:13:59.970 And we'll release a reference plus, and maybe an even better 00:13:59.970 --> 00:14:02.680 one later, which you can play with on the scrimmage sever. 00:14:02.680 --> 00:14:04.930 So I'll just do a really quick demo. 00:14:04.930 --> 00:14:09.030 So right now, since we haven't done the team formation yet, 00:14:09.030 --> 00:14:10.905 you are not able to log into this. 00:14:10.905 --> 00:14:12.780 But once you do your team formation, probably 00:14:12.780 --> 00:14:15.000 by tomorrow, you'll be able to log in. 00:14:15.000 --> 00:14:17.260 And, basically, you can see the general functionality. 00:14:17.260 --> 00:14:19.680 So this updates your player, pulls your player 00:14:19.680 --> 00:14:23.380 from your repo, whatever's on the master branch. 00:14:23.380 --> 00:14:26.160 And then right now, there's only reference, 00:14:26.160 --> 00:14:28.310 and reference plus, and reference TAs. 00:14:28.310 --> 00:14:30.480 And here's a team with me and Jess. 00:14:30.480 --> 00:14:33.030 But later on, we'll populate this list 00:14:33.030 --> 00:14:34.180 with everyone in the class. 00:14:34.180 --> 00:14:35.310 And then you can challenge anybody else 00:14:35.310 --> 00:14:36.910 in the class to see how you do. 00:14:36.910 --> 00:14:38.740 You can also challenge us. 00:14:38.740 --> 00:14:41.080 So you would just pick, for example, 00:14:41.080 --> 00:14:43.020 let's say I wanted to challenge reference. 00:14:43.020 --> 00:14:45.300 And then a hit send challenge. 00:14:45.300 --> 00:14:48.220 Now, you can see that there's some new matches spawned. 00:14:48.220 --> 00:14:51.030 And this is how I look at all the matches that I've played. 00:14:51.030 --> 00:14:52.793 So each time you hit send challenge, 00:14:52.793 --> 00:14:54.960 it spawns off two games, one where you're tangerine, 00:14:54.960 --> 00:14:55.960 and one you're lavender. 00:14:58.270 --> 00:15:00.660 So that's how you can watch the matches on the scrimmage 00:15:00.660 --> 00:15:01.160 server. 00:15:03.467 --> 00:15:04.050 Everyone good? 00:15:11.683 --> 00:15:13.600 I'm going to move on so don't run out of town. 00:15:16.120 --> 00:15:18.500 You can watch them later. 00:15:18.500 --> 00:15:19.840 And you can even play your own. 00:15:30.270 --> 00:15:30.770 OK. 00:15:34.120 --> 00:15:35.870 And, in addition to the scrimmage server-- 00:15:35.870 --> 00:15:36.860 so the scrimmage server, you can only 00:15:36.860 --> 00:15:38.068 spawn off one game at a time. 00:15:38.068 --> 00:15:39.140 But you can do more. 00:15:39.140 --> 00:15:42.290 And you don't have to necessarily do it 00:15:42.290 --> 00:15:45.290 on your master branch, or against opposing teams 00:15:45.290 --> 00:15:46.160 in the class. 00:15:46.160 --> 00:15:48.860 So there's something called the Cloud autotester, which you can 00:15:48.860 --> 00:15:50.443 run by going to your Athena. 00:15:50.443 --> 00:15:51.860 And then you type in this command. 00:15:51.860 --> 00:15:52.970 You do autotest run. 00:15:52.970 --> 00:15:55.388 And then you do the time control. 00:15:55.388 --> 00:15:57.680 And you give it a number of games that you want to run. 00:15:57.680 --> 00:15:59.630 And then you give it a list of binaries. 00:15:59.630 --> 00:16:01.590 So I'll go into each of these in more detail. 00:16:01.590 --> 00:16:04.490 So the time control is just what I talked about earlier, which 00:16:04.490 --> 00:16:07.550 is if you use Fisher time control, these are some set, 00:16:07.550 --> 00:16:08.510 preset things. 00:16:08.510 --> 00:16:10.427 So you would type in one of the preset things. 00:16:10.427 --> 00:16:14.630 So you would talk in blitz to do 60 and 0.5, for example. 00:16:14.630 --> 00:16:17.780 And the number of games is just whatever you want to do. 00:16:17.780 --> 00:16:19.310 And the list of binaries-- so let's 00:16:19.310 --> 00:16:21.800 say you had a reference invalidation, 00:16:21.800 --> 00:16:23.120 and then you made some change. 00:16:23.120 --> 00:16:25.670 So I called it Lesierchess with changes. 00:16:25.670 --> 00:16:27.800 And then you would just put those 00:16:27.800 --> 00:16:30.165 after the number of games, separated by spaces. 00:16:30.165 --> 00:16:31.790 And then it would upload your binaries, 00:16:31.790 --> 00:16:34.130 and play them in the cloud auto tester. 00:16:34.130 --> 00:16:37.520 And once you submit your job, you get a link. 00:16:37.520 --> 00:16:39.200 And you follow the link in your browser. 00:16:39.200 --> 00:16:40.993 And you can view the game running. 00:16:40.993 --> 00:16:42.410 And then after the games are done, 00:16:42.410 --> 00:16:45.950 you will get some output saying like, which bot, one more? 00:16:45.950 --> 00:16:50.950 And how many times have won, and some rankings. 00:16:50.950 --> 00:16:52.181 Yep? 00:16:52.181 --> 00:16:54.830 AUDIENCE: How fast do they run? 00:16:54.830 --> 00:16:57.200 HELEN XU: How fast do they run? 00:16:57.200 --> 00:16:58.427 AUDIENCE: [INAUDIBLE] 00:17:04.550 --> 00:17:06.819 HELEN XU: So it depends on how many other games are 00:17:06.819 --> 00:17:07.819 queued at the same time. 00:17:07.819 --> 00:17:09.579 So if a lot of people are running tests, 00:17:09.579 --> 00:17:10.579 it might take some time. 00:17:10.579 --> 00:17:13.732 But blitz is just how long the game itself will take. 00:17:13.732 --> 00:17:15.440 And it might take longer than 60 seconds, 00:17:15.440 --> 00:17:19.819 because if you use less than 0.5 seconds in your move, 00:17:19.819 --> 00:17:22.190 and then you add 0.5 seconds at the end of the move, 00:17:22.190 --> 00:17:25.579 then you would increase your time. 00:17:25.579 --> 00:17:29.630 But 60 is just the time control. 00:17:29.630 --> 00:17:31.465 Each side starts with 60 seconds. 00:17:31.465 --> 00:17:33.840 And depending on how they use it, they have more or less. 00:17:33.840 --> 00:17:34.820 Good question. 00:17:40.220 --> 00:17:41.137 Well, I'll keep going. 00:17:41.137 --> 00:17:43.762 And if there's time at the end, I'll do a demo of this one too. 00:17:43.762 --> 00:17:46.190 But it basically looks the same as the scrimmage server. 00:17:46.190 --> 00:17:48.148 Like, you just watch the games in the same way. 00:17:50.530 --> 00:17:53.030 So now, I'm going to go into the project organization, which 00:17:53.030 --> 00:17:54.613 is the organization of the directories 00:17:54.613 --> 00:17:56.850 that we handed out in this repo. 00:17:56.850 --> 00:17:58.100 So there are some directories. 00:17:58.100 --> 00:17:59.850 The first one is doc, which just includes 00:17:59.850 --> 00:18:02.760 the rules and documentation for the interface. 00:18:02.760 --> 00:18:05.840 There's the auto tester, which is the Java local auto tester. 00:18:05.840 --> 00:18:08.000 So if the cloud-- 00:18:08.000 --> 00:18:10.740 we recommend that you run tests using the cloud auto tester. 00:18:10.740 --> 00:18:15.730 But if there's some small change, or if you think that-- 00:18:15.730 --> 00:18:18.560 if the cue is too long, then you can do local tests. 00:18:18.560 --> 00:18:21.530 And you can also run these overnight. 00:18:21.530 --> 00:18:23.990 There's pgnstates, which just parses your statistics 00:18:23.990 --> 00:18:26.420 from the auto test results, like how many times you won, 00:18:26.420 --> 00:18:27.860 stuff like that. 00:18:27.860 --> 00:18:30.230 There's tests, which is how you specify tests. 00:18:30.230 --> 00:18:34.627 And I'll go into more detail about how you define this. 00:18:34.627 --> 00:18:36.710 There's the player, which is where you're actually 00:18:36.710 --> 00:18:37.668 going to be optimizing. 00:18:37.668 --> 00:18:39.860 So player is the code that actually 00:18:39.860 --> 00:18:41.540 runs the bot to play the game. 00:18:41.540 --> 00:18:44.960 And the webgui is a local webgui where you can watch the game 00:18:44.960 --> 00:18:45.500 and play it. 00:18:45.500 --> 00:18:49.100 So in the webgui, you can even play it yourself as a human 00:18:49.100 --> 00:18:51.270 so you can get a better sense of how the game works. 00:18:54.027 --> 00:18:56.110 To go into more detail, the Java local auto tester 00:18:56.110 --> 00:18:57.080 is an auto tester. 00:19:00.107 --> 00:19:02.690 You can make your changes, and then you can test your changes. 00:19:02.690 --> 00:19:06.270 And the test directory, which is parallel, holds configurations. 00:19:06.270 --> 00:19:09.260 So you can specify the number of games and the bots 00:19:09.260 --> 00:19:11.270 that you want to use, and the time control, 00:19:11.270 --> 00:19:12.830 and other things too. 00:19:12.830 --> 00:19:14.600 So this an example of the configuration 00:19:14.600 --> 00:19:16.670 file that you would use to run your auto tester. 00:19:16.670 --> 00:19:19.292 So this is saying that you run it on 12 CPUs. 00:19:19.292 --> 00:19:20.750 And book means that you're pointing 00:19:20.750 --> 00:19:23.640 to open a book, which I'll talk about later. 00:19:23.640 --> 00:19:26.140 Game rounds is how many games you're going to spawn off. 00:19:26.140 --> 00:19:28.840 Title is just the title of the test that you're running. 00:19:28.840 --> 00:19:30.840 And after that, you have the player definitions. 00:19:30.840 --> 00:19:33.860 So player reference is just the binary. 00:19:33.860 --> 00:19:37.250 And invoke is the path to the binary. 00:19:37.250 --> 00:19:39.770 And then fis is the time control. 00:19:39.770 --> 00:19:42.042 And the next one is just a second binary, 00:19:42.042 --> 00:19:44.000 if you made a change and you want to test them. 00:19:47.470 --> 00:19:48.470 Yeah, that's the binary. 00:19:52.600 --> 00:19:54.510 To interface with auto tester, Lesierchess 00:19:54.510 --> 00:19:57.730 uses the universal chest interface, or UCI, 00:19:57.730 --> 00:20:00.010 which is a communication protocol for automatic games. 00:20:00.010 --> 00:20:03.100 And you pass information between the auto tester and your bot. 00:20:03.100 --> 00:20:05.530 And it allows the programmer or the auto tester 00:20:05.530 --> 00:20:07.590 to enter moves to the game engine. 00:20:07.590 --> 00:20:10.060 So you could use UCI to start up your bot. 00:20:10.060 --> 00:20:11.860 And then you type in the moves that you 00:20:11.860 --> 00:20:14.290 want to make to see the changes in the state. 00:20:14.290 --> 00:20:16.420 And you could use this to debug to get to a state 00:20:16.420 --> 00:20:17.462 that you want to look at. 00:20:21.570 --> 00:20:23.790 We'll measure the bots using Elo ratings. 00:20:23.790 --> 00:20:26.880 So Elo is a rating system that measures relative skill 00:20:26.880 --> 00:20:29.010 level in zero sum games. 00:20:29.010 --> 00:20:32.550 The Elo rating depends on the Elo rating of your opponents. 00:20:32.550 --> 00:20:35.550 And on the bottom, you can see an example output. 00:20:35.550 --> 00:20:38.040 So I had three binaries. 00:20:38.040 --> 00:20:41.100 And I ran about 100 games. 00:20:41.100 --> 00:20:43.710 And you can see that the Elo of the top one 00:20:43.710 --> 00:20:45.360 is much higher than the other ones. 00:20:45.360 --> 00:20:47.940 And so higher Elo is good. 00:20:47.940 --> 00:20:50.490 And we'll be comparing the performance. 00:20:50.490 --> 00:20:53.100 We'll be comparing the Elo of your bot against our reference, 00:20:53.100 --> 00:20:56.520 and improved reference implementations. 00:20:56.520 --> 00:20:59.730 So notice that this is not, as before, 00:20:59.730 --> 00:21:01.680 just a straight measure of time. 00:21:01.680 --> 00:21:03.750 So like before, in previous projects, 00:21:03.750 --> 00:21:07.170 if you used less time, than you would get a higher 00:21:07.170 --> 00:21:08.935 grade or better performance. 00:21:08.935 --> 00:21:10.560 In general, I'll show you a graph later 00:21:10.560 --> 00:21:12.477 that actually shows if you searched the higher 00:21:12.477 --> 00:21:15.250 depth, which means that you are faster, you do improve. 00:21:15.250 --> 00:21:17.230 But it's not an exact correlation. 00:21:17.230 --> 00:21:19.290 And you can look at the nodes per second 00:21:19.290 --> 00:21:22.380 that you search using the UCI. 00:21:25.730 --> 00:21:28.700 And just above here, to local webgui lets you watch a game, 00:21:28.700 --> 00:21:31.100 or play one, without sending it to the scrimmage server. 00:21:31.100 --> 00:21:32.767 So if you wanted to play one as a human, 00:21:32.767 --> 00:21:34.550 you would use the local webgui. 00:21:34.550 --> 00:21:38.610 And you can run it using the commands in the readme. 00:21:38.610 --> 00:21:41.128 OK, so is everyone good so far? 00:21:41.128 --> 00:21:43.670 Now, I'm going to go into more details about how you actually 00:21:43.670 --> 00:21:44.253 play the game. 00:21:49.580 --> 00:21:52.843 So first, every player, or every bot, 00:21:52.843 --> 00:21:54.260 needs to generate the moves, which 00:21:54.260 --> 00:21:55.970 means that once you have a position, 00:21:55.970 --> 00:21:58.810 you need to look at the moves that you can do. 00:21:58.810 --> 00:22:01.070 And to do that, you need a board representation, which 00:22:01.070 --> 00:22:03.380 is to represent what pieces are on the board, 00:22:03.380 --> 00:22:06.290 and how big the board is, and where the pieces are. 00:22:06.290 --> 00:22:09.500 And the reference implantation uses a 16 by 16 board 00:22:09.500 --> 00:22:11.300 to store an 8 by 8 board. 00:22:11.300 --> 00:22:14.300 So you can see that the inner squares is actually the board. 00:22:14.300 --> 00:22:16.940 And the outer dark square is sentinels. 00:22:16.940 --> 00:22:18.380 So you use sentinels to keep track 00:22:18.380 --> 00:22:19.855 of when you go off the board. 00:22:19.855 --> 00:22:21.980 And then the inner square is just the actual board. 00:22:24.980 --> 00:22:26.870 We store the position using this struct. 00:22:26.870 --> 00:22:31.010 So you can see the fields in the position, which are the board. 00:22:31.010 --> 00:22:32.900 And the array size is just representing 00:22:32.900 --> 00:22:34.730 the board, plus the sentinels. 00:22:34.730 --> 00:22:36.450 And there's the history of the position, 00:22:36.450 --> 00:22:38.060 which is, how did we get here? 00:22:38.060 --> 00:22:40.960 And there's a key, which is a hash key for this position. 00:22:40.960 --> 00:22:43.550 There is ply, which tells you what side it is. 00:22:43.550 --> 00:22:44.840 So even means white. 00:22:44.840 --> 00:22:46.282 And odd means black. 00:22:46.282 --> 00:22:47.990 There is, what was the last move that was 00:22:47.990 --> 00:22:49.930 made to get to this position? 00:22:49.930 --> 00:22:52.790 There's a victim struct, which is the pieces destroyed 00:22:52.790 --> 00:22:55.030 by when you shot the laser. 00:22:55.030 --> 00:22:58.310 And there is the location of the kings. 00:22:58.310 --> 00:23:00.102 The position struct and Lesierchess struct 00:23:00.102 --> 00:23:02.060 stores the border presentation and other things 00:23:02.060 --> 00:23:03.102 that I just went through. 00:23:07.870 --> 00:23:13.030 So I talked about this move, which means just like a move 00:23:13.030 --> 00:23:14.990 that you make for one of your pieces. 00:23:14.990 --> 00:23:16.750 And I'll go into how it's represented. 00:23:16.750 --> 00:23:19.390 So right now, we already do the packing for you. 00:23:19.390 --> 00:23:21.190 So we use 28 bits. 00:23:21.190 --> 00:23:25.420 And the first two are the piece type. 00:23:25.420 --> 00:23:28.930 So there's a number of moves that you can make. 00:23:28.930 --> 00:23:31.300 And the first two bits represents the piece type, 00:23:31.300 --> 00:23:35.212 which is empty, pawn, king, or invalid. 00:23:35.212 --> 00:23:36.670 The orientation of the piece, which 00:23:36.670 --> 00:23:39.910 is just how you rotated it. 00:23:39.910 --> 00:23:44.177 The from square, which is where your piece already started. 00:23:44.177 --> 00:23:45.760 There's the intermediate square, which 00:23:45.760 --> 00:23:48.220 is used when you do a swap. 00:23:48.220 --> 00:23:50.770 And there's a two square, which is the final position 00:23:50.770 --> 00:23:52.990 that your piece will end up in. 00:23:52.990 --> 00:23:55.780 So if you're not doing a swap, then the intermediate and from 00:23:55.780 --> 00:23:56.892 should be the same. 00:23:56.892 --> 00:23:58.600 But if you are doing a swap, then there's 00:23:58.600 --> 00:23:59.830 some skipping that happens. 00:24:03.050 --> 00:24:04.940 At each turn, you need to see what 00:24:04.940 --> 00:24:06.410 moves you could possibly make. 00:24:06.410 --> 00:24:10.520 And in move gen, which is one of the files in the handout, 00:24:10.520 --> 00:24:12.440 we generate all the moves, given a position, 00:24:12.440 --> 00:24:13.690 depending on whose turn it is. 00:24:13.690 --> 00:24:15.065 So depending on whose turn it is, 00:24:15.065 --> 00:24:16.333 you can make different moves. 00:24:16.333 --> 00:24:17.750 And in the reference implantation, 00:24:17.750 --> 00:24:19.550 we iterate through the entire board. 00:24:19.550 --> 00:24:22.430 And once we find a piece, we generate all the moves 00:24:22.430 --> 00:24:23.210 from that piece. 00:24:26.790 --> 00:24:28.560 You can also debug using move generation. 00:24:28.560 --> 00:24:31.710 So there's something called perft, 00:24:31.710 --> 00:24:33.600 which is a debugging function that enumerates 00:24:33.600 --> 00:24:35.220 all moves at a certain depth. 00:24:35.220 --> 00:24:37.830 So use perft to make sure that if you make changes to the move 00:24:37.830 --> 00:24:39.205 generation that you're generating 00:24:39.205 --> 00:24:41.080 the same number of moves. 00:24:41.080 --> 00:24:42.763 And if you modify the move generated, 00:24:42.763 --> 00:24:44.430 just make sure that it returns the same, 00:24:44.430 --> 00:24:46.110 because regardless of what optimizations 00:24:46.110 --> 00:24:48.735 you do, you still should see the same moves from each position 00:24:48.735 --> 00:24:49.860 that you can possibly make. 00:24:58.500 --> 00:25:01.200 OK, so now that we talked about move generation, 00:25:01.200 --> 00:25:03.960 I'll talk about how you tell that a move is good. 00:25:03.960 --> 00:25:07.350 And for that, we use something called static evaluation. 00:25:07.350 --> 00:25:09.505 So we use static evaluation to determine 00:25:09.505 --> 00:25:11.130 which positions are better than others, 00:25:11.130 --> 00:25:13.230 and which moves that we should make. 00:25:13.230 --> 00:25:16.590 And the function eval, which is in eval.c, 00:25:16.590 --> 00:25:18.450 generate a score based on a position, 00:25:18.450 --> 00:25:20.280 using some heuristics. 00:25:20.280 --> 00:25:23.203 And at first, we suggest, instead of making up 00:25:23.203 --> 00:25:24.870 your own heuristics, we suggest focusing 00:25:24.870 --> 00:25:28.290 on optimizing the existing structs and evaluation 00:25:28.290 --> 00:25:30.150 heuristics before coming up with new ones, 00:25:30.150 --> 00:25:31.890 because it's kind of hard to come up with new ones. 00:25:31.890 --> 00:25:33.420 And there's a lot of optimizations 00:25:33.420 --> 00:25:35.045 that you can make to the existing ones. 00:25:39.460 --> 00:25:41.410 So I've just grouped these into categories. 00:25:41.410 --> 00:25:43.193 So there's a few regarding the king. 00:25:43.193 --> 00:25:44.610 So there's one called KFACE, which 00:25:44.610 --> 00:25:47.220 is a bonus for your king facing the enemy king. 00:25:47.220 --> 00:25:48.720 There's KAGGRESSIVE, which gives you 00:25:48.720 --> 00:25:50.550 a bonus for if your King is closer 00:25:50.550 --> 00:25:51.870 to the center of the board. 00:25:51.870 --> 00:25:54.190 And there's MOBILITY, which counts up, basically, 00:25:54.190 --> 00:25:57.840 how many squares around your king are free. 00:25:57.840 --> 00:26:02.195 You want to be able to move your king freely. 00:26:02.195 --> 00:26:03.570 And there's some regarding pawns. 00:26:03.570 --> 00:26:07.330 So there's PCENTRAL, which gives you a bonus if your pawns are 00:26:07.330 --> 00:26:08.520 in the center of the board. 00:26:08.520 --> 00:26:11.550 And there's PBETWEEN, which basically draw a bounding box 00:26:11.550 --> 00:26:13.110 with both kings at the corner. 00:26:13.110 --> 00:26:14.805 And then you count how many pawns 00:26:14.805 --> 00:26:15.930 are in the center of those. 00:26:19.400 --> 00:26:22.520 And then there's points based on distance. 00:26:22.520 --> 00:26:25.460 So there's LCOVERAGE, which means laser coverage, which 00:26:25.460 --> 00:26:28.460 is basically you make all the possible moves that you 00:26:28.460 --> 00:26:29.630 can make from your position. 00:26:29.630 --> 00:26:31.880 And then you draw the laser path. 00:26:31.880 --> 00:26:34.640 And then you do some scaling to determine 00:26:34.640 --> 00:26:37.608 how well you can possibly cover the board, 00:26:37.608 --> 00:26:38.900 based on your current position. 00:26:41.970 --> 00:26:44.800 So that's basically how you tell if a position is good or not, 00:26:44.800 --> 00:26:46.861 with these heuristics. 00:26:50.020 --> 00:26:53.590 So I'll just go through the high level of how you actually 00:26:53.590 --> 00:26:54.850 play the game using search. 00:26:57.640 --> 00:26:59.260 So at the very highest level, there's 00:26:59.260 --> 00:27:01.120 something called game search trees, which 00:27:01.120 --> 00:27:02.873 is we've invented in search.c. 00:27:02.873 --> 00:27:04.540 But, basically, this is a representation 00:27:04.540 --> 00:27:06.400 of how you play the game. 00:27:06.400 --> 00:27:08.050 At the top, there's an orange square, 00:27:08.050 --> 00:27:10.480 which is the orange side, which is the opening 00:27:10.480 --> 00:27:13.900 position, and then the arrows. 00:27:13.900 --> 00:27:16.000 So the top square-- 00:27:16.000 --> 00:27:19.180 actually, all the nodes are positions in the tree. 00:27:19.180 --> 00:27:21.760 And you use move generation that I just talked about, 00:27:21.760 --> 00:27:25.690 to enumerate all the possible moves from a single position. 00:27:25.690 --> 00:27:27.910 And each edge is a move. 00:27:27.910 --> 00:27:30.790 So to get from position to position, you do moves. 00:27:30.790 --> 00:27:34.870 And you can see that circle is the position 00:27:34.870 --> 00:27:37.450 after you've made the move. 00:27:37.450 --> 00:27:40.690 And you do this tree to some depth d. 00:27:40.690 --> 00:27:45.000 And then you do static evaluation of the leaves. 00:27:45.000 --> 00:27:48.062 So this is at a really high level how game playing programs 00:27:48.062 --> 00:27:49.020 actually play the game. 00:27:49.020 --> 00:27:50.750 They enumerate all the possible moves. 00:27:50.750 --> 00:27:52.000 And then they have a position. 00:27:52.000 --> 00:27:54.450 And then they pick which one is best, based on evaluation. 00:27:54.450 --> 00:27:56.358 But you can see that there's a lot of nodes. 00:27:56.358 --> 00:27:57.900 Like, if you do this naively, there'd 00:27:57.900 --> 00:28:03.060 be number of moves raised to d, which is a huge number, 00:28:03.060 --> 00:28:04.357 and too many to generate. 00:28:04.357 --> 00:28:06.690 So we're going to talk about how you reduce those later. 00:28:09.720 --> 00:28:12.293 There's something that you have to do on search series, which 00:28:12.293 --> 00:28:13.710 is called Quiescence search, which 00:28:13.710 --> 00:28:17.400 is if you fix your depth-- 00:28:17.400 --> 00:28:22.430 let's say you fix depth, and then you go down to the leaves, 00:28:22.430 --> 00:28:24.762 and you just captured a piece. 00:28:24.762 --> 00:28:26.970 But it's dangerous to just stop there at fixed depth, 00:28:26.970 --> 00:28:29.510 because maybe if you searched one level deeper, 00:28:29.510 --> 00:28:32.010 you would see that the opponent would capture your piece. 00:28:32.010 --> 00:28:34.590 And so if you do your search, and you 00:28:34.590 --> 00:28:36.493 see that you capture a piece at the leaves, 00:28:36.493 --> 00:28:38.910 or your opponent captures the piece at the leaves, we say, 00:28:38.910 --> 00:28:39.618 that's not quiet. 00:28:39.618 --> 00:28:41.610 And you keep searching the tree until there 00:28:41.610 --> 00:28:42.762 are no more captures. 00:28:42.762 --> 00:28:44.220 So that's called Quiescence search, 00:28:44.220 --> 00:28:46.037 because you quiet the position. 00:28:46.037 --> 00:28:47.870 And that's implemented in the search column. 00:28:51.190 --> 00:28:53.590 So this is a graph that I generated 00:28:53.590 --> 00:28:56.860 by doing the reference spot to different depths. 00:28:56.860 --> 00:28:59.500 And you can see that the Elo increases as you 00:28:59.500 --> 00:29:01.420 increase the search depth. 00:29:01.420 --> 00:29:03.420 So you just search the search tree. 00:29:03.420 --> 00:29:06.955 And so if you optimize your bot to make it faster, 00:29:06.955 --> 00:29:09.330 you can search deeper, which means that you'll do better. 00:29:16.320 --> 00:29:21.220 So next, I'll talk about min-max search, which 00:29:21.220 --> 00:29:26.380 is a more complex version of searching 00:29:26.380 --> 00:29:30.520 that can improve the amount of nodes you have to evaluate. 00:29:30.520 --> 00:29:34.063 So at a high level, there's two players, max and min. 00:29:34.063 --> 00:29:35.980 And in our example, there's orange and purple. 00:29:35.980 --> 00:29:37.570 And orange is a square. 00:29:37.570 --> 00:29:38.710 And purple is a circle. 00:29:38.710 --> 00:29:40.690 And the game trees represents all moves 00:29:40.690 --> 00:29:44.872 from the current position from a given ply, which means depth. 00:29:44.872 --> 00:29:46.330 And if the leaves, like I said, you 00:29:46.330 --> 00:29:48.190 play a static evaluation function. 00:29:48.190 --> 00:29:50.860 And max chooses the maximum score among its children. 00:29:50.860 --> 00:29:52.277 And min chooses the minimum score. 00:29:52.277 --> 00:29:53.693 So one side is trying to maximize, 00:29:53.693 --> 00:29:55.353 and one side is trying to minimize. 00:29:58.460 --> 00:30:01.100 To evaluate the search try, I'll first 00:30:01.100 --> 00:30:03.200 talk about an algorithm called alpha beta, which 00:30:03.200 --> 00:30:06.440 is that each search from a node has a window alpha beta. 00:30:06.440 --> 00:30:08.780 And if the value of the search falls below alpha, 00:30:08.780 --> 00:30:11.260 the move is not good enough, and you keep searching. 00:30:11.260 --> 00:30:13.878 And if the value falls within alpha and beta, 00:30:13.878 --> 00:30:16.170 then you increase your alpha, which is the lower bound, 00:30:16.170 --> 00:30:17.270 and you keep searching, because you know 00:30:17.270 --> 00:30:18.890 you can do at least that well. 00:30:18.890 --> 00:30:22.430 And if the value of the search falls above beta, 00:30:22.430 --> 00:30:24.440 than you generate a beta cut off in return. 00:30:24.440 --> 00:30:26.870 Beta basically means one side is trying to maximize, 00:30:26.870 --> 00:30:28.328 and one side is trying to minimize. 00:30:28.328 --> 00:30:30.950 So beta is basically saying, the opponent 00:30:30.950 --> 00:30:33.620 would never let you do that move, because it'd be too good. 00:30:33.620 --> 00:30:35.995 So you don't need to keep searching there, because you're 00:30:35.995 --> 00:30:38.930 not going to get there anyway. 00:30:38.930 --> 00:30:40.410 So I'll do an example. 00:30:40.410 --> 00:30:41.840 Let's say you have this tree. 00:30:41.840 --> 00:30:46.253 And if max discovered a move that min wouldn't 00:30:46.253 --> 00:30:47.670 let you do, because it's too good, 00:30:47.670 --> 00:30:49.170 then max's other children don't need 00:30:49.170 --> 00:30:51.640 to be searched, which is what a beta cut off is. 00:30:51.640 --> 00:30:53.780 So you'd start at the root. 00:30:53.780 --> 00:30:57.650 And then you go down to the lowest left leaf. 00:30:57.650 --> 00:31:00.060 And you see that it's three. 00:31:00.060 --> 00:31:01.648 So you propagate three up. 00:31:01.648 --> 00:31:03.440 And then you can see that in this sub-tree, 00:31:03.440 --> 00:31:06.200 you can do at least three. 00:31:06.200 --> 00:31:08.390 And then you keep searching your children. 00:31:08.390 --> 00:31:10.130 And then you see six. 00:31:10.130 --> 00:31:12.440 And then you say, OK, now you update your alpha value 00:31:12.440 --> 00:31:14.902 to be six. 00:31:14.902 --> 00:31:16.330 Now, you search four. 00:31:16.330 --> 00:31:18.555 But four is worse than six. 00:31:18.555 --> 00:31:19.930 So you don't have to do anything. 00:31:19.930 --> 00:31:22.960 So you first search the leftmost subtree. 00:31:22.960 --> 00:31:25.210 And then you see the best move that you could possibly 00:31:25.210 --> 00:31:27.760 make there. 00:31:27.760 --> 00:31:31.810 So you propagate six up to the root. 00:31:31.810 --> 00:31:34.700 And then you search your other subtrees. 00:31:34.700 --> 00:31:36.190 But now, you have this value of six 00:31:36.190 --> 00:31:38.780 that you basically use in the other subtrees. 00:31:38.780 --> 00:31:40.457 So you look at two. 00:31:40.457 --> 00:31:42.040 And you see that two is less than six. 00:31:42.040 --> 00:31:44.190 So you propagate it up. 00:31:44.190 --> 00:31:45.520 But now, you look at nine. 00:31:45.520 --> 00:31:48.880 And you see that nine is greater than six. 00:31:48.880 --> 00:31:52.780 So you say that this subtree would let purple do nine, 00:31:52.780 --> 00:31:54.520 which is greater than six. 00:31:54.520 --> 00:32:00.100 And so that would be too good, because orange would never 00:32:00.100 --> 00:32:01.420 let purple do that well. 00:32:01.420 --> 00:32:04.090 So you don't have to evaluate five anymore. 00:32:04.090 --> 00:32:06.235 So you cut off five. 00:32:06.235 --> 00:32:07.110 Does that make sense? 00:32:11.140 --> 00:32:13.580 OK, so, basically, now you apply the same thing 00:32:13.580 --> 00:32:15.003 to the regular subtree. 00:32:15.003 --> 00:32:15.920 And you look at seven. 00:32:15.920 --> 00:32:18.150 And you see that seven is greater than six. 00:32:18.150 --> 00:32:19.208 So you propagate that up. 00:32:19.208 --> 00:32:21.500 And now you're done, because seven is greater than six. 00:32:21.500 --> 00:32:24.810 So you don't have to search the rest of the subtree. 00:32:24.810 --> 00:32:27.830 So that's how you evaluate fewer moves than the entire tree. 00:32:35.290 --> 00:32:38.280 And there's a theorem that says for a game tree 00:32:38.280 --> 00:32:41.220 with branching factor b and depth d, and alpha beta search 00:32:41.220 --> 00:32:43.140 with moves searched in best-first order 00:32:43.140 --> 00:32:46.470 examines exactly b raised to the d over 2, 00:32:46.470 --> 00:32:50.580 plus b raised to the d over 2 minus 1 nodes apply d. 00:32:50.580 --> 00:32:53.760 So best first order means that you sorted the moves in terms 00:32:53.760 --> 00:32:55.273 of your static evaluation. 00:32:58.340 --> 00:33:00.680 The naive algorithm examines b to the d nodes. 00:33:00.680 --> 00:33:04.190 And in the example I did, you can see how you prune. 00:33:04.190 --> 00:33:06.427 And for the same work, the search stuff is doubled. 00:33:06.427 --> 00:33:08.510 And for the same depth, the work is square rooted. 00:33:08.510 --> 00:33:13.846 So this is a huge benefit over the naive evaluation. 00:33:13.846 --> 00:33:15.240 Is everyone good on alpha beta? 00:33:19.890 --> 00:33:23.210 Great, so the code is pretty short. 00:33:23.210 --> 00:33:25.610 So I'll just go through some pseudocode for it. 00:33:25.610 --> 00:33:28.443 Basically, the main point is that at line 11, 00:33:28.443 --> 00:33:30.235 one side is trying to minimize and one side 00:33:30.235 --> 00:33:31.152 is trying to maximize. 00:33:31.152 --> 00:33:33.080 But if you negate, then that's just the same 00:33:33.080 --> 00:33:34.880 as minimizing and maximizing. 00:33:34.880 --> 00:33:38.360 And you get all the possible moves 00:33:38.360 --> 00:33:40.550 that you could possibly make using gen moves. 00:33:40.550 --> 00:33:42.920 And you go through the entire move list. 00:33:42.920 --> 00:33:44.720 And then you make each of the children. 00:33:44.720 --> 00:33:47.480 And you search for the score. 00:33:47.480 --> 00:33:49.820 And then you see whether you had a beta cut off. 00:33:49.820 --> 00:33:52.195 And then you don't need to search the subtree If you did. 00:34:00.160 --> 00:34:02.080 So that was basic alpha beta. 00:34:02.080 --> 00:34:04.630 And we actually implement a variation of alpha beta called 00:34:04.630 --> 00:34:06.072 principle variation search. 00:34:06.072 --> 00:34:08.530 And the main idea is that you assume that the first move is 00:34:08.530 --> 00:34:09.639 the best one. 00:34:09.639 --> 00:34:13.739 And you run scout search, which is also called zero window 00:34:13.739 --> 00:34:16.840 search, on the remaining moves to verify that they're worse. 00:34:16.840 --> 00:34:19.880 So in this example, you, again, search the most leftmost 00:34:19.880 --> 00:34:20.380 subtree. 00:34:20.380 --> 00:34:23.420 And you see that the best you can do in the left-most subtree 00:34:23.420 --> 00:34:24.610 is three. 00:34:24.610 --> 00:34:27.030 And you evaluate the ones to the right 00:34:27.030 --> 00:34:31.750 of it using scout search, which is not a full search. 00:34:31.750 --> 00:34:33.340 You're basically assuming that you 00:34:33.340 --> 00:34:35.139 can do no better than three. 00:34:35.139 --> 00:34:38.080 And then now you're kind of doing an initial search to see 00:34:38.080 --> 00:34:40.489 whether or not that's true. 00:34:40.489 --> 00:34:43.230 And see you see that some of them are-- 00:34:43.230 --> 00:34:46.532 the one after that is seven. 00:34:46.532 --> 00:34:47.949 The first one after that is seven. 00:34:47.949 --> 00:34:50.215 And the one after that in the other subtree is six. 00:34:54.600 --> 00:34:59.255 So then you can prune them, because those are better-- 00:34:59.255 --> 00:35:00.630 because you know already in those 00:35:00.630 --> 00:35:02.430 subtrees that you can do better than three. 00:35:02.430 --> 00:35:06.120 So you don't have to keep evaluating them. 00:35:06.120 --> 00:35:08.364 And you don't have to-- yeah? 00:35:08.364 --> 00:35:10.930 AUDIENCE: How do we know the score of the subtree 00:35:10.930 --> 00:35:14.430 before we evaluate? 00:35:14.430 --> 00:35:17.340 How can we prune something? 00:35:20.020 --> 00:35:21.920 HELEN XU: So you actually had to find seven. 00:35:21.920 --> 00:35:23.212 Like, zero and eight are there. 00:35:23.212 --> 00:35:25.990 But you haven't found them yet. 00:35:25.990 --> 00:35:29.430 So, basically, if you thought about doing it serially, 00:35:29.430 --> 00:35:32.790 you do the leftmost subtree, which has 2, 3, and 0. 00:35:32.790 --> 00:35:34.220 And then you would find seven. 00:35:34.220 --> 00:35:35.970 And that would be a cut off, because seven 00:35:35.970 --> 00:35:36.900 is bigger than three. 00:35:39.570 --> 00:35:41.490 So you're not actually finding zero and eight. 00:35:48.260 --> 00:35:50.390 The point is that you wouldn't get to that subtree, 00:35:50.390 --> 00:35:54.323 because the opponent wouldn't let you get there, 00:35:54.323 --> 00:35:55.490 because you can do too well. 00:35:55.490 --> 00:36:00.590 So they would just not let you go down that path. 00:36:00.590 --> 00:36:04.160 Like, let's say you were purple, and the opponent is orange. 00:36:04.160 --> 00:36:06.500 And you want to get 7 and 8. 00:36:06.500 --> 00:36:08.615 But the opponent can also search that, and see 00:36:08.615 --> 00:36:09.740 that you would get 7 and 8. 00:36:09.740 --> 00:36:12.320 So they would prefer you to do something like two or three. 00:36:19.700 --> 00:36:21.320 AUDIENCE: So what do you do instead? 00:36:26.620 --> 00:36:29.170 HELEN XU: You're not always making the best move that you 00:36:29.170 --> 00:36:32.690 could possibly do, because-- 00:36:32.690 --> 00:36:35.320 like, if you just searched without this pruning, 00:36:35.320 --> 00:36:37.150 and you just picked-- 00:36:37.150 --> 00:36:40.420 let's say you wanted to make the best move. 00:36:40.420 --> 00:36:42.833 Like, if you don't take into account the opponent, 00:36:42.833 --> 00:36:44.500 then you're never going to get to there. 00:36:44.500 --> 00:36:45.940 So you're basically trying to find a move 00:36:45.940 --> 00:36:47.398 that the opponent would let you get 00:36:47.398 --> 00:36:53.080 to that's also good for you, because you switch off. 00:36:59.056 --> 00:37:00.550 Yes? 00:37:00.550 --> 00:37:02.542 AUDIENCE: [INAUDIBLE] 00:37:06.050 --> 00:37:10.120 HELEN XU: I guess in this example, you're purple. 00:37:10.120 --> 00:37:13.760 No, sorry, you're orange, because you're cutting off-- 00:37:13.760 --> 00:37:15.590 no, you're purple, because you're 00:37:15.590 --> 00:37:18.513 trying to maximize what you get at the leaves. 00:37:18.513 --> 00:37:20.395 AUDIENCE: [INAUDIBLE] 00:37:20.395 --> 00:37:20.978 HELEN XU: Yes. 00:37:33.310 --> 00:37:36.368 The main point of-- sorry. 00:37:36.368 --> 00:37:36.910 AUDIENCE: Oh. 00:37:41.502 --> 00:37:42.960 We're trying to minimize the score. 00:37:46.270 --> 00:37:47.470 HELEN XU: Yes. 00:37:47.470 --> 00:37:49.490 So orange is trying to minimize the score. 00:37:49.490 --> 00:37:51.282 And purple is trying to maximize the score. 00:37:53.950 --> 00:37:55.450 AUDIENCE: So we're cutting that off, 00:37:55.450 --> 00:37:58.932 you're saying you don't need to search this because we already 00:37:58.932 --> 00:38:01.680 know they're the same here. 00:38:01.680 --> 00:38:03.535 So we shouldn't go down this path anyway. 00:38:11.790 --> 00:38:13.860 HELEN XU: Does anyone have questions? 00:38:13.860 --> 00:38:14.850 Does that make sense? 00:38:14.850 --> 00:38:16.558 Yeah, it's basically exactly as you said. 00:38:16.558 --> 00:38:22.710 So there's kind of this balance between one side trying-- 00:38:22.710 --> 00:38:24.235 both sides are just trying to make-- 00:38:24.235 --> 00:38:25.610 you're trying to make good moves. 00:38:25.610 --> 00:38:27.960 But you're also trying to make the opponent make 00:38:27.960 --> 00:38:30.850 not good moves, if that makes sense. 00:38:30.850 --> 00:38:33.530 So you're not only searching for your maximum. 00:38:33.530 --> 00:38:37.550 But you're also searching to minimize the opponent. 00:38:37.550 --> 00:38:38.534 Good question. 00:38:44.974 --> 00:38:46.555 AUDIENCE: [INAUDIBLE] 00:38:58.180 --> 00:39:00.580 HELEN XU: Sorry? 00:39:00.580 --> 00:39:02.150 AUDIENCE: So we don't want to choose 00:39:02.150 --> 00:39:04.220 either of those orange ones. 00:39:04.220 --> 00:39:06.090 We don't want to let-- 00:39:06.090 --> 00:39:06.860 I think it's OK. 00:39:06.860 --> 00:39:08.180 I think you can move on. 00:39:08.180 --> 00:39:10.860 HELEN XU: Oh, OK. 00:39:10.860 --> 00:39:11.775 Yes? 00:39:11.775 --> 00:39:13.400 AUDIENCE: What if you and your opponent 00:39:13.400 --> 00:39:15.870 have different reward criteria? 00:39:15.870 --> 00:39:19.100 Like, you guys evaluate-- 00:39:19.100 --> 00:39:21.140 HELEN XU: That's OK. 00:39:21.140 --> 00:39:23.145 It's fine. 00:39:23.145 --> 00:39:24.770 The actual evaluation, like what number 00:39:24.770 --> 00:39:28.070 you assign to each position, is not exposed to the opponent. 00:39:28.070 --> 00:39:30.710 The main point is that, at the end of each move, you pick one. 00:39:30.710 --> 00:39:34.398 And they can do with it what they want. 00:39:34.398 --> 00:39:36.440 Like, that may not have been the one they picked. 00:39:36.440 --> 00:39:37.050 But it's OK. 00:39:51.420 --> 00:39:54.560 Sorry, I think you're orange in this one, 00:39:54.560 --> 00:39:57.370 because the root is orange. 00:39:57.370 --> 00:39:58.590 AUDIENCE: [INAUDIBLE] 00:40:21.100 --> 00:40:22.470 HELEN XU: So let's start over. 00:40:22.470 --> 00:40:25.770 So I think that we are orange. 00:40:25.770 --> 00:40:28.290 So remember that each edge is a move. 00:40:28.290 --> 00:40:30.030 And each node is a position. 00:40:30.030 --> 00:40:31.020 And so you're orange. 00:40:31.020 --> 00:40:32.580 And you start at the root. 00:40:32.580 --> 00:40:35.370 And now you, for example, make the move left. 00:40:35.370 --> 00:40:39.300 And purple now can make moves whatever three after that. 00:40:39.300 --> 00:40:40.590 And now, you're orange again. 00:40:40.590 --> 00:40:42.215 And then you can make moves after that. 00:40:42.215 --> 00:40:45.120 And now, you evaluate the position after that as a leaf. 00:40:48.700 --> 00:40:51.190 And so, basically, you're searching 00:40:51.190 --> 00:40:53.680 past like the second level of orange. 00:40:53.680 --> 00:40:57.732 And you are cutting off if you see that you would do better, 00:40:57.732 --> 00:40:59.440 because you think that purple would never 00:40:59.440 --> 00:41:02.620 let you get to that orange node right above. 00:41:02.620 --> 00:41:03.417 Yes? 00:41:03.417 --> 00:41:05.310 AUDIENCE: [INAUDIBLE] 00:41:08.867 --> 00:41:10.950 HELEN XU: Yeah, I guess that's the score that you, 00:41:10.950 --> 00:41:13.420 as orange would receive. 00:41:13.420 --> 00:41:14.594 Yes? 00:41:14.594 --> 00:41:17.700 AUDIENCE: [INAUDIBLE] 00:41:24.520 --> 00:41:27.317 HELEN XU: You're not trying to give-- 00:41:27.317 --> 00:41:29.650 it's not so much like you're trying to give purple zero, 00:41:29.650 --> 00:41:33.000 as you think that purple would not give you seven and eight, 00:41:33.000 --> 00:41:35.332 because purple would have to go down the left subtree 00:41:35.332 --> 00:41:36.040 to give you that. 00:41:46.798 --> 00:41:47.940 Any other questions? 00:41:52.660 --> 00:41:54.160 I'm going to move on with the search 00:41:54.160 --> 00:41:58.192 then, if there are no questions. 00:41:58.192 --> 00:41:59.800 [INTERPOSING VOICES] 00:42:11.510 --> 00:42:14.420 HELEN XU: Is everyone good? 00:42:14.420 --> 00:42:16.620 Can I keep going? 00:42:16.620 --> 00:42:22.600 OK, so just going back to principal variations pruning, 00:42:22.600 --> 00:42:25.870 the main idea is that you go down 00:42:25.870 --> 00:42:28.300 the first path on the left side, thinking 00:42:28.300 --> 00:42:31.330 that that's the best path. 00:42:31.330 --> 00:42:33.247 And then you're basically doing initial passes 00:42:33.247 --> 00:42:35.497 through the trees to make sure that your assumption is 00:42:35.497 --> 00:42:36.040 correct. 00:42:36.040 --> 00:42:37.030 And if they're not correct, then you 00:42:37.030 --> 00:42:38.590 have to search the entire subtree. 00:42:38.590 --> 00:42:40.360 But if they are correct, then you kind of 00:42:40.360 --> 00:42:44.350 fail, you early exit. 00:42:44.350 --> 00:42:47.230 So you search down the left subtree. 00:42:47.230 --> 00:42:50.007 And you find three in the leftmost subtree. 00:42:50.007 --> 00:42:52.090 And now, you search the ones to the right of that. 00:42:52.090 --> 00:42:53.530 And those are seven and eight. 00:42:53.530 --> 00:42:56.500 So those produce a cutoff, because seven and eight 00:42:56.500 --> 00:42:57.513 is higher than three. 00:42:57.513 --> 00:42:58.930 So you think that purple would not 00:42:58.930 --> 00:43:00.097 let you get to that subtree. 00:43:03.040 --> 00:43:08.640 And now, you do a scout search again on the middle subtree. 00:43:08.640 --> 00:43:11.630 And then you see that-- 00:43:11.630 --> 00:43:14.280 you find this first node of each one of those subtrees 00:43:14.280 --> 00:43:15.660 underneath the middle subtree. 00:43:15.660 --> 00:43:18.300 And you see that they're all higher than three. 00:43:18.300 --> 00:43:24.990 So it turns out that you failed to prove that you 00:43:24.990 --> 00:43:26.603 can do no better than three. 00:43:26.603 --> 00:43:28.020 The main point of the scout search 00:43:28.020 --> 00:43:29.970 is that you assume that your first move that you search 00:43:29.970 --> 00:43:31.170 is the best you can do. 00:43:31.170 --> 00:43:34.530 And then you do initial passes to verify that assumption. 00:43:34.530 --> 00:43:37.375 And if you search later subtrees, and you find that-- 00:43:37.375 --> 00:43:39.000 for example, in this one in the middle, 00:43:39.000 --> 00:43:40.292 they're all higher than threes. 00:43:40.292 --> 00:43:41.650 So your assumption is not true. 00:43:41.650 --> 00:43:43.320 So now you have to do a full search 00:43:43.320 --> 00:43:46.765 of that entire middle subtree. 00:43:46.765 --> 00:43:48.745 Is that OK? 00:43:48.745 --> 00:43:50.725 Are there questions? 00:43:56.170 --> 00:44:00.280 So once you find that you have to actually search 00:44:00.280 --> 00:44:02.950 the middle subtree, you can recursively apply scout search. 00:44:02.950 --> 00:44:05.530 So you have to search the left subtree in the middle. 00:44:05.530 --> 00:44:09.610 But now, you apply scout search to the lower middle 00:44:09.610 --> 00:44:11.867 and the lower right. 00:44:11.867 --> 00:44:13.450 And you do a zero window search there. 00:44:13.450 --> 00:44:16.210 And, again, you assume that you can do no better than six. 00:44:16.210 --> 00:44:17.918 And now, you're trying to verify that you 00:44:17.918 --> 00:44:19.570 can do better than six. 00:44:19.570 --> 00:44:20.620 But you actually can. 00:44:20.620 --> 00:44:23.780 So you have to search them. 00:44:23.780 --> 00:44:27.320 And then you apply the same thing again to the subtree. 00:44:27.320 --> 00:44:29.450 And you see that you can do better than six 00:44:29.450 --> 00:44:30.640 on the left one. 00:44:30.640 --> 00:44:34.660 But you do worse than six on the right one. 00:44:34.660 --> 00:44:38.510 And you cut off two, because the middle subtree already gave you 00:44:38.510 --> 00:44:40.660 two. 00:44:40.660 --> 00:44:43.220 And so you don't have to search that one. 00:44:43.220 --> 00:44:46.822 So in this example, there were 13 leaves pruned. 00:44:46.822 --> 00:44:48.530 And the point of scout search is that you 00:44:48.530 --> 00:44:51.340 can improve pruning a little bit over alpha beta, 00:44:51.340 --> 00:44:53.090 and that you process most of the game tree 00:44:53.090 --> 00:44:54.507 with zero window searches. 00:44:54.507 --> 00:44:56.840 The main point is that it reduces your work, because you 00:44:56.840 --> 00:44:57.770 have to process less. 00:45:02.234 --> 00:45:03.226 Questions? 00:45:08.700 --> 00:45:11.430 So now we're going to talk about-- so I kind of glossed 00:45:11.430 --> 00:45:12.870 over how you order the moves. 00:45:12.870 --> 00:45:15.660 So the ordering determines which order 00:45:15.660 --> 00:45:18.360 you explore the subtrees in. 00:45:18.360 --> 00:45:20.360 Alpha-beta search and principal variation search 00:45:20.360 --> 00:45:22.320 depend on putting the best moves in the front 00:45:22.320 --> 00:45:24.240 to trigger an early cut off. 00:45:24.240 --> 00:45:25.990 And the main question is, how do we 00:45:25.990 --> 00:45:27.630 determine moves, which moves are good, 00:45:27.630 --> 00:45:29.588 without doing static evaluation at every level? 00:45:29.588 --> 00:45:31.650 Like, for example, we only did static evaluation 00:45:31.650 --> 00:45:32.790 with the leaves. 00:45:32.790 --> 00:45:34.590 And we can't get sortable move list, 00:45:34.590 --> 00:45:36.510 which is a function in search. 00:45:36.510 --> 00:45:40.043 And sortable move lists, kind of talk 00:45:40.043 --> 00:45:41.460 about how you populate that later. 00:45:45.060 --> 00:45:47.410 As I said before, moves are represented in 128 bits. 00:45:47.410 --> 00:45:49.260 So you can use it in 32. 00:45:49.260 --> 00:45:51.760 And to make them sortable, you store a sort key 00:45:51.760 --> 00:45:54.510 in the upper 32 bits in 64. 00:45:54.510 --> 00:45:58.060 And then you sort, based on that key. 00:45:58.060 --> 00:45:58.820 That make sense? 00:46:05.940 --> 00:46:09.420 So I'll just go over some search optimizations that you can do. 00:46:09.420 --> 00:46:10.920 We actually implement these already. 00:46:10.920 --> 00:46:11.940 So I'm just going to go through them 00:46:11.940 --> 00:46:14.640 so it's not super confusing when you look at the code. 00:46:14.640 --> 00:46:17.940 The most important one is called the transposition table. 00:46:17.940 --> 00:46:20.070 The main idea in the transposition table 00:46:20.070 --> 00:46:22.650 is that chess programs often encounter the same positions 00:46:22.650 --> 00:46:24.450 repeatedly during a search. 00:46:24.450 --> 00:46:27.150 And you can store those results in a transposition table 00:46:27.150 --> 00:46:29.642 to avoid unnecessary feature searches. 00:46:29.642 --> 00:46:31.350 And I've listed where you can find those. 00:46:35.590 --> 00:46:37.370 There's something called Zobrist hashing, 00:46:37.370 --> 00:46:39.760 which is a technique for hashing a board position which 00:46:39.760 --> 00:46:42.142 you use to index the transmission table. 00:46:42.142 --> 00:46:44.350 And it's a table of random numbers, indexed by piece, 00:46:44.350 --> 00:46:45.700 orientation, and square. 00:46:45.700 --> 00:46:49.948 So each position has a unique hash. 00:46:49.948 --> 00:46:51.490 And it produces the hash by exporting 00:46:51.490 --> 00:46:53.560 all of these random numbers together. 00:46:53.560 --> 00:46:55.660 And the advantage of Zobrist hashing 00:46:55.660 --> 00:46:58.330 is that the hash function can be updated incrementally, which 00:46:58.330 --> 00:47:00.670 is like if you move a position-- if you move a piece, 00:47:00.670 --> 00:47:01.630 you just xor it out. 00:47:01.630 --> 00:47:03.670 And then you xor the new one, so you 00:47:03.670 --> 00:47:06.244 don't have to recompute the hash each time. 00:47:11.330 --> 00:47:14.660 So the transposition table saves you a lot of work 00:47:14.660 --> 00:47:17.697 by preventing you from researching things. 00:47:17.697 --> 00:47:20.030 And there's also something called the killer move table. 00:47:20.030 --> 00:47:21.613 So the transposition table is like how 00:47:21.613 --> 00:47:25.430 you determine how to do sorting at things 00:47:25.430 --> 00:47:27.860 that are not the leaves, and also the killing moves table. 00:47:27.860 --> 00:47:29.770 So the killer moves people stores 00:47:29.770 --> 00:47:32.270 moves that are really good so that the opponent wouldn't let 00:47:32.270 --> 00:47:34.160 you go down that path, so you have to keep 00:47:34.160 --> 00:47:36.410 recomputing the same values. 00:47:36.410 --> 00:47:38.480 And the table is indexed by ply, because you 00:47:38.480 --> 00:47:41.960 tend to see the same moves at the same depth. 00:47:41.960 --> 00:47:44.180 So the killer move table, basically, just stores 00:47:44.180 --> 00:47:46.870 move that trigger the beta cut off before in your search. 00:47:53.270 --> 00:47:55.967 There's a best move table, which is stored 00:47:55.967 --> 00:47:57.050 at the root of the search. 00:47:57.050 --> 00:48:00.230 And it is the move that got the maximum score 00:48:00.230 --> 00:48:01.820 in your evaluation. 00:48:01.820 --> 00:48:04.040 And the best move table is indexed by color, 00:48:04.040 --> 00:48:06.560 piece, square, and orientation. 00:48:06.560 --> 00:48:09.715 And there's a history table in the code. 00:48:09.715 --> 00:48:11.090 So these are all, basically, just 00:48:11.090 --> 00:48:12.757 things to help you optimize your search, 00:48:12.757 --> 00:48:14.400 and produce early cut offs. 00:48:17.862 --> 00:48:20.070 And there's something called null-move pruning, which 00:48:20.070 --> 00:48:22.463 tries to reduce your search space by first 00:48:22.463 --> 00:48:24.630 not moving, and then doing a shallower search to see 00:48:24.630 --> 00:48:26.760 if this subtree is worth further exploring. 00:48:29.318 --> 00:48:31.110 Basically, it says, don't move, and then do 00:48:31.110 --> 00:48:32.830 a little bit of evaluation. 00:48:32.830 --> 00:48:35.520 And if you're still doing really well, 00:48:35.520 --> 00:48:37.350 even if you didn't move in the subtree, 00:48:37.350 --> 00:48:39.642 then it's not worth exploring, because the opponent 00:48:39.642 --> 00:48:41.850 would never let you go there, because the position is 00:48:41.850 --> 00:48:42.350 too good. 00:48:45.890 --> 00:48:47.990 There's futility pruning, which explores 00:48:47.990 --> 00:48:51.050 moves that only have the potential to increase alpha. 00:48:51.050 --> 00:48:52.550 And it calculates that possibility 00:48:52.550 --> 00:48:54.320 by adding a futility margin, which 00:48:54.320 --> 00:48:57.770 is the most you could possibly gain from going there, and then 00:48:57.770 --> 00:48:59.380 evaluating a little bit. 00:48:59.380 --> 00:49:01.380 And if the result does not go higher than alpha, 00:49:01.380 --> 00:49:03.298 then you skip it, because there's 00:49:03.298 --> 00:49:05.090 no point in even going that way, because it 00:49:05.090 --> 00:49:06.298 wouldn't increase your alpha. 00:49:11.410 --> 00:49:13.600 There's late move reduction, which 00:49:13.600 --> 00:49:15.880 is after you order the moves at a position, 00:49:15.880 --> 00:49:19.090 you explore the-- the-- ones in front are likely to be better. 00:49:19.090 --> 00:49:20.890 So you explore those in higher depth. 00:49:20.890 --> 00:49:24.102 And then you explore the ones later with shallower depth, 00:49:24.102 --> 00:49:25.810 because those are less likely to be good. 00:49:29.770 --> 00:49:33.340 And some things that you can optimize 00:49:33.340 --> 00:49:37.480 are implementing a better opening book. 00:49:37.480 --> 00:49:40.000 I think we have produced a very basic opening 00:49:40.000 --> 00:49:41.365 book in the handout. 00:49:41.365 --> 00:49:43.240 But this is something that you can definitely 00:49:43.240 --> 00:49:44.710 work on, and make better, because it doesn't have 00:49:44.710 --> 00:49:46.450 many positions in it right now. 00:49:46.450 --> 00:49:47.500 And the main point of an opening book 00:49:47.500 --> 00:49:49.540 is that you store the positions at the beginning of the game 00:49:49.540 --> 00:49:51.052 that you've already pre-computed. 00:49:51.052 --> 00:49:53.260 And that saves time and search, and can store results 00:49:53.260 --> 00:49:54.670 to a higher depth. 00:49:54.670 --> 00:49:57.310 And the KM75 theorem implies it's better 00:49:57.310 --> 00:50:00.220 to keep separate opening books than to keep the same opening 00:50:00.220 --> 00:50:01.570 book for both sides. 00:50:01.570 --> 00:50:03.070 So opening books are really helpful, 00:50:03.070 --> 00:50:05.650 because in the beginning, there's a huge number of moves 00:50:05.650 --> 00:50:06.910 that you could possibly make. 00:50:06.910 --> 00:50:08.720 And searching those takes a lot of time. 00:50:08.720 --> 00:50:11.710 But if you pre-compute them, you can save them for later. 00:50:14.930 --> 00:50:16.705 And another useful table you can keep 00:50:16.705 --> 00:50:18.080 is an end game database, which is 00:50:18.080 --> 00:50:21.710 a table for guiding your chess program through the end game. 00:50:21.710 --> 00:50:24.050 For end game positions, the distance from the end 00:50:24.050 --> 00:50:26.060 might be too far to search entirely. 00:50:26.060 --> 00:50:27.570 So you can pre-compute them. 00:50:27.570 --> 00:50:29.570 And then you store who will win, and how far you 00:50:29.570 --> 00:50:31.130 are from the end of the game. 00:50:31.130 --> 00:50:34.960 And we've given you a c file that you can implement it in. 00:50:44.270 --> 00:50:46.400 OK, so I'll just go through some guidelines, 00:50:46.400 --> 00:50:48.950 some tips for the project. 00:50:48.950 --> 00:50:50.960 I was giving links at most of the bottom 00:50:50.960 --> 00:50:54.770 of the slides for where you can read up more on these topics. 00:50:54.770 --> 00:50:56.550 But there's a chess programming wiki. 00:50:56.550 --> 00:51:00.170 The link is there, which has many more pages about reading 00:51:00.170 --> 00:51:03.933 about chess playing programs. 00:51:03.933 --> 00:51:05.600 Just in general, it's a really good idea 00:51:05.600 --> 00:51:07.142 to test your code often, because it's 00:51:07.142 --> 00:51:09.290 easy to make a mistake with your optimizations. 00:51:09.290 --> 00:51:12.320 And it doesn't appear when you search to fixed depth. 00:51:12.320 --> 00:51:15.470 So if you start up your bot, you can say, like, 00:51:15.470 --> 00:51:17.700 search to depth 5, for example. 00:51:17.700 --> 00:51:20.628 And then it will tell you like how many nodes per seconds 00:51:20.628 --> 00:51:21.170 you searched. 00:51:21.170 --> 00:51:24.320 And then I'll tell you the best move at the end of that search. 00:51:24.320 --> 00:51:27.298 But you should test full games using 00:51:27.298 --> 00:51:29.090 the auto tester, and the cloud auto tester, 00:51:29.090 --> 00:51:32.090 and the script server, just to watch your bot 00:51:32.090 --> 00:51:34.280 to make sure that it doesn't do anything weird. 00:51:34.280 --> 00:51:36.950 And the testing methodology, I went through some of it. 00:51:36.950 --> 00:51:37.730 There's a webgui. 00:51:37.730 --> 00:51:38.870 There's a Java autotester. 00:51:38.870 --> 00:51:40.343 There's a cloud autotester. 00:51:40.343 --> 00:51:42.260 And you can do node counts, which is basically 00:51:42.260 --> 00:51:44.960 just counting the number of nodes in the tree 00:51:44.960 --> 00:51:45.740 that you searched. 00:51:45.740 --> 00:51:47.407 And there's function comparison testing, 00:51:47.407 --> 00:51:49.160 which is, if you optimize a function, 00:51:49.160 --> 00:51:51.290 you should save the old version, and then 00:51:51.290 --> 00:51:52.370 just compare the results. 00:51:55.990 --> 00:52:01.710 PROFESSOR: Let me make a comment about testing. 00:52:01.710 --> 00:52:03.750 I can't tell you how often in this class 00:52:03.750 --> 00:52:09.090 we've had student groups who discover that they've 00:52:09.090 --> 00:52:11.610 made a whole bunch of changes. 00:52:11.610 --> 00:52:14.700 And then there's something wrong with their bot. 00:52:14.700 --> 00:52:17.310 And they can't get back to a stable place 00:52:17.310 --> 00:52:18.420 when things were correct. 00:52:18.420 --> 00:52:20.100 They discover the problem. 00:52:20.100 --> 00:52:23.430 But they've made 30 changes. 00:52:23.430 --> 00:52:27.130 And now, which of those 30 is responsible for the problem? 00:52:27.130 --> 00:52:32.010 So it's really important to test, 00:52:32.010 --> 00:52:33.780 and have a good test infrastructure 00:52:33.780 --> 00:52:34.803 for this project. 00:52:34.803 --> 00:52:36.720 If you have a really good test infrastructure, 00:52:36.720 --> 00:52:40.290 it's really easy to be innovative in the kinds 00:52:40.290 --> 00:52:42.870 of optimizations that you do, because then you 00:52:42.870 --> 00:52:45.055 know that what you're doing is right. 00:52:45.055 --> 00:52:46.680 And then you can make forward progress. 00:52:46.680 --> 00:52:50.400 Otherwise, you'll find yourself self debugging like crazy, 00:52:50.400 --> 00:52:53.130 and not being able to find the bugs. 00:52:53.130 --> 00:52:57.060 Some other tips are, especially when 00:52:57.060 --> 00:52:58.650 we get to the parallel part, it's 00:52:58.650 --> 00:53:02.220 non-deterministic programming. 00:53:02.220 --> 00:53:03.690 And the reason is because as you're 00:53:03.690 --> 00:53:07.350 executing you're going to be looking up things 00:53:07.350 --> 00:53:10.620 in transposition table that you're going to want to share, 00:53:10.620 --> 00:53:15.060 so that if one branch discovers a value then 00:53:15.060 --> 00:53:18.450 another branch can use that. 00:53:18.450 --> 00:53:20.520 So it's really important to be able to turn that 00:53:20.520 --> 00:53:23.880 off so that you're, for example, able to search 00:53:23.880 --> 00:53:25.920 without a transposition table to get all 00:53:25.920 --> 00:53:29.040 the searching stuff right, and be able to turn that 00:53:29.040 --> 00:53:30.220 on independently. 00:53:30.220 --> 00:53:34.360 So that's another really important place to do it. 00:53:34.360 --> 00:53:38.670 Another thing is that when you do timed searches, 00:53:38.670 --> 00:53:42.120 the time it takes to do the search will vary. 00:53:42.120 --> 00:53:44.070 And what you'll end up exploring varies. 00:53:44.070 --> 00:53:49.020 So as much as possible, you wanted to fix depth searches. 00:53:49.020 --> 00:53:52.980 Search to five ply to test something, 00:53:52.980 --> 00:53:56.670 rather than searching for a minute, 00:53:56.670 --> 00:53:59.190 or whatever the amount of time is, 00:53:59.190 --> 00:54:01.800 because when you start searching for time, 00:54:01.800 --> 00:54:04.290 that's, in fact, what you're going to end up doing. 00:54:04.290 --> 00:54:08.580 But you can't repeat what just happened if you end up 00:54:08.580 --> 00:54:10.020 searching for that amount of time 00:54:10.020 --> 00:54:14.220 again, because the machines are not deterministic. 00:54:14.220 --> 00:54:16.380 And there may be something else going 00:54:16.380 --> 00:54:21.000 on that causes the amount of time to be different. 00:54:21.000 --> 00:54:26.130 And so, for example, if you're making a change that 00:54:26.130 --> 00:54:28.410 doesn't affect the logic of the program, 00:54:28.410 --> 00:54:31.710 it's just strictly an optimization, 00:54:31.710 --> 00:54:33.750 you should get exactly the same result 00:54:33.750 --> 00:54:36.930 if you do a five ply search, for example. 00:54:36.930 --> 00:54:39.660 Shouldn't have changed the five ply search. 00:54:39.660 --> 00:54:42.512 Just a five ply search should be faster. 00:54:42.512 --> 00:54:44.470 And so that's a good way-- as much as possible, 00:54:44.470 --> 00:54:48.300 you want to check things that are deterministic and so forth. 00:54:48.300 --> 00:54:52.680 And, really, as I say, I can't emphasize this enough, 00:54:52.680 --> 00:54:54.750 how having a good test infrastructure, 00:54:54.750 --> 00:54:58.410 the ability to control turn off non-determinism, 00:54:58.410 --> 00:55:03.160 the ability to test various parts of this program, 00:55:03.160 --> 00:55:05.430 this is a pretty big piece of code 00:55:05.430 --> 00:55:09.300 for a project of this nature. 00:55:09.300 --> 00:55:11.430 And you'll feel pretty overwhelmed by it 00:55:11.430 --> 00:55:12.540 to begin with. 00:55:12.540 --> 00:55:14.580 Once you settle, you'll discover, 00:55:14.580 --> 00:55:17.970 it's this wonderful thing, where by the end of the project 00:55:17.970 --> 00:55:21.420 everybody feels really confident about their ability to handle 00:55:21.420 --> 00:55:23.243 a decent sized piece of code. 00:55:23.243 --> 00:55:25.660 But when you first get into it, it's like, oh my goodness. 00:55:25.660 --> 00:55:26.577 There's move ordering. 00:55:26.577 --> 00:55:28.050 And there's static evaluation. 00:55:28.050 --> 00:55:29.310 And there's the search. 00:55:29.310 --> 00:55:31.770 And what's going on with that transposition table? 00:55:31.770 --> 00:55:34.200 Because every one of these things has got 00:55:34.200 --> 00:55:35.910 cleverness in it. 00:55:35.910 --> 00:55:39.240 OK, so it's really hard code to deal with. 00:55:39.240 --> 00:55:41.490 But you guys are going to just fine. 00:55:41.490 --> 00:55:48.240 HELEN XU: So this is the eval.c file in the handout. 00:55:48.240 --> 00:55:51.430 So this in 32 here is the evaluation score. 00:55:51.430 --> 00:55:54.510 And the main function is called eval. 00:55:54.510 --> 00:55:56.430 And it takes in a position. 00:55:56.430 --> 00:56:01.020 And it outputs two scores, one for white and one for black. 00:56:03.720 --> 00:56:05.280 And right now, it does-- 00:56:08.720 --> 00:56:10.920 I guess it does counts of the number of pawns. 00:56:10.920 --> 00:56:15.220 OK, so I was talking before about, p between and p central, 00:56:15.220 --> 00:56:17.050 which are you pawn heuristics. 00:56:17.050 --> 00:56:18.730 And so basically, right now, it iterates 00:56:18.730 --> 00:56:20.440 through the entire board. 00:56:20.440 --> 00:56:23.680 You can see for rank and file are just row and column. 00:56:23.680 --> 00:56:26.890 And it looks at each square in the iteration. 00:56:26.890 --> 00:56:30.190 And then it looks at the piece and the color of the piece. 00:56:30.190 --> 00:56:33.152 And based on the type of the piece, it does some evaluation. 00:56:33.152 --> 00:56:35.110 So if it's a pawn, it does the pawn heuristics. 00:56:35.110 --> 00:56:38.380 If it's a fits king, it does these king heuristics. 00:56:38.380 --> 00:56:40.860 And otherwise, or both-- 00:56:40.860 --> 00:56:43.900 or not otherwise, I guess-- 00:56:43.900 --> 00:56:47.122 yeah, in both cases it'll do-- 00:56:47.122 --> 00:56:48.080 this is an old version. 00:56:48.080 --> 00:56:49.163 So it's not there anymore. 00:56:49.163 --> 00:56:51.430 But this is laser coverage, which 00:56:51.430 --> 00:56:55.030 we talked about earlier, which doesn't 00:56:55.030 --> 00:56:56.690 depend on what piece it is. 00:56:56.690 --> 00:57:01.570 This is after you iterate through the entire board. 00:57:01.570 --> 00:57:04.350 And then this isn't here anymore either. 00:57:04.350 --> 00:57:06.100 But we can look at each of these in depth. 00:57:06.100 --> 00:57:07.517 So right now, for example, there's 00:57:07.517 --> 00:57:18.500 p between, which goes through every single pawn 00:57:18.500 --> 00:57:19.280 in your iteration. 00:57:19.280 --> 00:57:21.230 And then it will determine whether or not 00:57:21.230 --> 00:57:26.300 it's between both kings, and the return slide. 00:57:26.300 --> 00:57:30.980 So it will add it to the score, if you find that it's true. 00:57:30.980 --> 00:57:38.920 And there's p central, which takes in a rank and a file. 00:57:38.920 --> 00:57:41.913 And, basically, it increments something, 00:57:41.913 --> 00:57:43.330 or it gives you a bonus, depending 00:57:43.330 --> 00:57:46.863 on how close you are to the center of the board. 00:57:46.863 --> 00:57:47.530 So look at this. 00:57:47.530 --> 00:57:49.630 There's a board with-- 00:57:49.630 --> 00:57:51.740 and F as your file. 00:57:51.740 --> 00:57:52.600 And R is your rank. 00:57:56.860 --> 00:57:59.380 PROFESSOR: I think you have a slightly older version. 00:57:59.380 --> 00:58:01.740 HELEN XU: Potentially. 00:58:01.740 --> 00:58:04.530 PROFESSOR: It's correct on the screen. 00:58:04.530 --> 00:58:06.125 HELEN XU: Is correct in this one? 00:58:06.125 --> 00:58:06.750 AUDIENCE: Yeah. 00:58:25.930 --> 00:58:28.310 HELEN XU: OK, so this is just the-- 00:58:28.310 --> 00:58:29.810 I guess is the most updated version. 00:58:29.810 --> 00:58:31.070 The first one is p central. 00:58:31.070 --> 00:58:33.680 So this just count the difference 00:58:33.680 --> 00:58:35.930 between where you are and the center of the board. 00:58:35.930 --> 00:58:38.750 And it gives you some bonus, depending on how far 00:58:38.750 --> 00:58:40.430 you are from the center. 00:58:40.430 --> 00:58:42.750 And this one is between. 00:58:42.750 --> 00:58:45.472 Yeah, so this is between, which is a helper for p between. 00:58:45.472 --> 00:58:47.180 And it tells you whether or not your pawn 00:58:47.180 --> 00:58:51.200 is in the bounding box determined by the kings. 00:58:51.200 --> 00:58:57.580 And this one is k face, which is given a king, 00:58:57.580 --> 00:59:00.020 you look at its orientation. 00:59:00.020 --> 00:59:02.240 And then you give it a bonus, depending 00:59:02.240 --> 00:59:05.840 on which way you're facing, and how far you 00:59:05.840 --> 00:59:07.730 are from the center, I think-- 00:59:07.730 --> 00:59:10.250 no, how far you are from the opponent. 00:59:10.250 --> 00:59:12.140 So f and r where you are. 00:59:12.140 --> 00:59:18.140 And now it does the delta between you and the opposing 00:59:18.140 --> 00:59:20.520 king. 00:59:20.520 --> 00:59:23.300 And then you do some scaling, depending on which direction 00:59:23.300 --> 00:59:23.960 you're facing. 00:59:23.960 --> 00:59:25.668 So this is just your orientation. 00:59:28.360 --> 00:59:30.790 And then this is k aggressive, which 00:59:30.790 --> 00:59:33.070 gives you a bonus for how far you 00:59:33.070 --> 00:59:35.380 are from the edge of the board. 00:59:35.380 --> 00:59:41.740 So you can see here op square is where do the opposing king is. 00:59:41.740 --> 00:59:47.020 And delta file and delta rank are how far 00:59:47.020 --> 00:59:49.150 you are from the opposing king. 00:59:49.150 --> 00:59:54.130 And then you add the bonus, depending on which case 00:59:54.130 --> 00:59:55.400 the deltas fall into. 00:59:59.700 --> 01:00:04.180 And this gives you a bonus if you're farther 01:00:04.180 --> 01:00:07.180 from the edge of the board. 01:00:07.180 --> 01:00:12.520 Yeah, and there's l coverage, which 01:00:12.520 --> 01:00:15.970 is the most complicated one, probably. 01:00:15.970 --> 01:00:19.090 And, basically, what laser coverage does is that, 01:00:19.090 --> 01:00:20.560 basically, it takes a position. 01:00:20.560 --> 01:00:22.120 And depending on what side you are, 01:00:22.120 --> 01:00:24.203 it generates all the moves that you could possibly 01:00:24.203 --> 01:00:25.300 make from that position. 01:00:25.300 --> 01:00:30.310 So you generate all with color, which 01:00:30.310 --> 01:00:31.720 means that, given your color, you 01:00:31.720 --> 01:00:34.030 generate all the possible moves that you can make. 01:00:34.030 --> 01:00:35.260 And you get a list of moves. 01:00:35.260 --> 01:00:37.060 And you iterate through it. 01:00:37.060 --> 01:00:38.890 And then you make each of them. 01:00:38.890 --> 01:00:40.510 And you draw a laser path. 01:00:40.510 --> 01:00:43.990 And what the laser path does is, basically, it 01:00:43.990 --> 01:00:45.760 bounces off some pause. 01:00:45.760 --> 01:00:49.240 And for each square, you increment the distance, 01:00:49.240 --> 01:00:51.410 basically, along the path. 01:00:51.410 --> 01:00:54.163 And if it takes the minimum distance 01:00:54.163 --> 01:00:56.080 over all these possible paths for each square. 01:00:56.080 --> 01:00:59.290 And if it doesn't touch a square, then it's just 0. 01:00:59.290 --> 01:01:00.710 And it divides it. 01:01:00.710 --> 01:01:01.870 I can go into this. 01:01:04.620 --> 01:01:08.390 So it draws the path through this while true. 01:01:11.970 --> 01:01:14.100 Or this is just changing the orientation 01:01:14.100 --> 01:01:16.290 if you need to bounce off a pawn. 01:01:16.290 --> 01:01:19.990 But this one is setting the-- 01:01:19.990 --> 01:01:21.000 you keep a laser map. 01:01:21.000 --> 01:01:23.670 And you keep the minimum path of a laser 01:01:23.670 --> 01:01:26.250 that would possibly touch that. 01:01:26.250 --> 01:01:31.290 And, no, this is just changing the orientation. 01:01:34.117 --> 01:01:36.450 So then you generate this map for all the possible moves 01:01:36.450 --> 01:01:37.680 that you could do. 01:01:37.680 --> 01:01:39.660 And then you do some scaling. 01:01:39.660 --> 01:01:44.350 So, depending on the distance from the opposing king, 01:01:44.350 --> 01:01:46.350 you iterate through the entire board. 01:01:46.350 --> 01:01:52.110 And you divide the minimum distance 01:01:52.110 --> 01:01:54.670 by the actual distance from the laser. 01:01:54.670 --> 01:01:58.710 So the maximum that this ratio can be is 1. 01:01:58.710 --> 01:02:06.000 And then you multiply it by 1 over the distance. 01:02:08.583 --> 01:02:10.000 So this one is really complicated. 01:02:10.000 --> 01:02:11.790 And there's a lot to optimize here. 01:02:11.790 --> 01:02:13.740 For example, you probably don't have 01:02:13.740 --> 01:02:15.700 to iterate through the entire board 01:02:15.700 --> 01:02:23.280 each time, because even in eval, like here, you 01:02:23.280 --> 01:02:25.290 have to iterate through the entire board 01:02:25.290 --> 01:02:27.092 to find each piece. 01:02:27.092 --> 01:02:28.800 And if you start a better representation, 01:02:28.800 --> 01:02:30.360 you might not have to do that, like if you just 01:02:30.360 --> 01:02:32.010 kept track of where the pawns were, 01:02:32.010 --> 01:02:34.538 because you already keep track of the king separately. 01:02:34.538 --> 01:02:35.830 So that's one thing you can do. 01:02:40.080 --> 01:02:42.000 PROFESSOR: There are two basic strategies 01:02:42.000 --> 01:02:44.820 for changing the representation of the board. 01:02:44.820 --> 01:02:46.740 And maybe there are more. 01:02:46.740 --> 01:02:49.770 But the two basic ones are, instead 01:02:49.770 --> 01:02:55.590 of keeping the whole board with a piece on each square, 01:02:55.590 --> 01:02:58.890 and then having to go and search for where the pieces are, 01:02:58.890 --> 01:03:02.400 you can keep just a list of where the pawns are, 01:03:02.400 --> 01:03:05.010 and what the locations of the kings are, 01:03:05.010 --> 01:03:06.670 so that when you want to make a move, 01:03:06.670 --> 01:03:09.690 you can just go through where they are, 01:03:09.690 --> 01:03:12.420 rather than having to search through all 64 squares 01:03:12.420 --> 01:03:13.800 on the board. 01:03:13.800 --> 01:03:15.570 Then the other strategy that you can do 01:03:15.570 --> 01:03:18.150 is use what's called bit boards, where 01:03:18.150 --> 01:03:27.480 you have a 64-bit word for which, if there's 01:03:27.480 --> 01:03:32.460 a pawn in a given position, you set that bit. 01:03:32.460 --> 01:03:35.970 And so there are different ways of representing 01:03:35.970 --> 01:03:41.860 things that could possibly be, definitely be, more efficient. 01:03:41.860 --> 01:03:43.440 But you have some choices there. 01:03:43.440 --> 01:03:46.260 And also, one of the complexities of this 01:03:46.260 --> 01:03:48.630 is that to change the representation, 01:03:48.630 --> 01:03:50.940 there's going to be places in the code you 01:03:50.940 --> 01:03:56.700 need to find out where they're assuming that things are. 01:03:56.700 --> 01:03:59.310 So you say, oh, I'll change the board representation. 01:03:59.310 --> 01:04:01.530 Oh, I didn't realize that over here, there's 01:04:01.530 --> 01:04:04.410 another place that it's using the board representation, 01:04:04.410 --> 01:04:05.340 and so forth. 01:04:05.340 --> 01:04:08.820 A good strategy for changing board representation 01:04:08.820 --> 01:04:15.720 is to actually keep both representations around 01:04:15.720 --> 01:04:18.600 while you migrate functionality from the old one 01:04:18.600 --> 01:04:20.940 to the new one. 01:04:20.940 --> 01:04:25.620 And then the advantage of that is that you can actually 01:04:25.620 --> 01:04:28.560 then use assertions to say, you know, 01:04:28.560 --> 01:04:32.860 the old one and the new one are the same. 01:04:32.860 --> 01:04:38.385 So implementing conversion functions is really good. 01:04:38.385 --> 01:04:39.760 For example, if you decide you're 01:04:39.760 --> 01:04:42.460 going to use a bit board representation, 01:04:42.460 --> 01:04:45.700 have a function that converts the bit board 01:04:45.700 --> 01:04:50.050 to the standard board so that then you 01:04:50.050 --> 01:04:55.660 can compare whether you've got the same thing. 01:04:55.660 --> 01:05:00.678 And, eventually, you'll want to get rid of that. 01:05:00.678 --> 01:05:02.470 And, of course, that'll slow down you down, 01:05:02.470 --> 01:05:04.480 because you're doing more things. 01:05:04.480 --> 01:05:06.640 But it will allow you to get it correct 01:05:06.640 --> 01:05:08.880 with a new representation. 01:05:08.880 --> 01:05:11.290 And once you've got it correct with a new representation 01:05:11.290 --> 01:05:14.710 with the old one gone, that's when you have a chance 01:05:14.710 --> 01:05:17.320 to make things go fast. 01:05:17.320 --> 01:05:21.430 But it kind of is taking two steps backwards 01:05:21.430 --> 01:05:23.260 to take five steps forward. 01:05:23.260 --> 01:05:27.640 I say not one step and two steps, because really, often, 01:05:27.640 --> 01:05:31.870 you really are slowing things down considerably in order 01:05:31.870 --> 01:05:35.350 to convert from one representation to another. 01:05:35.350 --> 01:05:38.560 The most important thing is you maintain the invariant 01:05:38.560 --> 01:05:41.235 of correctness in your code. 01:05:41.235 --> 01:05:42.610 You do not want to make something 01:05:42.610 --> 01:05:45.340 that goes faster, but is wrong, and have 01:05:45.340 --> 01:05:47.620 to debug the correctness. 01:05:47.620 --> 01:05:52.262 You'd much rather ensure that things are correct, 01:05:52.262 --> 01:05:54.220 are moving to the place that you want to do it. 01:05:54.220 --> 01:05:58.600 And then you can optimize for performance. 01:05:58.600 --> 01:06:00.250 So the most important thing is keep 01:06:00.250 --> 01:06:02.122 that invariant of correctness. 01:06:02.122 --> 01:06:03.580 And that's where the testing and so 01:06:03.580 --> 01:06:06.700 forth comes in, having good test infrastructure, 01:06:06.700 --> 01:06:09.400 and having assertions littered throughout your code. 01:06:09.400 --> 01:06:12.820 HELEN XU: And then we can go through the [INAUDIBLE].. 01:06:17.010 --> 01:06:20.760 Actually, OK, so, just as an example 01:06:20.760 --> 01:06:23.610 of how you would possibly, one way 01:06:23.610 --> 01:06:27.000 of determining whether or not you state correct-- 01:06:27.000 --> 01:06:31.560 so this is an example of a place where I compiled the code. 01:06:31.560 --> 01:06:33.857 See the binary code is called Lesierchess. 01:06:33.857 --> 01:06:35.940 And if you look at help, it gives you some options 01:06:35.940 --> 01:06:37.596 for what you can do. 01:06:40.490 --> 01:06:41.890 For example, there's display. 01:06:41.890 --> 01:06:43.430 And that's the opening position. 01:06:43.430 --> 01:06:45.410 And let's say I want to search. 01:06:45.410 --> 01:06:49.460 So I do a fixed depth, and go depth three. 01:06:49.460 --> 01:06:52.910 And it tells me the number of nodes 01:06:52.910 --> 01:06:55.790 that I searched at each depth. 01:06:55.790 --> 01:06:59.660 And so if you make changes, if they are deterministic, 01:06:59.660 --> 01:07:01.752 these node counts should stay the same. 01:07:01.752 --> 01:07:02.960 So that's one way of telling. 01:07:02.960 --> 01:07:04.335 So you should keep track of this, 01:07:04.335 --> 01:07:05.960 and make sure that they're the same. 01:07:05.960 --> 01:07:09.020 And also, you can do perft, which 01:07:09.020 --> 01:07:12.680 gives you the number of possible moves you can make. 01:07:12.680 --> 01:07:16.270 And that should be the same, no matter what you do. 01:07:19.312 --> 01:07:20.520 So that's one way of testing. 01:07:20.520 --> 01:07:23.150 There's other ways. 01:07:23.150 --> 01:07:27.150 So if you go to higher depth, you'll get more node counts. 01:07:30.600 --> 01:07:35.430 And here, this is nodes that you searched at this depth. 01:07:35.430 --> 01:07:37.150 And this is nodes per second. 01:07:37.150 --> 01:07:38.650 So you want to make this one faster. 01:07:47.638 --> 01:07:48.930 So that's how you run the code. 01:07:52.220 --> 01:07:55.100 And I was supposed to do a demo for the auto tester. 01:07:57.790 --> 01:07:59.210 So let's say I wanted to do-- 01:08:02.010 --> 01:08:05.325 so when I made it, it's in a binary called Lesierchess. 01:08:08.620 --> 01:08:11.390 And then here, you can type in commands. 01:08:11.390 --> 01:08:13.710 So you're basically just typing commands from this. 01:08:13.710 --> 01:08:16.470 Like, you run your binary. 01:08:16.470 --> 01:08:20.310 PROFESSOR: This is the UCI interface that we talked about. 01:08:20.310 --> 01:08:25.240 And in Lesierchess.c is the implementation of that. 01:08:25.240 --> 01:08:29.670 And so if you want to add your commands to it to help debug, 01:08:29.670 --> 01:08:32.550 you can enter-- if we go into Lesierchess.c, 01:08:32.550 --> 01:08:34.350 you can see the table. 01:08:39.941 --> 01:08:41.399 What I want to do is show the table 01:08:41.399 --> 01:08:45.270 of all the options, which is-- 01:08:45.270 --> 01:08:46.560 there we go, OK. 01:08:46.560 --> 01:08:48.350 HELEN XU: This is just the heuristics. 01:08:48.350 --> 01:08:51.149 PROFESSOR: So these are tables of heuristics 01:08:51.149 --> 01:08:56.460 and so forth, which allow you to set 01:08:56.460 --> 01:09:02.939 the values of the various things, 01:09:02.939 --> 01:09:05.729 and to say, how much is this heuristic 01:09:05.729 --> 01:09:08.069 worth to the static evaluation? 01:09:10.950 --> 01:09:12.600 And through these, all these can be 01:09:12.600 --> 01:09:15.569 set, so you don't have to recompile 01:09:15.569 --> 01:09:20.100 the binary if you want to try out things with different-- 01:09:20.100 --> 01:09:22.830 if you want to auto test with, let 01:09:22.830 --> 01:09:25.229 me count this as worth a third of a pawn. 01:09:25.229 --> 01:09:29.580 Let me count this as worth half a pawn, or whatever. 01:09:29.580 --> 01:09:32.790 You can just enter it through the UCI interface. 01:09:32.790 --> 01:09:35.383 And in the auto tester, you can specify that. 01:09:35.383 --> 01:09:37.800 So it will just test those without you having to recompile 01:09:37.800 --> 01:09:40.710 binaries for every one of them. 01:09:40.710 --> 01:09:43.600 And so there's a table here which basically says, 01:09:43.600 --> 01:09:45.210 what's the name of the heuristic? 01:09:45.210 --> 01:09:48.330 What's the variable that is going to be 01:09:48.330 --> 01:09:52.109 set what the default value is? 01:09:52.109 --> 01:09:55.770 And pawn ev value is the value of a pawn. 01:09:55.770 --> 01:09:59.790 And if there's any restrictions on the range of those values, 01:09:59.790 --> 01:10:01.440 what's the smallest it can be? 01:10:01.440 --> 01:10:03.990 What's the largest it can be? 01:10:03.990 --> 01:10:07.470 So you can edit this table, and so forth. 01:10:07.470 --> 01:10:11.570 And as I say, you can set it through the UCI interface. 01:10:11.570 --> 01:10:14.730 So it's really a very flexible way 01:10:14.730 --> 01:10:18.630 of getting access to anything that you want to do. 01:10:18.630 --> 01:10:21.360 You can put your own commands in there, 01:10:21.360 --> 01:10:24.030 including new heuristics, or whatever. 01:10:27.870 --> 01:10:29.430 And there's some things in there. 01:10:29.430 --> 01:10:32.370 For example, if we go to the other part 01:10:32.370 --> 01:10:41.500 where they actually are passing the UCI stuff, 01:10:41.500 --> 01:10:43.090 so it basically takes it. 01:10:43.090 --> 01:10:45.760 It parses it, figures out what the command is, and then 01:10:45.760 --> 01:10:47.080 implements the command. 01:10:47.080 --> 01:10:50.220 So all that kind of stuff, you have control over. 01:10:50.220 --> 01:10:55.970 So that that will help you in choosing to do other things. 01:10:55.970 --> 01:10:59.030 So, for example, if you search for perft or something 01:10:59.030 --> 01:10:59.530 in there-- 01:11:02.500 --> 01:11:04.630 so if you have perft, here's what 01:11:04.630 --> 01:11:06.220 the correct outputs should be. 01:11:06.220 --> 01:11:09.910 And now, here's the code that it executes. 01:11:09.910 --> 01:11:11.682 And perft is in a different file. 01:11:11.682 --> 01:11:13.390 I think it's in the move generation file. 01:11:21.262 --> 01:11:24.070 HELEN XU: Do I have the wrong output? 01:11:24.070 --> 01:11:26.080 PROFESSOR: That may be for the older game, yeah. 01:11:26.080 --> 01:11:28.420 I actually noticed a couple of other bugs in there 01:11:28.420 --> 01:11:31.960 that hadn't been fixed. 01:11:31.960 --> 01:11:34.450 So we will make sure that those are-- 01:11:34.450 --> 01:11:36.810 basically, it's just dead code, is what's in there. 01:11:36.810 --> 01:11:38.560 We need to clean up some of the dead code. 01:11:38.560 --> 01:11:40.030 Some of the code is from last year. 01:11:40.030 --> 01:11:41.830 And we changed the game. 01:11:41.830 --> 01:11:43.900 And not all the dead code got eliminated. 01:11:43.900 --> 01:11:46.150 HELEN XU: That'll be fixed for when I make the repost. 01:11:46.150 --> 01:11:46.817 PROFESSOR: Yeah. 01:11:49.660 --> 01:11:53.530 So we're just finishing up some-- 01:11:53.530 --> 01:11:56.710 right now, I think it's all cleanliness. 01:11:56.710 --> 01:11:59.080 But if you find any bugs like that, let us know. 01:11:59.080 --> 01:12:02.080 We'll fix them, and so forth. 01:12:02.080 --> 01:12:08.260 Appreciate if you do see other inconsistencies, 01:12:08.260 --> 01:12:09.374 or what have you. 01:12:13.110 --> 01:12:18.360 Good, so great project, this is like lots of fun. 01:12:18.360 --> 01:12:21.005 Next month is going to be lots of fun for all of you. 01:12:21.005 --> 01:12:23.130 You may not think it's fun every minute of the day. 01:12:23.130 --> 01:12:26.310 But you'll have a good time. 01:12:26.310 --> 01:12:28.160 It is fun.