1 00:00:00,080 --> 00:00:02,430 The following content is provided under a Creative 2 00:00:02,430 --> 00:00:03,810 Commons license. 3 00:00:03,810 --> 00:00:06,060 Your support will help MIT OpenCourseWare 4 00:00:06,060 --> 00:00:10,150 continue to offer high quality educational resources for free. 5 00:00:10,150 --> 00:00:12,700 To make a donation or to view additional materials 6 00:00:12,700 --> 00:00:16,600 from hundreds of MIT courses, visit MIT OpenCourseWare 7 00:00:16,600 --> 00:00:17,305 at ocw.mit.edu. 8 00:00:25,941 --> 00:00:27,316 PROFESSOR: Everyone, welcome back 9 00:00:27,316 --> 00:00:28,565 to Poker Theory and Analytics. 10 00:00:28,565 --> 00:00:31,760 We're very lucky today to have a guest speaker, Matt Hawrilenko. 11 00:00:31,760 --> 00:00:34,340 Matt's background is really interesting. 12 00:00:34,340 --> 00:00:37,130 He was a Princeton grad who went to work for a Cisco 13 00:00:37,130 --> 00:00:38,880 International group for a couple of years, 14 00:00:38,880 --> 00:00:40,838 and then he left to become a professional poker 15 00:00:40,838 --> 00:00:41,640 player full time. 16 00:00:41,640 --> 00:00:44,180 He was considered one of the best limit hold'em players 17 00:00:44,180 --> 00:00:47,165 in the world in addition to winning a World Series of Poker 18 00:00:47,165 --> 00:00:48,070 bracelet. 19 00:00:48,070 --> 00:00:49,720 More recently he retired from poker 20 00:00:49,720 --> 00:00:52,380 and is focusing on clinical psychology 21 00:00:52,380 --> 00:00:54,910 where he studies in Boston at both Clark 22 00:00:54,910 --> 00:00:56,730 University and Harvard. 23 00:00:56,730 --> 00:00:59,570 So with that, I'll pass it along to Matt Hawrilenko. 24 00:00:59,570 --> 00:01:01,920 [APPLAUSE] 25 00:01:03,906 --> 00:01:04,739 MATT HAWRILENKO: OK. 26 00:01:04,739 --> 00:01:05,238 Hey. 27 00:01:05,238 --> 00:01:07,230 So I'm super excited to be here today. 28 00:01:07,230 --> 00:01:10,280 And as I understand, I've been told that I'm your second game 29 00:01:10,280 --> 00:01:12,680 theory guy. 30 00:01:12,680 --> 00:01:15,391 And I guess Bill, Bill Chen, one of my best friends 31 00:01:15,391 --> 00:01:16,890 in poker who I've done a lot of work 32 00:01:16,890 --> 00:01:18,807 with came in and talked to you guys last week. 33 00:01:18,807 --> 00:01:20,640 I'm going to take a slightly different angle 34 00:01:20,640 --> 00:01:21,930 than Bill did last week. 35 00:01:21,930 --> 00:01:23,880 So first I kind of just want to get 36 00:01:23,880 --> 00:01:25,290 a sense of who's in the room. 37 00:01:25,290 --> 00:01:27,530 So my presumption is that there might 38 00:01:27,530 --> 00:01:30,780 be sort of like widely varying levels of experience 39 00:01:30,780 --> 00:01:32,080 with game theory. 40 00:01:32,080 --> 00:01:37,450 So if you just don't mind kind of helping me out, 41 00:01:37,450 --> 00:01:39,890 so who here has seen a game theory game before, 42 00:01:39,890 --> 00:01:41,950 like prisoner's dilemma, something like that? 43 00:01:41,950 --> 00:01:42,450 OK. 44 00:01:42,450 --> 00:01:44,702 So most of us. 45 00:01:44,702 --> 00:01:47,160 Who here has actually solved a couple of game theory games, 46 00:01:47,160 --> 00:01:50,376 like with pen and paper, matrix algebra, whatever? 47 00:01:50,376 --> 00:01:51,252 OK. 48 00:01:51,252 --> 00:01:52,900 About half. 49 00:01:52,900 --> 00:01:55,680 Has anyone actually taken a game theory class? 50 00:01:55,680 --> 00:01:56,320 All right. 51 00:01:56,320 --> 00:01:57,180 Great. 52 00:01:57,180 --> 00:02:00,410 So I'm kind of hoping this talk is 53 00:02:00,410 --> 00:02:04,620 sort of going to be equally useful for everyone, 54 00:02:04,620 --> 00:02:06,730 but we'll find out. 55 00:02:06,730 --> 00:02:09,850 So Bill talked to you guys about Cepheus last week. 56 00:02:09,850 --> 00:02:13,270 I'm going to talk about something a little different 57 00:02:13,270 --> 00:02:14,520 than Bill usually talks about. 58 00:02:14,520 --> 00:02:17,700 So I'm going to try to talk about how to play good poker. 59 00:02:17,700 --> 00:02:20,820 And so if we think of this problem of playing good poker 60 00:02:20,820 --> 00:02:22,100 is this big game space. 61 00:02:22,100 --> 00:02:26,700 There are two ways that people generally approach it 62 00:02:26,700 --> 00:02:29,430 in that they'll take a read-based approach, which 63 00:02:29,430 --> 00:02:31,990 is pretty much what everybody does, right? 64 00:02:31,990 --> 00:02:34,230 You try to figure out what the other guy has, 65 00:02:34,230 --> 00:02:37,185 what he might have, and go from there. 66 00:02:37,185 --> 00:02:38,890 You can take a game theoretic approach. 67 00:02:38,890 --> 00:02:40,850 So I'm going to try today discriminate 68 00:02:40,850 --> 00:02:43,080 a little bit between these two approaches, 69 00:02:43,080 --> 00:02:45,460 and I'm going to talk about why, whatever level of poker 70 00:02:45,460 --> 00:02:48,250 you're at, game theory is something they can complement 71 00:02:48,250 --> 00:02:50,190 your game or just be your game. 72 00:02:50,190 --> 00:02:51,480 For me it is my game. 73 00:02:54,555 --> 00:02:56,180 And broadly speaking, the reason that I 74 00:02:56,180 --> 00:02:59,570 think game theory is particularly useful for poker 75 00:02:59,570 --> 00:03:01,290 goes something like this. 76 00:03:01,290 --> 00:03:05,180 So one of the things that I love to do off the table, 77 00:03:05,180 --> 00:03:05,722 I do jujitsu. 78 00:03:05,722 --> 00:03:07,096 Which if you guys don't know what 79 00:03:07,096 --> 00:03:09,510 that is, it's kind of like wrestling where you're trying 80 00:03:09,510 --> 00:03:12,210 to choke the guy or hyperextend their arm or something 81 00:03:12,210 --> 00:03:13,190 like that. 82 00:03:13,190 --> 00:03:15,900 And when you start out doing jujitsu, 83 00:03:15,900 --> 00:03:18,500 you start out as a white belt, and you're competing against, 84 00:03:18,500 --> 00:03:20,770 rolling with other white belts. 85 00:03:20,770 --> 00:03:23,620 And you can learn this whole repertoire of moves. 86 00:03:23,620 --> 00:03:26,410 And tons of stuff works against white belts, right? 87 00:03:26,410 --> 00:03:27,910 Like, whatever you do, it's probably 88 00:03:27,910 --> 00:03:29,900 going to work against white belts. 89 00:03:29,900 --> 00:03:32,960 As you get better or as you start 90 00:03:32,960 --> 00:03:35,310 going against better competition-- blue belts, 91 00:03:35,310 --> 00:03:37,440 purple, brown, black belts-- a lot 92 00:03:37,440 --> 00:03:41,370 of the moves that worked against white belts don't work anymore. 93 00:03:41,370 --> 00:03:44,200 Not only do they not work, they can 94 00:03:44,200 --> 00:03:47,630 tend to get you in quite a lot of trouble. 95 00:03:47,630 --> 00:03:49,370 So I think that the best way to approach 96 00:03:49,370 --> 00:03:51,740 this game is from day one, you're not 97 00:03:51,740 --> 00:03:53,290 training to be white belts. 98 00:03:53,290 --> 00:03:56,080 You're training to be black belts, right? 99 00:03:56,080 --> 00:03:59,070 You want to learn the moves that work all the way along 100 00:03:59,070 --> 00:04:00,527 against the best competition. 101 00:04:00,527 --> 00:04:02,860 And I think it's sort of the same way with poker, right? 102 00:04:02,860 --> 00:04:05,026 So if you think about it, if you play in a home game 103 00:04:05,026 --> 00:04:06,810 or whatever with a bunch of buddies, 104 00:04:06,810 --> 00:04:10,600 you might have one strategy that works fairly well, right? 105 00:04:10,600 --> 00:04:14,701 Maybe you play really tight, you bet a lot with your best hands, 106 00:04:14,701 --> 00:04:15,950 and you don't bluff that much. 107 00:04:15,950 --> 00:04:17,870 And this works really well because most people 108 00:04:17,870 --> 00:04:21,450 don't really have a sense of what's what, 109 00:04:21,450 --> 00:04:22,760 of the strength of hands. 110 00:04:22,760 --> 00:04:24,230 They overvalue their hands. 111 00:04:24,230 --> 00:04:28,650 So you take that strategy to the Bellagio 112 00:04:28,650 --> 00:04:32,900 and you play in even mid limit games with reasonable players, 113 00:04:32,900 --> 00:04:35,480 and all of a sudden you're starting to get eaten alive. 114 00:04:35,480 --> 00:04:39,810 So I'm going to talk about how game theory can sort of help 115 00:04:39,810 --> 00:04:42,740 you avoid this and help you be strong and grow stronger 116 00:04:42,740 --> 00:04:44,199 all the way along. 117 00:04:44,199 --> 00:04:45,740 So now if we think about game theory, 118 00:04:45,740 --> 00:04:48,720 really there are two audiences that we could be speaking to, 119 00:04:48,720 --> 00:04:49,220 right? 120 00:04:49,220 --> 00:04:52,240 So Bill came in last week and he talked 121 00:04:52,240 --> 00:04:58,740 about Cepheus, this algorithm that solved my best game. 122 00:04:58,740 --> 00:05:01,100 And, well, that is sad for me. 123 00:05:01,100 --> 00:05:04,320 I'm not going to spend a lot of time dwelling on that here. 124 00:05:04,320 --> 00:05:07,130 Rather I'm going to talk about what humans can do, 125 00:05:07,130 --> 00:05:11,270 how humans can apply game theory at the table to their game. 126 00:05:14,420 --> 00:05:15,950 And this is for a couple of reasons, 127 00:05:15,950 --> 00:05:20,590 but maybe the bigger one is I've had a fair bit of math, 128 00:05:20,590 --> 00:05:23,740 but I can't solve the kinds of problems that Bill can solve. 129 00:05:23,740 --> 00:05:26,850 But my work has sort of been on taking game theory, 130 00:05:26,850 --> 00:05:29,150 taking these concepts, and really using them 131 00:05:29,150 --> 00:05:30,170 in a practical sense. 132 00:05:30,170 --> 00:05:31,760 So that's what I want to talk about today. 133 00:05:31,760 --> 00:05:32,730 So if we're thinking about this there 134 00:05:32,730 --> 00:05:34,320 are, again, a couple angles we could take. 135 00:05:34,320 --> 00:05:36,486 We could talk about it from a theoretic perspective. 136 00:05:36,486 --> 00:05:37,770 We could solve a lot of games. 137 00:05:37,770 --> 00:05:40,350 We could solve dynamical systems, 138 00:05:40,350 --> 00:05:41,580 and see how that works. 139 00:05:41,580 --> 00:05:43,290 Or we could talk about it in practice. 140 00:05:43,290 --> 00:05:44,539 What does game theory tell me? 141 00:05:44,539 --> 00:05:46,957 How does it tell me I should think about this situation? 142 00:05:46,957 --> 00:05:48,540 Of course, I think the theory practice 143 00:05:48,540 --> 00:05:50,370 dichotomy is a false economy. 144 00:05:50,370 --> 00:05:54,120 So what I want to do is I want to spend a little bit a time 145 00:05:54,120 --> 00:05:56,900 solving some really, really simple toy games, two toy 146 00:05:56,900 --> 00:05:57,720 games. 147 00:05:57,720 --> 00:06:00,070 And I want to sort of use that to bridge the theory 148 00:06:00,070 --> 00:06:01,330 and practice gap. 149 00:06:01,330 --> 00:06:04,580 So I want to take a couple of toy games 150 00:06:04,580 --> 00:06:08,180 and then apply them to a real hand of high stakes poker 151 00:06:08,180 --> 00:06:08,680 I played. 152 00:06:08,680 --> 00:06:12,375 So I'm going to use that hand to motivate how we might 153 00:06:12,375 --> 00:06:14,760 apply some of these ideas. 154 00:06:14,760 --> 00:06:17,780 So then finally at the end of the day, 155 00:06:17,780 --> 00:06:19,350 we can come up with a list, right? 156 00:06:19,350 --> 00:06:21,320 We can think of a rule-based strategy. 157 00:06:21,320 --> 00:06:24,670 That's something that learning from Cepheus might give you. 158 00:06:24,670 --> 00:06:29,572 It might tell you what to do in every specific situation. 159 00:06:29,572 --> 00:06:30,530 But that's really hard. 160 00:06:30,530 --> 00:06:31,350 Poker's really big. 161 00:06:31,350 --> 00:06:33,390 You can't really remember all of that. 162 00:06:33,390 --> 00:06:37,540 So the thing that I really hope you guys take away from my talk 163 00:06:37,540 --> 00:06:41,190 today is some training principles, some ways 164 00:06:41,190 --> 00:06:44,170 to think about the game which, as you finish this class 165 00:06:44,170 --> 00:06:47,810 I guess in a couple of days and move on throughout your poker 166 00:06:47,810 --> 00:06:51,480 careers, whatever those might be, 167 00:06:51,480 --> 00:06:53,980 some tools that can sort of help you 168 00:06:53,980 --> 00:06:56,880 continue working on your game. 169 00:06:56,880 --> 00:07:01,025 So let's just get going. 170 00:07:01,025 --> 00:07:05,300 So sometimes in poker we get put in really tough spots, 171 00:07:05,300 --> 00:07:07,340 and it can start to feel like we're trying 172 00:07:07,340 --> 00:07:09,770 to guess our way out of them. 173 00:07:09,770 --> 00:07:11,840 Varying degrees of guess our way out of them. 174 00:07:11,840 --> 00:07:14,960 Sometimes we might be sort of making educated guesses, 175 00:07:14,960 --> 00:07:16,740 sometimes they might be less educated. 176 00:07:16,740 --> 00:07:19,220 But what do we do? 177 00:07:19,220 --> 00:07:22,450 What do you do in that really tough spot where you just 178 00:07:22,450 --> 00:07:24,800 don't know what's going on? 179 00:07:24,800 --> 00:07:28,480 So this happened to me a couple of years ago in-- this 180 00:07:28,480 --> 00:07:29,830 happens to me all the time. 181 00:07:29,830 --> 00:07:34,439 But this happened to me a couple of years ago in a World Series 182 00:07:34,439 --> 00:07:35,480 tournament that I played. 183 00:07:35,480 --> 00:07:36,021 We were deep. 184 00:07:36,021 --> 00:07:37,229 We were in the money. 185 00:07:37,229 --> 00:07:39,270 And the one thing I want you guys to keep in mind 186 00:07:39,270 --> 00:07:41,353 here is I'm playing this hand against a player who 187 00:07:41,353 --> 00:07:43,970 is just much better than me. 188 00:07:43,970 --> 00:07:47,090 So that sucks. 189 00:07:47,090 --> 00:07:48,720 On the other hand, I have aces. 190 00:07:48,720 --> 00:07:49,830 So what I'm going to do is I'm going to take you really 191 00:07:49,830 --> 00:07:52,790 briefly through the hand and let you know how I was thinking 192 00:07:52,790 --> 00:07:55,920 about it, and we'll kind of look at it 193 00:07:55,920 --> 00:07:57,550 from a couple perspectives. 194 00:07:57,550 --> 00:08:01,810 So we're both really, really deep. 195 00:08:01,810 --> 00:08:04,666 The blinds are 12 and 24,000 with a $3,000 ante, 196 00:08:04,666 --> 00:08:05,540 and we're six handed. 197 00:08:05,540 --> 00:08:07,206 So I raise two off the button with aces. 198 00:08:07,206 --> 00:08:09,070 I raise a little bit, he calls. 199 00:08:09,070 --> 00:08:10,640 Flop comes, king, jack, eight. 200 00:08:10,640 --> 00:08:13,190 He checks, I bet, he calls. 201 00:08:13,190 --> 00:08:13,940 It turns a five. 202 00:08:13,940 --> 00:08:15,880 He checks, I bet about 2/3 of the pot. 203 00:08:15,880 --> 00:08:17,800 He calls. 204 00:08:17,800 --> 00:08:19,300 And then the river's a king. 205 00:08:19,300 --> 00:08:21,470 And then he reaches for his chips, and I feel good. 206 00:08:21,470 --> 00:08:23,570 I'm like, oh, money. 207 00:08:23,570 --> 00:08:29,070 And then he bets just about $1.1 million to a $700,000 pot. 208 00:08:29,070 --> 00:08:32,095 And now I'm like, I don't know. 209 00:08:32,095 --> 00:08:33,086 I have no idea. 210 00:08:33,086 --> 00:08:34,169 So he's betting I'm happy. 211 00:08:34,169 --> 00:08:35,419 I see the amount. 212 00:08:35,419 --> 00:08:37,340 I'm confused. 213 00:08:37,340 --> 00:08:40,530 So here's how the hand looks. 214 00:08:40,530 --> 00:08:43,882 So I'm sitting there and I'm just 215 00:08:43,882 --> 00:08:45,340 trying to get a sense of his range, 216 00:08:45,340 --> 00:08:48,210 and I'm thinking, like, bet of 1.5 times the pot. 217 00:08:48,210 --> 00:08:49,590 What does that mean? 218 00:08:49,590 --> 00:08:51,570 What kind of hands is he betting so much with? 219 00:08:51,570 --> 00:08:53,540 Why isn't he putting me all in? 220 00:08:53,540 --> 00:08:54,950 Why is it a little below all in? 221 00:08:54,950 --> 00:08:57,350 Is he trying to entice me? 222 00:08:57,350 --> 00:08:59,930 Or maybe he's trying to save $300,000 if I fold. 223 00:08:59,930 --> 00:09:03,100 All these thoughts are going through my head. 224 00:09:03,100 --> 00:09:06,045 So before we talk about what I did, I'm actually curious. 225 00:09:06,045 --> 00:09:08,170 Are you guys happy with the information I gave you? 226 00:09:08,170 --> 00:09:10,769 Is there more information that you want? 227 00:09:10,769 --> 00:09:11,810 What do you want to know? 228 00:09:11,810 --> 00:09:14,445 AUDIENCE: How big is the gap between getting out 229 00:09:14,445 --> 00:09:15,831 now and getting out next? 230 00:09:15,831 --> 00:09:17,330 MATT HAWRILENKO: Ooh, good question. 231 00:09:17,330 --> 00:09:21,519 So let's just say it's pretty linear at this point. 232 00:09:21,519 --> 00:09:22,060 AUDIENCE: OK. 233 00:09:24,935 --> 00:09:27,132 MATT HAWRILENKO: Anything else you want to know? 234 00:09:27,132 --> 00:09:28,310 Oh, you want to know lots. 235 00:09:28,310 --> 00:09:28,920 What do you want to know? 236 00:09:28,920 --> 00:09:30,870 AUDIENCE: Has he shown down big bluffs? 237 00:09:30,870 --> 00:09:33,010 MATT HAWRILENKO: Has he shown down big bluffs? 238 00:09:33,010 --> 00:09:37,342 Good question, we've played with him a little bit, 239 00:09:37,342 --> 00:09:39,950 and I don't actually recall. 240 00:09:39,950 --> 00:09:43,335 But he's certainly capable of showing down big bluffs. 241 00:09:43,335 --> 00:09:45,800 I fancied myself a pretty good player at the time, 242 00:09:45,800 --> 00:09:48,799 and he is someone that I would consider one 243 00:09:48,799 --> 00:09:50,090 of the top players in the game. 244 00:09:53,400 --> 00:09:54,700 Anything else? 245 00:09:54,700 --> 00:09:55,250 Anyone else? 246 00:09:55,250 --> 00:09:55,833 Any questions? 247 00:09:58,770 --> 00:09:59,270 Right. 248 00:09:59,270 --> 00:10:00,350 And so it sounds like what you're 249 00:10:00,350 --> 00:10:02,350 trying to do is you're trying to get a sense of, 250 00:10:02,350 --> 00:10:03,401 what is his range? 251 00:10:03,401 --> 00:10:05,150 Does he have a lot of bluffs in this spot? 252 00:10:05,150 --> 00:10:08,700 Does he have any bluffs in this spot? 253 00:10:08,700 --> 00:10:11,587 And I think that's how pretty much most of us 254 00:10:11,587 --> 00:10:12,670 tend to approach the game. 255 00:10:12,670 --> 00:10:15,580 It's most natural way to approach the game. 256 00:10:15,580 --> 00:10:16,810 Is he bluffing, isn't he? 257 00:10:16,810 --> 00:10:20,030 Does he have too many bluffs here? 258 00:10:20,030 --> 00:10:21,530 Out of curiosity, does anyone want 259 00:10:21,530 --> 00:10:24,129 to stare him down for tells? 260 00:10:24,129 --> 00:10:25,420 Nobody wants to stare him down. 261 00:10:25,420 --> 00:10:26,795 You might want to stare him down. 262 00:10:26,795 --> 00:10:28,238 This guy wants to stare him down. 263 00:10:28,238 --> 00:10:30,437 [LAUGHTER] 264 00:10:30,437 --> 00:10:32,270 This guy definitely wants to stare him down. 265 00:10:35,390 --> 00:10:38,237 This guy wants to stare him down for sure. 266 00:10:38,237 --> 00:10:40,070 By the way, if you get this look, good work. 267 00:10:40,070 --> 00:10:41,320 It means you've done your job. 268 00:10:41,320 --> 00:10:42,210 It's uncomfortable. 269 00:10:42,210 --> 00:10:45,560 But I want to tell you exactly what he's thinking right now. 270 00:10:45,560 --> 00:10:47,850 What he's thinking goes something kind of like this. 271 00:10:47,850 --> 00:10:50,290 [MUSIC PLAYING] 272 00:10:53,086 --> 00:10:54,460 But it can feel like this, right? 273 00:10:54,460 --> 00:10:58,660 Tough players can put us in spots where we're just thinking 274 00:10:58,660 --> 00:11:00,870 about monkeys clashing symbols. 275 00:11:00,870 --> 00:11:02,400 And when we don't have a repertoire, 276 00:11:02,400 --> 00:11:05,700 I think, that we start reading really heavily 277 00:11:05,700 --> 00:11:07,970 into small signals, right? 278 00:11:07,970 --> 00:11:10,320 We're trying to figure something out. 279 00:11:10,320 --> 00:11:12,730 So generally speaking, my view, there 280 00:11:12,730 --> 00:11:14,440 are some tells that are OK. 281 00:11:14,440 --> 00:11:19,480 There are some tells that kind of work against weak players 282 00:11:19,480 --> 00:11:22,190 and less and less against better players. 283 00:11:22,190 --> 00:11:26,810 But these are small signals in a whole lot of noise. 284 00:11:26,810 --> 00:11:29,570 Very small signal in a very noisy environment. 285 00:11:29,570 --> 00:11:33,840 Certainly not something to build a career on, right? 286 00:11:33,840 --> 00:11:36,365 In the big games, you rarely see tells. 287 00:11:36,365 --> 00:11:38,740 You just don't see them enough for that to be profitable. 288 00:11:41,370 --> 00:11:43,650 But actually some people do build careers on them. 289 00:11:43,650 --> 00:11:46,720 So FBI interrogators build careers 290 00:11:46,720 --> 00:11:48,640 on these kinds of tells. 291 00:11:48,640 --> 00:11:50,444 So how do they do? 292 00:11:50,444 --> 00:11:52,360 Well, we actually have some data in that spot. 293 00:11:52,360 --> 00:11:54,068 There have been a whole series of studies 294 00:11:54,068 --> 00:11:56,670 where basically the paradigm is you bring in some FBI 295 00:11:56,670 --> 00:11:59,150 interrogators, and then you bring in some random people 296 00:11:59,150 --> 00:12:00,190 from the street. 297 00:12:00,190 --> 00:12:03,020 And you have them watch someone interview a person. 298 00:12:03,020 --> 00:12:05,270 And then at the end of the day you have to figure out, 299 00:12:05,270 --> 00:12:09,940 is this person telling the truth, or is this person lying? 300 00:12:09,940 --> 00:12:11,430 How do you think they do? 301 00:12:11,430 --> 00:12:12,140 AUDIENCE: Same. 302 00:12:12,140 --> 00:12:13,056 MATT HAWRILENKO: Same? 303 00:12:13,056 --> 00:12:13,930 Yeah. 304 00:12:13,930 --> 00:12:15,500 Same in every category. 305 00:12:15,500 --> 00:12:18,820 So everyone is basically chance, or maybe like 53%. 306 00:12:18,820 --> 00:12:20,940 So they do exactly the same as the random people 307 00:12:20,940 --> 00:12:23,940 off the street, these body language experts, 308 00:12:23,940 --> 00:12:25,960 except for one difference. 309 00:12:25,960 --> 00:12:29,960 The one difference is they are way more confident 310 00:12:29,960 --> 00:12:31,521 that they are right, OK? 311 00:12:31,521 --> 00:12:33,270 So you ask them their level of confidence, 312 00:12:33,270 --> 00:12:35,200 and most people are like, eh, I don't know. 313 00:12:35,200 --> 00:12:36,400 Like 50%. 314 00:12:36,400 --> 00:12:40,110 The interrogators are, like, 90% sure that they're right. 315 00:12:40,110 --> 00:12:43,575 So they're not alone, right? 316 00:12:43,575 --> 00:12:46,200 So I don't know if you guys have heard of self-assessment bias. 317 00:12:46,200 --> 00:12:48,210 It's one of my favorite biases. 318 00:12:48,210 --> 00:12:50,370 So one more study. 319 00:12:50,370 --> 00:12:54,620 So it was sort of motivated by this old study of GE engineers. 320 00:12:54,620 --> 00:12:56,200 It's like 30 years ago. 321 00:12:56,200 --> 00:13:02,380 And what they do is they ask, OK, of all the engineers at GE, 322 00:13:02,380 --> 00:13:03,300 where do you rank? 323 00:13:03,300 --> 00:13:05,980 What is your percentile rank of everyone? 324 00:13:05,980 --> 00:13:08,620 And they ask basically everyone. 325 00:13:08,620 --> 00:13:11,030 So you would think these being engineers, 326 00:13:11,030 --> 00:13:13,660 engineers being math guys, that they have 327 00:13:13,660 --> 00:13:15,140 a good sense of percentiles. 328 00:13:15,140 --> 00:13:18,160 You'd think that they might get this right. 329 00:13:18,160 --> 00:13:19,982 The average engineer ranks themself right 330 00:13:19,982 --> 00:13:21,190 about at the 80th percentile. 331 00:13:23,930 --> 00:13:25,657 Of all the people they asked-- they 332 00:13:25,657 --> 00:13:27,990 asked, like, maybe a hundred of them-- of all the people 333 00:13:27,990 --> 00:13:30,850 they asked, two ranked themselves as below average. 334 00:13:30,850 --> 00:13:33,310 That is my favorite data point from this study. 335 00:13:33,310 --> 00:13:36,620 Two ranked themselves as below average. 336 00:13:36,620 --> 00:13:37,550 Should be about half. 337 00:13:40,076 --> 00:13:41,450 And they're not alone too, right? 338 00:13:41,450 --> 00:13:44,881 So poker players also famous for their self-assessment bias. 339 00:13:44,881 --> 00:13:46,630 And one of the things that I think sort of 340 00:13:46,630 --> 00:13:48,080 feeds into this, at the beginning 341 00:13:48,080 --> 00:13:49,700 of Rounders-- I haven't seen this movie for, like, five 342 00:13:49,700 --> 00:13:49,820 years. 343 00:13:49,820 --> 00:13:51,910 I don't know if you guys have seen Rounders. 344 00:13:51,910 --> 00:13:53,374 But at the beginning of Rounders, 345 00:13:53,374 --> 00:13:55,290 Matt Damon's character quotes this poker book. 346 00:13:55,290 --> 00:13:56,915 It's one of my all time favorite quotes 347 00:13:56,915 --> 00:14:00,230 from a poker movie which, I guess, isn't saying much. 348 00:14:00,230 --> 00:14:02,740 But gives this quote, "Few players 349 00:14:02,740 --> 00:14:04,590 can remember the big pots they've won, 350 00:14:04,590 --> 00:14:07,640 but every player can remember with remarkable accuracy 351 00:14:07,640 --> 00:14:10,430 the outstanding tough beats of their career." 352 00:14:10,430 --> 00:14:12,310 And I think it's these sort of memory biases 353 00:14:12,310 --> 00:14:14,690 that feed into our self-assessment bias, right? 354 00:14:14,690 --> 00:14:18,350 So you walk into the Bellagio, you see a table of all pros. 355 00:14:18,350 --> 00:14:20,960 There has to be self-assessment bias here, right? 356 00:14:20,960 --> 00:14:22,840 There has to be. 357 00:14:22,840 --> 00:14:26,479 So don't be that person. 358 00:14:26,479 --> 00:14:27,770 Let me circle back to my point. 359 00:14:27,770 --> 00:14:29,645 I'm going to tell you about my favorite poker 360 00:14:29,645 --> 00:14:30,570 hand of all time. 361 00:14:30,570 --> 00:14:32,710 Of every hand I've ever played, this 362 00:14:32,710 --> 00:14:34,800 is my favorite for a number of reasons. 363 00:14:34,800 --> 00:14:36,800 So I'm playing a tournament in the World Series. 364 00:14:36,800 --> 00:14:38,020 This is a big tournament. 365 00:14:38,020 --> 00:14:40,380 And we're on the exact money bubble. 366 00:14:40,380 --> 00:14:43,370 And what that means is that the next person to bust 367 00:14:43,370 --> 00:14:44,620 out gets nothing. 368 00:14:44,620 --> 00:14:47,360 Everyone else is guaranteed something, couple dozen bucks. 369 00:14:47,360 --> 00:14:48,890 I don't know. 370 00:14:48,890 --> 00:14:53,780 So I'm sitting there, and there's this guy at my table 371 00:14:53,780 --> 00:14:55,640 who, as we approach the money bubble, 372 00:14:55,640 --> 00:14:58,120 he's so excited to be there. 373 00:14:58,120 --> 00:15:00,390 It's his first World Series tournament, 374 00:15:00,390 --> 00:15:01,810 he's about to make the money. 375 00:15:01,810 --> 00:15:05,190 He's calling his girlfriend and his buddies every hour 376 00:15:05,190 --> 00:15:07,720 telling them, yeah, I think we're almost in the money. 377 00:15:07,720 --> 00:15:08,860 He's so excited. 378 00:15:08,860 --> 00:15:10,790 And then it gets to the point where, 379 00:15:10,790 --> 00:15:13,409 like, 40 minutes before the bubble, he just leaves. 380 00:15:13,409 --> 00:15:14,700 He doesn't want to play a hand. 381 00:15:14,700 --> 00:15:19,660 He just leaves the table so he doesn't have to bust out. 382 00:15:19,660 --> 00:15:21,440 So he comes back. 383 00:15:21,440 --> 00:15:25,890 And it's now the actual bubble. 384 00:15:25,890 --> 00:15:27,200 He's to my direct left. 385 00:15:27,200 --> 00:15:29,520 I'm in the small blind, he's in the big blind, 386 00:15:29,520 --> 00:15:31,325 and it folds around to me. 387 00:15:31,325 --> 00:15:33,200 And at this point, I feel like there are just 388 00:15:33,200 --> 00:15:34,790 dollar signs in my eyes, right? 389 00:15:34,790 --> 00:15:35,670 I'm so excited. 390 00:15:35,670 --> 00:15:39,590 So I look down and I see four deuce off suit. 391 00:15:39,590 --> 00:15:42,460 And we both have medium stacks, but I 392 00:15:42,460 --> 00:15:45,120 have this hell of a read on this guy, so I shove all in. 393 00:15:47,630 --> 00:15:52,650 He says, I knew you were going to do that. 394 00:15:52,650 --> 00:15:54,355 I call blind. 395 00:15:57,100 --> 00:15:59,120 He calls without looking at his cards 396 00:15:59,120 --> 00:16:01,137 because he knew I was going to shove in. 397 00:16:01,137 --> 00:16:03,220 It's like the strongest [INAUDIBLE] I've ever had. 398 00:16:03,220 --> 00:16:04,210 He flips over his hand. 399 00:16:04,210 --> 00:16:05,830 He has nine deuce off the suit. 400 00:16:05,830 --> 00:16:09,750 He has me dominated with a terrible hand. 401 00:16:09,750 --> 00:16:11,710 Let's think about this. 402 00:16:11,710 --> 00:16:14,540 How terrible does my read have to be? 403 00:16:14,540 --> 00:16:15,832 How far off does it have to be? 404 00:16:15,832 --> 00:16:17,873 What has to happen here for him to call with nine 405 00:16:17,873 --> 00:16:18,600 deuce off suit. 406 00:16:18,600 --> 00:16:20,730 Not only does he have to not care 407 00:16:20,730 --> 00:16:23,720 about bursting out, busting out on the bubble. 408 00:16:23,720 --> 00:16:26,790 He has to not care so much that he won't even 409 00:16:26,790 --> 00:16:28,770 look at his cards. 410 00:16:28,770 --> 00:16:32,540 If he looks at his hand, he has to fold. 411 00:16:32,540 --> 00:16:36,809 So he proceeds to win the hand. 412 00:16:36,809 --> 00:16:39,100 And they count us down, and he has me literally covered 413 00:16:39,100 --> 00:16:40,840 by one or two chips. 414 00:16:40,840 --> 00:16:45,075 And I walk away thinking I have to go home. 415 00:16:45,075 --> 00:16:46,950 We rent a math house every year out in Vegas. 416 00:16:46,950 --> 00:16:49,040 Me and Bill Chen, Jerrod Ankenman, 417 00:16:49,040 --> 00:16:50,630 Mike who's sitting right over there, 418 00:16:50,630 --> 00:16:51,420 and a bunch of other of us. 419 00:16:51,420 --> 00:16:53,810 I have to go home and I have to tell these guys what 420 00:16:53,810 --> 00:16:55,226 just-- Kenny, who's right here-- I 421 00:16:55,226 --> 00:16:57,260 have to tell these guys what just happened, 422 00:16:57,260 --> 00:16:59,300 and I still don't hear the end of it. 423 00:16:59,300 --> 00:17:01,786 So what does this mean? 424 00:17:01,786 --> 00:17:03,410 So I realize the beginning of this talk 425 00:17:03,410 --> 00:17:05,834 sounds a little bit like a commercial for like, 426 00:17:05,834 --> 00:17:07,050 just be humble. 427 00:17:07,050 --> 00:17:08,859 Don't be an idiot. 428 00:17:08,859 --> 00:17:11,670 But I think it's a little more than that. 429 00:17:11,670 --> 00:17:13,329 Here's the takeaway. 430 00:17:13,329 --> 00:17:17,800 Any time you try to divine your opponent's strategy, 431 00:17:17,800 --> 00:17:21,619 she can do the same thing back to you. 432 00:17:21,619 --> 00:17:23,990 And this happens in really obvious ways, 433 00:17:23,990 --> 00:17:30,660 like when my super tight guy all of a sudden doesn't care. 434 00:17:30,660 --> 00:17:33,190 But it also happens in subtle ways, right? 435 00:17:33,190 --> 00:17:35,100 So a lot of times we think about pot odds. 436 00:17:35,100 --> 00:17:37,030 So you might be sitting there thinking, 437 00:17:37,030 --> 00:17:40,060 OK, I'm getting two to one. 438 00:17:40,060 --> 00:17:43,800 Do I have the best hand here at least one in three times? 439 00:17:43,800 --> 00:17:46,280 Very natural way to think, right? 440 00:17:46,280 --> 00:17:48,105 But now you're kind of trying to do magic. 441 00:17:48,105 --> 00:17:49,980 That's one of my favorite quotes of all time, 442 00:17:49,980 --> 00:17:51,590 by the way, from Harry Potter. 443 00:17:51,590 --> 00:17:53,795 And the trouble is, the other side can do magic too. 444 00:17:53,795 --> 00:17:55,920 I'm trying to figure out what their distribution is 445 00:17:55,920 --> 00:17:57,470 and respond to it. 446 00:17:57,470 --> 00:18:00,280 They're trying to figure out what 447 00:18:00,280 --> 00:18:03,220 I think their distribution is and shape it around that. 448 00:18:03,220 --> 00:18:05,880 And all of a sudden, we're playing this leveling game. 449 00:18:05,880 --> 00:18:10,140 And we're both kind of trying to do magic, right? 450 00:18:10,140 --> 00:18:12,512 So in the hand that I showed you guys in the beginning, 451 00:18:12,512 --> 00:18:13,970 I could be sitting there and trying 452 00:18:13,970 --> 00:18:16,680 to figure out exactly what my opponent's range is 453 00:18:16,680 --> 00:18:20,680 when she bets one and a half times the pot. 454 00:18:20,680 --> 00:18:24,250 I can try to figure out why he's not putting me all in. 455 00:18:24,250 --> 00:18:26,637 I can try to figure out a million other little things 456 00:18:26,637 --> 00:18:28,220 that are going to help me get a little 457 00:18:28,220 --> 00:18:31,957 more sense of this range, but I'm trying to do magic. 458 00:18:31,957 --> 00:18:34,540 And I think that's kind of our go to move when we don't really 459 00:18:34,540 --> 00:18:37,830 have a repertoire, right? 460 00:18:37,830 --> 00:18:40,157 And this is going to happen more and more-- well, 461 00:18:40,157 --> 00:18:41,615 it happens with really bad players, 462 00:18:41,615 --> 00:18:43,448 bu that's OK-- but it's going to happen more 463 00:18:43,448 --> 00:18:44,845 and more with good players. 464 00:18:44,845 --> 00:18:46,220 They'll take you to a place where 465 00:18:46,220 --> 00:18:48,680 they have this paved road. 466 00:18:48,680 --> 00:18:50,140 They've been there before. 467 00:18:50,140 --> 00:18:53,110 They take people to these weird places. 468 00:18:53,110 --> 00:18:54,570 And you haven't. 469 00:18:54,570 --> 00:18:57,310 And what do you do? 470 00:18:57,310 --> 00:19:03,530 So what I would say is forget their hand. 471 00:19:03,530 --> 00:19:05,765 Forget their range. 472 00:19:05,765 --> 00:19:06,640 Don't think about it. 473 00:19:09,750 --> 00:19:14,084 So one of my favorite people in the world, Jerrod Ankenman, 474 00:19:14,084 --> 00:19:15,500 he's the one who wrote Bill's book 475 00:19:15,500 --> 00:19:18,060 and let Bill put his name on it, by the way. 476 00:19:18,060 --> 00:19:22,430 He has this quote, "If I truly played optimally, 477 00:19:22,430 --> 00:19:24,860 I could write down my entire strategy 478 00:19:24,860 --> 00:19:26,560 on a piece of paper, what I would 479 00:19:26,560 --> 00:19:29,340 do in every single situation, and I could give it to you 480 00:19:29,340 --> 00:19:31,920 and you couldn't beat me." 481 00:19:31,920 --> 00:19:34,080 That's what we're trying to do here. 482 00:19:34,080 --> 00:19:36,540 So how do we get there? 483 00:19:36,540 --> 00:19:39,860 Well, heads-up limit hold'em turns out to be a pretty big 484 00:19:39,860 --> 00:19:40,360 game. 485 00:19:40,360 --> 00:19:42,570 It has about a quintillion game states, 486 00:19:42,570 --> 00:19:44,590 and that's the smallest poker game 487 00:19:44,590 --> 00:19:46,550 that we really play for money. 488 00:19:46,550 --> 00:19:49,570 So we can do a couple things, right? 489 00:19:49,570 --> 00:19:53,660 We can try to do some, like, sweet programming like the team 490 00:19:53,660 --> 00:19:55,422 out in Alberta did. 491 00:19:55,422 --> 00:19:56,130 And that's great. 492 00:20:00,000 --> 00:20:03,790 You know, for example, humans play chess, right? 493 00:20:03,790 --> 00:20:07,550 And computers now crush them, but human learning is really 494 00:20:07,550 --> 00:20:10,340 strongly aided by computers. 495 00:20:10,340 --> 00:20:12,300 But you can't memorize every position. 496 00:20:12,300 --> 00:20:14,550 You can't memorize every line. 497 00:20:14,550 --> 00:20:17,650 You have to know what's going on underneath the hood. 498 00:20:17,650 --> 00:20:20,710 And these algorithms, these programs like Cepheus, they 499 00:20:20,710 --> 00:20:22,380 will give you the strategy. 500 00:20:22,380 --> 00:20:24,440 They will not tell you why. 501 00:20:24,440 --> 00:20:27,570 And as humans, we need to start to understand why 502 00:20:27,570 --> 00:20:30,870 if we have any hope of carrying these strategies with us 503 00:20:30,870 --> 00:20:33,990 and actually playing them in real life. 504 00:20:33,990 --> 00:20:35,587 So they're a black box, right? 505 00:20:35,587 --> 00:20:36,670 So we can solve the games. 506 00:20:36,670 --> 00:20:40,720 But solving the games does not get us out of the woods. 507 00:20:40,720 --> 00:20:44,460 So if we want to wrap our puny human minds around it, 508 00:20:44,460 --> 00:20:46,310 we have to be a little more clever. 509 00:20:46,310 --> 00:20:49,340 So we're going to look at a couple of toy games here, 510 00:20:49,340 --> 00:20:50,880 really simple ones that can start 511 00:20:50,880 --> 00:20:53,620 to help us wrap our minds around how 512 00:20:53,620 --> 00:20:55,780 to behave in these situations. 513 00:20:55,780 --> 00:20:58,105 So the first one is a clairvoyance game. 514 00:20:58,105 --> 00:21:00,970 And a clairvoyance game is basically 515 00:21:00,970 --> 00:21:04,920 when either one or both players have complete game state 516 00:21:04,920 --> 00:21:06,130 information. 517 00:21:06,130 --> 00:21:08,370 So what would you do if you lived in a world 518 00:21:08,370 --> 00:21:10,960 where you always knew your opponent's hand 519 00:21:10,960 --> 00:21:12,565 and he knew that you knew? 520 00:21:12,565 --> 00:21:14,190 That's the idea of a clairvoyance game. 521 00:21:14,190 --> 00:21:17,344 So we're going to look at a game called Coin Flip Clairvoyance. 522 00:21:17,344 --> 00:21:18,510 And the game goes like this. 523 00:21:18,510 --> 00:21:21,225 You can and should play it for money by the way. 524 00:21:21,225 --> 00:21:22,954 So each player antes a dollar. 525 00:21:22,954 --> 00:21:23,870 There are two players. 526 00:21:23,870 --> 00:21:24,911 And then you flip a coin. 527 00:21:24,911 --> 00:21:26,820 If it's heads, you win. 528 00:21:26,820 --> 00:21:28,970 If it's tails, your opponent wins. 529 00:21:28,970 --> 00:21:31,950 However, there's a round of betting. 530 00:21:31,950 --> 00:21:34,350 Only you see the coin after the flip. 531 00:21:34,350 --> 00:21:37,370 Then you can bet or check. 532 00:21:37,370 --> 00:21:39,520 So you choose to bet a dollar or check, 533 00:21:39,520 --> 00:21:41,730 and your opponent can only check. 534 00:21:41,730 --> 00:21:44,340 If you check, they have to flip over hand or call. 535 00:21:44,340 --> 00:21:49,040 If you bet, they either have to call a dollar or fold, OK? 536 00:21:49,040 --> 00:21:51,382 So you know if you win or not. 537 00:21:51,382 --> 00:21:53,590 Your opponent doesn't know if they'll win a showdown. 538 00:21:53,590 --> 00:21:54,798 That's the idea of this game. 539 00:21:54,798 --> 00:21:56,650 Make sense? 540 00:21:56,650 --> 00:21:58,780 Yeah OK, easy game. 541 00:21:58,780 --> 00:22:00,250 So how do we play? 542 00:22:00,250 --> 00:22:02,110 So scenario one. 543 00:22:02,110 --> 00:22:02,860 Flip the coin. 544 00:22:02,860 --> 00:22:03,840 It's heads. 545 00:22:03,840 --> 00:22:05,773 What do we do? 546 00:22:05,773 --> 00:22:06,715 AUDIENCE: Bet. 547 00:22:06,715 --> 00:22:07,657 MATT HAWRILENKO: Bet. 548 00:22:07,657 --> 00:22:08,600 OK. 549 00:22:08,600 --> 00:22:09,700 Scenario two. 550 00:22:09,700 --> 00:22:10,950 It's tails. 551 00:22:10,950 --> 00:22:12,180 What do we do? 552 00:22:12,180 --> 00:22:14,100 So there are two main questions. 553 00:22:14,100 --> 00:22:16,720 How often should your opponent call, 554 00:22:16,720 --> 00:22:19,130 and how often should you bluff? 555 00:22:19,130 --> 00:22:20,710 So how do we solve this? 556 00:22:20,710 --> 00:22:23,700 What we want to do is we want to call 557 00:22:23,700 --> 00:22:26,870 enough to make your opponent indifferent to bluffing 558 00:22:26,870 --> 00:22:27,480 or giving up. 559 00:22:27,480 --> 00:22:29,230 That's what your opponent should be doing. 560 00:22:29,230 --> 00:22:30,930 So to do that, we're going to set 561 00:22:30,930 --> 00:22:34,680 the expectation of bluffing equal to the expectation 562 00:22:34,680 --> 00:22:35,390 of giving up. 563 00:22:35,390 --> 00:22:38,510 So the expectation of bluffing is just this, right? 564 00:22:38,510 --> 00:22:41,084 It's the pot times the amount they fold, 565 00:22:41,084 --> 00:22:43,000 which is one minus the proportion of the times 566 00:22:43,000 --> 00:22:44,040 they called, right? 567 00:22:44,040 --> 00:22:46,290 That's how much you win when you bluff. 568 00:22:46,290 --> 00:22:48,400 So now how much do you lose when you 569 00:22:48,400 --> 00:22:50,250 bluff and get caught, right? 570 00:22:50,250 --> 00:22:52,170 It's the amount you bluff, which is 571 00:22:52,170 --> 00:22:56,420 going to be one unit, times the amount you get called. 572 00:22:56,420 --> 00:23:00,880 So we can just sort of do a little simple algebra, 573 00:23:00,880 --> 00:23:03,830 and it'll reduce to-- you should be calling p over p 574 00:23:03,830 --> 00:23:07,030 plus 1 of the time, where p is the pot, right? 575 00:23:07,030 --> 00:23:11,550 So if the pot is two units and you're bluffing one unit, 576 00:23:11,550 --> 00:23:15,570 we should be calling with a proportion of two over three. 577 00:23:15,570 --> 00:23:17,260 2/3 of the time with our kings. 578 00:23:17,260 --> 00:23:20,180 That is how we make the opponent indifferent to bluffing 579 00:23:20,180 --> 00:23:21,428 or giving up. 580 00:23:21,428 --> 00:23:22,640 OK? 581 00:23:22,640 --> 00:23:26,250 So a couple of things to note about this before we push on. 582 00:23:26,250 --> 00:23:28,930 So what happens here as the pot gets bigger? 583 00:23:28,930 --> 00:23:31,294 Do you call more or less? 584 00:23:31,294 --> 00:23:32,074 AUDIENCE: More 585 00:23:32,074 --> 00:23:32,990 MATT HAWRILENKO: More. 586 00:23:32,990 --> 00:23:36,469 Yeah/ So as the pot gets bigger, this asymptotes to 1 which 587 00:23:36,469 --> 00:23:37,260 makes sense, right? 588 00:23:37,260 --> 00:23:38,884 Most of the value's already in the pot. 589 00:23:38,884 --> 00:23:40,780 So there's more money in there. 590 00:23:40,780 --> 00:23:44,290 You have to protect against being bluffed at more. 591 00:23:44,290 --> 00:23:47,290 Totally intuitive with poker, right? 592 00:23:47,290 --> 00:23:48,634 So how often do you bluff? 593 00:23:48,634 --> 00:23:50,300 Well, you want to set the expected value 594 00:23:50,300 --> 00:23:53,416 of calling equal to the expected value of folding. 595 00:23:53,416 --> 00:23:55,257 So the expected value of calling here 596 00:23:55,257 --> 00:23:57,840 is just-- we're going to use the ratio of bluffs to value bets 597 00:23:57,840 --> 00:23:58,881 rather than a percentage. 598 00:23:58,881 --> 00:24:00,610 It just works out nicer. 599 00:24:00,610 --> 00:24:04,520 So the ratio of bluffs to value bets, so how frequently 600 00:24:04,520 --> 00:24:08,250 are you bluffing, times the pot plus one 601 00:24:08,250 --> 00:24:11,946 because that is what they win when they call. 602 00:24:11,946 --> 00:24:13,945 So bluffs value that times the pot plus the unit 603 00:24:13,945 --> 00:24:16,020 that you bluff. 604 00:24:16,020 --> 00:24:19,285 And then what do they lose when they call in their wrong? 605 00:24:19,285 --> 00:24:20,910 They lose the amount you bet, so that's 606 00:24:20,910 --> 00:24:23,450 going to be one unit, the value you bet. 607 00:24:23,450 --> 00:24:26,400 So you're going to bluff p plus 1. 608 00:24:26,400 --> 00:24:29,480 So you're going to bluff 1 over p plus 1 of the time. 609 00:24:29,480 --> 00:24:31,800 So now what happens here? 610 00:24:31,800 --> 00:24:33,850 So as the pot gets bigger, what are you doing? 611 00:24:33,850 --> 00:24:35,880 Bluffing more or less? 612 00:24:35,880 --> 00:24:37,004 AUDIENCE: Less. 613 00:24:37,004 --> 00:24:37,920 MATT HAWRILENKO: Less. 614 00:24:37,920 --> 00:24:38,590 Yeah. 615 00:24:38,590 --> 00:24:41,370 Is that counterintuitive? 616 00:24:41,370 --> 00:24:42,280 AUDIENCE: No. 617 00:24:42,280 --> 00:24:42,640 MATT HAWRILENKO: Is it? 618 00:24:42,640 --> 00:24:43,182 I don't know. 619 00:24:43,182 --> 00:24:45,640 It was counterintuitive to me because I'm like, oh, there's 620 00:24:45,640 --> 00:24:46,560 more money in the pot. 621 00:24:46,560 --> 00:24:50,150 But what it means is there's more money in the pot, 622 00:24:50,150 --> 00:24:53,270 so I don't really need to bluff very frequently to make sure 623 00:24:53,270 --> 00:24:55,640 I get value, because the values in there, 624 00:24:55,640 --> 00:25:00,180 and my opponent is calling more of the time. 625 00:25:00,180 --> 00:25:02,875 So the bigger the pot is, the more my opponent calls, right? 626 00:25:02,875 --> 00:25:04,250 And what I'm doing essentially is 627 00:25:04,250 --> 00:25:07,140 I'm bluffing so I can get value from the time that I'm winning. 628 00:25:07,140 --> 00:25:07,640 Yeah? 629 00:25:11,262 --> 00:25:12,110 OK. 630 00:25:12,110 --> 00:25:14,026 So we can actually generalize this too, right? 631 00:25:14,026 --> 00:25:16,907 So we can generalize it to no limit games pretty simply. 632 00:25:16,907 --> 00:25:18,740 So we've sort of flipped things around here. 633 00:25:18,740 --> 00:25:22,035 So here the pot is 1 and s is the proportion of the pot 634 00:25:22,035 --> 00:25:25,000 that you bet, so you're going to be calling 1 over 1 635 00:25:25,000 --> 00:25:26,050 plus s, right? 636 00:25:26,050 --> 00:25:31,030 So if the pot is two units, s is one unit, 637 00:25:31,030 --> 00:25:32,410 so s would be 0.5, right? 638 00:25:32,410 --> 00:25:36,570 1 plus 0.5 is one half. 639 00:25:36,570 --> 00:25:39,140 And you'd be bluffing s over 1 plus s, right? 640 00:25:39,140 --> 00:25:42,230 So you're going to be calling 1 minus the bluff ratio. 641 00:25:42,230 --> 00:25:44,105 Sometimes we call the bluff ratio alpha. 642 00:25:44,105 --> 00:25:47,270 1 minus alpha. 643 00:25:47,270 --> 00:25:49,400 But we can actually calculate a value for this game 644 00:25:49,400 --> 00:25:50,830 and for all toy games. 645 00:25:50,830 --> 00:25:53,110 So Bowling and their team with Cepheus they calculated 646 00:25:53,110 --> 00:25:55,550 the value of having the button in limit hold'em. 647 00:25:55,550 --> 00:25:57,070 We always kind of knew it was good, 648 00:25:57,070 --> 00:25:59,195 but they calculated precisely just how good it was. 649 00:25:59,195 --> 00:26:01,569 And if you're looking for a job at a place like [? Sig ?] 650 00:26:01,569 --> 00:26:03,360 or somewhere else in finance, you actually 651 00:26:03,360 --> 00:26:05,480 probably should just calculate the value of this, 652 00:26:05,480 --> 00:26:06,896 because you're going to be getting 653 00:26:06,896 --> 00:26:10,100 interview questions like this. 654 00:26:10,100 --> 00:26:14,600 So again, what we're taking here is the larger amount 655 00:26:14,600 --> 00:26:18,720 your opponent gets, the less frequently you have to call. 656 00:26:18,720 --> 00:26:19,550 Right? 657 00:26:19,550 --> 00:26:22,040 The more frequently your opponent bluffs, 658 00:26:22,040 --> 00:26:25,450 the more frequently she has to value that, right? 659 00:26:25,450 --> 00:26:29,130 So as a bluffing region gets larger, 660 00:26:29,130 --> 00:26:31,707 the value betting region has to get larger with it. 661 00:26:31,707 --> 00:26:33,540 So in a coin flip game it doesn't make sense 662 00:26:33,540 --> 00:26:37,655 to think of regions, but in poker it's going to. 663 00:26:37,655 --> 00:26:39,280 So a question I get here a lot is, what 664 00:26:39,280 --> 00:26:40,700 if it's not a repeated game? 665 00:26:40,700 --> 00:26:42,810 What if you're playing it just this one time? 666 00:26:42,810 --> 00:26:44,930 Or what if you're at a table with a player 667 00:26:44,930 --> 00:26:47,080 that you'll never play with again? 668 00:26:47,080 --> 00:26:49,640 How do you play that? 669 00:26:49,640 --> 00:26:52,570 And the answer is that it's a repeated game. 670 00:26:52,570 --> 00:26:57,480 So I have a feeling this will be intuitive for you guys, 671 00:26:57,480 --> 00:26:59,160 so I'll do it quickly. 672 00:26:59,160 --> 00:27:01,040 But I want you to imagine a scenario 673 00:27:01,040 --> 00:27:03,248 where you're going to play the Coin Flip Clairvoyance 674 00:27:03,248 --> 00:27:06,260 game a thousand times against different players. 675 00:27:06,260 --> 00:27:09,340 So against a thousand different players, right? 676 00:27:09,340 --> 00:27:11,550 And suppose you take the position, 677 00:27:11,550 --> 00:27:13,910 since my opponents can't learn from my past, 678 00:27:13,910 --> 00:27:16,710 I'm going to bluff 100% of the time. 679 00:27:16,710 --> 00:27:19,180 So what's actually happening here? 680 00:27:19,180 --> 00:27:23,170 You can sort of think of each opponent as a random sampling 681 00:27:23,170 --> 00:27:26,089 from the distribution of possible strategies 682 00:27:26,089 --> 00:27:28,380 that are out there for the Coin Flip Clairvoyance game. 683 00:27:28,380 --> 00:27:32,070 So some of them will fold too much, and you will own them. 684 00:27:32,070 --> 00:27:34,700 And then some of them will call too much, 685 00:27:34,700 --> 00:27:37,900 and they will own you if you're bluffing all of the time, 686 00:27:37,900 --> 00:27:38,460 right? 687 00:27:38,460 --> 00:27:40,920 So even if you haven't seen this person before, 688 00:27:40,920 --> 00:27:43,470 even if it's your first hand of poker against them, 689 00:27:43,470 --> 00:27:46,130 it is a repeated game, OK? 690 00:27:46,130 --> 00:27:49,200 So get that, it's not a repeated game notion out of your heads. 691 00:27:49,200 --> 00:27:52,320 It's bad for business. 692 00:27:52,320 --> 00:27:54,165 So taking like a half a step back, 693 00:27:54,165 --> 00:27:55,790 what have we learned about this so far? 694 00:27:55,790 --> 00:27:56,420 OK. 695 00:27:56,420 --> 00:28:00,020 So the Coin Flip Clairvoyance game, it's not about just value 696 00:28:00,020 --> 00:28:01,840 betting or just bluffing. 697 00:28:01,840 --> 00:28:04,390 It's about the combination of the two. 698 00:28:04,390 --> 00:28:07,110 We're also trying to maximize the value of our entire set 699 00:28:07,110 --> 00:28:08,400 of hands, right? 700 00:28:08,400 --> 00:28:09,620 Because what happens? 701 00:28:09,620 --> 00:28:12,190 So suppose our strategy is, we're 702 00:28:12,190 --> 00:28:13,970 going to bet every time we have heads, 703 00:28:13,970 --> 00:28:16,020 we're never going to bet when we have tails? 704 00:28:16,020 --> 00:28:18,984 What's our opponent going to do? 705 00:28:18,984 --> 00:28:20,150 AUDIENCE: Fold to every bet. 706 00:28:20,150 --> 00:28:22,316 MATT HAWRILENKO: They're going to fold to every bet. 707 00:28:22,316 --> 00:28:24,240 Yeah, exactly. 708 00:28:24,240 --> 00:28:27,230 So we sort of can calculate this ratio 709 00:28:27,230 --> 00:28:31,985 where now they don't do so well if they fold to every bet. 710 00:28:31,985 --> 00:28:34,360 And so what's cool about this is the math in this game is 711 00:28:34,360 --> 00:28:35,151 very simple, right? 712 00:28:35,151 --> 00:28:35,870 It's not hard. 713 00:28:35,870 --> 00:28:37,750 But it buys you a lot. 714 00:28:37,750 --> 00:28:41,690 It buys you a lot of intuition about poker. 715 00:28:41,690 --> 00:28:44,660 Some really useful concepts. 716 00:28:44,660 --> 00:28:46,890 So I want to move on. 717 00:28:46,890 --> 00:28:49,310 This is probably my favorite of all the toy games, 718 00:28:49,310 --> 00:28:51,310 and there are actually a million versions of it. 719 00:28:51,310 --> 00:28:52,726 We're going to do the simplest one 720 00:28:52,726 --> 00:28:57,460 because I think it sort of gets everything that you 721 00:28:57,460 --> 00:28:58,914 need to know, more or less. 722 00:28:58,914 --> 00:29:00,580 So this is an ace, king, and queen game. 723 00:29:00,580 --> 00:29:02,870 It's an incomplete information game. 724 00:29:02,870 --> 00:29:06,290 So each player antes $1 and is dealt one card. 725 00:29:06,290 --> 00:29:07,820 So if I get delta ace, my opponent 726 00:29:07,820 --> 00:29:09,700 only has the king or the queen. 727 00:29:09,700 --> 00:29:12,070 They can't also have an ace. 728 00:29:12,070 --> 00:29:14,340 So then you can check of bet and your opponent, 729 00:29:14,340 --> 00:29:16,090 just like the Coin Flip Clairvoyance game, 730 00:29:16,090 --> 00:29:20,060 can only check or call or fold. 731 00:29:20,060 --> 00:29:22,760 They can't bet if you check. 732 00:29:22,760 --> 00:29:26,480 So this is going to be our first mapping, our only mapping, 733 00:29:26,480 --> 00:29:30,880 of a toy game that resembles real poker, right? 734 00:29:30,880 --> 00:29:33,960 Now we have a real range. 735 00:29:33,960 --> 00:29:36,620 Again, I think that you probably can and should 736 00:29:36,620 --> 00:29:37,662 play this game for money. 737 00:29:37,662 --> 00:29:39,828 I think there's a real difference between what we're 738 00:29:39,828 --> 00:29:41,960 about to do, which is solve it and sort of get it 739 00:29:41,960 --> 00:29:44,570 intuitively, and actually get it experientially. 740 00:29:44,570 --> 00:29:46,930 So go forth and gamble. 741 00:29:46,930 --> 00:29:49,280 But what do we do? 742 00:29:49,280 --> 00:29:50,250 So case one. 743 00:29:50,250 --> 00:29:51,430 So you get the ace. 744 00:29:51,430 --> 00:29:53,443 Are you going to check or bet? 745 00:29:53,443 --> 00:29:54,026 AUDIENCE: Bet. 746 00:29:54,026 --> 00:29:55,567 MATT HAWRILENKO: You're going to bet. 747 00:29:55,567 --> 00:29:56,970 Yeah. 748 00:29:56,970 --> 00:30:00,689 Now your opponent bets and you have an ace. 749 00:30:00,689 --> 00:30:01,730 What are you going to do? 750 00:30:01,730 --> 00:30:02,510 AUDIENCE: Call. 751 00:30:02,510 --> 00:30:04,093 MATT HAWRILENKO: You're going to call. 752 00:30:04,093 --> 00:30:05,050 All right, good. 753 00:30:05,050 --> 00:30:06,790 And now your opponent bets, and you have a queen. 754 00:30:06,790 --> 00:30:07,745 What are you going to do? 755 00:30:07,745 --> 00:30:08,220 AUDIENCE: Fold. 756 00:30:08,220 --> 00:30:09,136 MATT HAWRILENKO: Yeah. 757 00:30:09,136 --> 00:30:09,700 Hey, yeah. 758 00:30:09,700 --> 00:30:10,200 OK. 759 00:30:10,200 --> 00:30:11,690 So it seems trivial, right? 760 00:30:11,690 --> 00:30:14,365 These first three cases seem really trivial. 761 00:30:14,365 --> 00:30:15,740 But an important thing to note is 762 00:30:15,740 --> 00:30:19,430 that they are dominant strategies 763 00:30:19,430 --> 00:30:20,880 or dominated strategies. 764 00:30:20,880 --> 00:30:23,570 So a dominated strategy in game theory, for example, 765 00:30:23,570 --> 00:30:26,325 calling with a queen here would be dominated. 766 00:30:26,325 --> 00:30:30,390 A dominated strategy is one where the decision has 767 00:30:30,390 --> 00:30:33,240 equal or lesser-- strictly equal or lesser value 768 00:30:33,240 --> 00:30:34,580 to another decision. 769 00:30:34,580 --> 00:30:37,370 If I call with a queen, I cannot win. 770 00:30:37,370 --> 00:30:38,700 I just lose money. 771 00:30:38,700 --> 00:30:42,450 That has strictly lesser value than folding, OK? 772 00:30:42,450 --> 00:30:45,360 So dominated strategies, important concept. 773 00:30:45,360 --> 00:30:47,540 So how about this one. 774 00:30:47,540 --> 00:30:48,630 You have a king. 775 00:30:48,630 --> 00:30:50,148 Check or bet? 776 00:30:50,148 --> 00:30:50,945 AUDIENCE: Check. 777 00:30:50,945 --> 00:30:51,570 AUDIENCE: Check 778 00:30:51,570 --> 00:30:52,000 MATT HAWRILENKO: Check. 779 00:30:52,000 --> 00:30:52,666 AUDIENCE: Split. 780 00:30:52,666 --> 00:30:53,710 MATT HAWRILENKO: Split? 781 00:30:53,710 --> 00:30:54,210 OK. 782 00:30:54,210 --> 00:30:57,599 All right, well, I actually want to see where everyone's in. 783 00:30:57,599 --> 00:30:59,140 So we're going to have three options. 784 00:30:59,140 --> 00:31:01,126 Who wants to check? 785 00:31:01,126 --> 00:31:05,540 All right, who wants to bet all the time? 786 00:31:05,540 --> 00:31:08,090 Who wants to bet sometimes? 787 00:31:08,090 --> 00:31:08,965 OK. 788 00:31:08,965 --> 00:31:10,630 See, I tricked you. 789 00:31:10,630 --> 00:31:14,420 This is also a dominated strategy. 790 00:31:14,420 --> 00:31:16,880 So what happens if you have a king and you bet? 791 00:31:16,880 --> 00:31:18,910 What is your opponent going to do with an ace? 792 00:31:18,910 --> 00:31:19,980 AUDIENCE: He's either going to call with an ace 793 00:31:19,980 --> 00:31:21,050 or fold with a queen. 794 00:31:21,050 --> 00:31:22,091 MATT HAWRILENKO: Exactly. 795 00:31:22,091 --> 00:31:24,550 Your opponent-- because the ace and the queen, 796 00:31:24,550 --> 00:31:26,260 dominant strategies, right? 797 00:31:26,260 --> 00:31:28,060 Your opponents always calling with an ace, 798 00:31:28,060 --> 00:31:29,620 always folding a queen. 799 00:31:29,620 --> 00:31:34,700 So betting with a king here would be a dominated strategy. 800 00:31:34,700 --> 00:31:37,580 Strictly dominated by checking. 801 00:31:37,580 --> 00:31:38,730 How about here? 802 00:31:38,730 --> 00:31:40,814 Now we have a queen. 803 00:31:40,814 --> 00:31:41,730 What do we want to do? 804 00:31:41,730 --> 00:31:42,623 Check or bet? 805 00:31:42,623 --> 00:31:43,449 AUDIENCE: Bet. 806 00:31:43,449 --> 00:31:44,990 MATT HAWRILENKO: Check, bet, exactly. 807 00:31:44,990 --> 00:31:48,121 We want to bet some of the time. 808 00:31:48,121 --> 00:31:48,620 Right? 809 00:31:51,135 --> 00:31:52,510 And we'll go through [INAUDIBLE]. 810 00:31:52,510 --> 00:31:54,540 And now we have a king and our opponent bets. 811 00:31:54,540 --> 00:31:56,584 What do we want to do? 812 00:31:56,584 --> 00:31:57,560 AUDIENCE: Mix. 813 00:31:57,560 --> 00:31:58,460 MATT HAWRILENKO: Mix. 814 00:31:58,460 --> 00:31:58,959 Good. 815 00:31:58,959 --> 00:31:59,880 You got the idea. 816 00:31:59,880 --> 00:32:04,647 Does anyone have any guess as to how the mix might break down? 817 00:32:04,647 --> 00:32:06,105 AUDIENCE: Depends on his proportion 818 00:32:06,105 --> 00:32:09,017 of bluffing with the queen. 819 00:32:09,017 --> 00:32:09,850 MATT HAWRILENKO: OK. 820 00:32:09,850 --> 00:32:12,046 But suppose we're trying to solve it. 821 00:32:12,046 --> 00:32:14,420 So it depends on his proportions bluffing with the queen. 822 00:32:14,420 --> 00:32:15,400 Exactly. 823 00:32:15,400 --> 00:32:16,940 And let's get tighter. 824 00:32:16,940 --> 00:32:18,464 How do we solve it, right? 825 00:32:18,464 --> 00:32:19,880 So if we have a king, our opponent 826 00:32:19,880 --> 00:32:21,550 has an ace half the time and has a queen half the time. 827 00:32:21,550 --> 00:32:23,510 They're going to bet all the time with the ace 828 00:32:23,510 --> 00:32:25,516 and sometimes with the queen. 829 00:32:25,516 --> 00:32:29,000 Turns out in this game that it's going 830 00:32:29,000 --> 00:32:32,920 to be about the same or exactly the same. 831 00:32:32,920 --> 00:32:37,300 She should be calling 1 over 1 plus s, s 832 00:32:37,300 --> 00:32:38,900 being the fraction of the pot. 833 00:32:38,900 --> 00:32:43,670 So you should be calling with 2/3 of hands that beat a bluff. 834 00:32:43,670 --> 00:32:47,350 So the hands that beat a bluff are aces and kings, not queens, 835 00:32:47,350 --> 00:32:47,850 right? 836 00:32:52,150 --> 00:32:55,000 So if we're thinking about it this way, before-- eh, no. 837 00:32:55,000 --> 00:32:56,490 I'll show this first. 838 00:32:56,490 --> 00:32:59,197 So aces are going to represent 50% of the hands that 839 00:32:59,197 --> 00:33:00,030 beat a bluff, right? 840 00:33:00,030 --> 00:33:01,405 Because you're going to have aces 841 00:33:01,405 --> 00:33:03,950 50% of the time and kings 50% of the time. 842 00:33:03,950 --> 00:33:07,140 So calling with aces seems better than calling with kings. 843 00:33:07,140 --> 00:33:09,260 So we're going to call with all of our aces. 844 00:33:09,260 --> 00:33:12,180 So now we're up to half, but we need to get to 2/3, right? 845 00:33:12,180 --> 00:33:16,100 We want to be calling 2/3 of the time, kind of per our formula. 846 00:33:16,100 --> 00:33:18,030 So we're calling with all of our aces, 847 00:33:18,030 --> 00:33:20,030 and then a third of our kings times having 848 00:33:20,030 --> 00:33:24,440 a king half the time, that's another sixth, right? 849 00:33:24,440 --> 00:33:28,320 So all of our aces and a third of our kings. 850 00:33:28,320 --> 00:33:32,800 So how is thinking about it this way 851 00:33:32,800 --> 00:33:37,540 different from thinking about it using pot odds? 852 00:33:37,540 --> 00:33:41,120 So for pot odds we're trying to figure out, 853 00:33:41,120 --> 00:33:45,080 what does this person have in this situation? 854 00:33:45,080 --> 00:33:47,310 So I'm sitting here with a king with pot odds, 855 00:33:47,310 --> 00:33:53,240 and I'm thinking, am I ahead at least a third of the time here? 856 00:33:53,240 --> 00:33:54,395 I don't know exactly. 857 00:33:54,395 --> 00:33:55,770 But I know that I can try to make 858 00:33:55,770 --> 00:33:59,110 my opponent indifferent to bluffing or calling. 859 00:33:59,110 --> 00:34:00,920 So I'm thinking about what I'm doing 860 00:34:00,920 --> 00:34:02,635 with my whole range of hands. 861 00:34:06,540 --> 00:34:09,655 So yeah, OK. 862 00:34:09,655 --> 00:34:11,030 So these are the two observations 863 00:34:11,030 --> 00:34:12,863 we had from the Coin Flip Clairvoyance game. 864 00:34:12,863 --> 00:34:14,326 So adding one. 865 00:34:14,326 --> 00:34:16,909 One thing that we're noting here with the ace, king, and queen 866 00:34:16,909 --> 00:34:17,908 game, what are we doing? 867 00:34:17,908 --> 00:34:21,480 We're sort of implicitly mapping three different types of hands. 868 00:34:21,480 --> 00:34:24,159 Value hands, bluff catchers, and bluffs. 869 00:34:27,449 --> 00:34:29,710 And the big thing here is your strategy 870 00:34:29,710 --> 00:34:32,870 for what you do with one hand determines your strategy 871 00:34:32,870 --> 00:34:34,440 for other hands, all right? 872 00:34:34,440 --> 00:34:37,010 I'm definitely calling with the aces, 873 00:34:37,010 --> 00:34:39,090 so I need to call with some kings, right? 874 00:34:39,090 --> 00:34:41,800 I'm definitely betting all my aces, 875 00:34:41,800 --> 00:34:45,309 so I need to bluff with the lowest-- like, the worst 876 00:34:45,309 --> 00:34:46,600 part of my distribution, right? 877 00:34:46,600 --> 00:34:50,400 That's the part that's going to gain the most. 878 00:34:50,400 --> 00:34:54,679 So a more subtle thing that I think is super important 879 00:34:54,679 --> 00:34:57,450 and is going to play into sort of the last half of this talk 880 00:34:57,450 --> 00:35:00,830 is if I am playing a hand differently from you, 881 00:35:00,830 --> 00:35:04,220 I should do different things with other hands 882 00:35:04,220 --> 00:35:05,450 than you should. 883 00:35:05,450 --> 00:35:10,450 Say for whatever reason I'm only betting half of my aces 884 00:35:10,450 --> 00:35:13,440 but I'm still betting a third of my kings. 885 00:35:13,440 --> 00:35:14,480 Whoops. 886 00:35:14,480 --> 00:35:16,370 Now I'm out of whack, right? 887 00:35:16,370 --> 00:35:19,701 Now I'm out of balance, and I'm going to lose more in this game 888 00:35:19,701 --> 00:35:20,700 by being out of balance. 889 00:35:23,810 --> 00:35:27,620 So your strategy for one hand determines your strategy 890 00:35:27,620 --> 00:35:29,480 for other hands. 891 00:35:29,480 --> 00:35:32,450 That's the whole key here, OK? 892 00:35:32,450 --> 00:35:35,390 So to sort of summarize what we've done so far 893 00:35:35,390 --> 00:35:36,390 is the Temple of Apollo. 894 00:35:36,390 --> 00:35:38,750 This is where I'd like you to go to see the oracle. 895 00:35:38,750 --> 00:35:40,500 Like, you want to go and get a prediction, 896 00:35:40,500 --> 00:35:41,830 this is where you would go. 897 00:35:41,830 --> 00:35:44,080 And walking into the Temple of Apollo 898 00:35:44,080 --> 00:35:45,875 back in the day in ancient Greece, 899 00:35:45,875 --> 00:35:48,380 I'm wondering if they knew a thing or two about game theory. 900 00:35:48,380 --> 00:35:50,421 So there are three inscriptions above the temple. 901 00:35:50,421 --> 00:35:53,210 The first one is know thyself, right? 902 00:35:53,210 --> 00:35:54,660 Know your own hand. 903 00:35:54,660 --> 00:35:58,090 Know your own distribution. 904 00:35:58,090 --> 00:36:00,810 The second is nothing in excess. 905 00:36:00,810 --> 00:36:03,030 Play with balance. 906 00:36:03,030 --> 00:36:06,620 So know thyself, nothing in excess. 907 00:36:06,620 --> 00:36:10,390 And the last one is make a pledge and mischief is nigh. 908 00:36:10,390 --> 00:36:12,732 Yeah, it's really a real stretch to make that one work, 909 00:36:12,732 --> 00:36:14,190 so we'll just leave it at mischief. 910 00:36:14,190 --> 00:36:15,970 Mischief can sometimes be good. 911 00:36:15,970 --> 00:36:19,880 So let me be very clear on how important I 912 00:36:19,880 --> 00:36:23,310 think this concept of knowing your own hand, 913 00:36:23,310 --> 00:36:26,190 knowing where you are in your own distribution is. 914 00:36:26,190 --> 00:36:30,190 I think you should not think about anything else in poker 915 00:36:30,190 --> 00:36:34,380 until you have bought and paid for a house by knowing where 916 00:36:34,380 --> 00:36:37,170 you are in your own distribution, 917 00:36:37,170 --> 00:36:38,887 in shaping it to be balanced. 918 00:36:38,887 --> 00:36:40,220 Don't think about anything else. 919 00:36:40,220 --> 00:36:43,260 Everything else is just window dressing 920 00:36:43,260 --> 00:36:46,570 compared to this concept. 921 00:36:46,570 --> 00:36:48,260 So here we are again. 922 00:36:48,260 --> 00:36:50,430 So we're going to go through this hand, the one 923 00:36:50,430 --> 00:36:52,555 that I told you about at the beginning of the talk, 924 00:36:52,555 --> 00:36:54,429 and we're going to try to read our own hand. 925 00:36:54,429 --> 00:36:56,470 So again, we're playing against this player who's 926 00:36:56,470 --> 00:36:58,800 better than us, some stuff happens, 927 00:36:58,800 --> 00:37:00,360 what do we do on the river? 928 00:37:00,360 --> 00:37:04,599 How do we think about that from a game theoretic perspective? 929 00:37:04,599 --> 00:37:06,140 So there are kind of three ways again 930 00:37:06,140 --> 00:37:07,550 that I alluded to in the beginning 931 00:37:07,550 --> 00:37:08,900 that people might think about it, right? 932 00:37:08,900 --> 00:37:11,240 So the first one is my hand versus your hand, OK? 933 00:37:11,240 --> 00:37:12,330 Well, I have aces. 934 00:37:12,330 --> 00:37:13,510 What do I think he has? 935 00:37:13,510 --> 00:37:15,280 King queen? 936 00:37:15,280 --> 00:37:15,780 King 10? 937 00:37:15,780 --> 00:37:17,765 Maybe he has queen 10? 938 00:37:17,765 --> 00:37:19,210 Maybe he's bluffing? 939 00:37:19,210 --> 00:37:20,930 Maybe he has queen nine? 940 00:37:20,930 --> 00:37:22,784 What is his most likely hand? 941 00:37:22,784 --> 00:37:24,450 And probably as most of you have already 942 00:37:24,450 --> 00:37:26,540 realized-- so Kevin told me that you'd all played at least 943 00:37:26,540 --> 00:37:28,040 100 tournaments so far, I'm guessing 944 00:37:28,040 --> 00:37:33,140 some a lot more-- it's really hard to put someone 945 00:37:33,140 --> 00:37:37,040 on a particular hand, not particularly useful. 946 00:37:37,040 --> 00:37:39,620 So the next thing you might try to do 947 00:37:39,620 --> 00:37:42,070 is my hand versus your distribution. 948 00:37:42,070 --> 00:37:46,790 How are my aces doing against all the hands 949 00:37:46,790 --> 00:37:50,060 that you might have given the actions you've taken? 950 00:37:50,060 --> 00:37:51,850 I can't really put you on one hand, 951 00:37:51,850 --> 00:37:55,990 but I can look at your actions and see 952 00:37:55,990 --> 00:38:00,814 what sort of distribution they might suggest. 953 00:38:00,814 --> 00:38:02,480 And then the last one is my distribution 954 00:38:02,480 --> 00:38:04,070 versus your distribution. 955 00:38:04,070 --> 00:38:06,260 And this is I can look at your actions 956 00:38:06,260 --> 00:38:08,080 and I can look at my actions, and I 957 00:38:08,080 --> 00:38:11,470 can try to shape my actions such that they maximally 958 00:38:11,470 --> 00:38:13,960 exploit your actions. 959 00:38:13,960 --> 00:38:16,390 So it's not so much about what I'm doing with my aces. 960 00:38:16,390 --> 00:38:20,590 It's about what I'm doing with all the hands that I'd have, 961 00:38:20,590 --> 00:38:24,309 where I just happen to have aces here. 962 00:38:24,309 --> 00:38:26,600 And this is the style that's most complimentary to game 963 00:38:26,600 --> 00:38:27,900 theory. 964 00:38:27,900 --> 00:38:32,250 So again, we're on this river and with pot odds with my aces 965 00:38:32,250 --> 00:38:35,410 I might be thinking, am I good at least a third of the time 966 00:38:35,410 --> 00:38:37,215 here? 967 00:38:37,215 --> 00:38:39,090 But if I'm doing that I'm trying to do magic, 968 00:38:39,090 --> 00:38:42,180 because I'm trying to figure out exactly what he has. 969 00:38:42,180 --> 00:38:44,660 And I don't think we need to do that here. 970 00:38:44,660 --> 00:38:45,540 Right? 971 00:38:45,540 --> 00:38:48,460 What I want to be thinking is, well, how much of the time 972 00:38:48,460 --> 00:38:51,260 do I need to call to make my opponent 973 00:38:51,260 --> 00:38:54,910 indifferent to bluffing? 974 00:38:54,910 --> 00:38:57,466 Any guesses? 975 00:38:57,466 --> 00:38:57,965 Yeah? 976 00:38:57,965 --> 00:39:00,290 AUDIENCE: Like 40% of the time? 977 00:39:00,290 --> 00:39:01,230 MATT HAWRILENKO: Yeah. 978 00:39:01,230 --> 00:39:04,980 So something like 1 over 1 plus s. 979 00:39:07,670 --> 00:39:09,389 So how do we get there? 980 00:39:09,389 --> 00:39:11,430 So this is the slide-- guys, if you pay attention 981 00:39:11,430 --> 00:39:13,790 to one slide this whole talk, this 982 00:39:13,790 --> 00:39:15,675 is the slide to pay attention to. 983 00:39:15,675 --> 00:39:17,800 This is the slide where we map the ace, king, queen 984 00:39:17,800 --> 00:39:19,130 game to actual poker. 985 00:39:19,130 --> 00:39:22,030 So the whole idea of poker from a game theory perspective 986 00:39:22,030 --> 00:39:24,380 is we're going to try to make bluffing zero 987 00:39:24,380 --> 00:39:25,510 EV for our opponents. 988 00:39:25,510 --> 00:39:28,130 So we're going to call with the proportion of our hands. 989 00:39:28,130 --> 00:39:30,960 We're going to make bluffing zero EV. 990 00:39:30,960 --> 00:39:33,520 So in real poker, games that allow raising, 991 00:39:33,520 --> 00:39:37,440 that means we could potentially be raising. 992 00:39:37,440 --> 00:39:40,270 So we want to be continuing 1 over 1 plus s 993 00:39:40,270 --> 00:39:43,680 at the time, at least calling, pondering arrays. 994 00:39:43,680 --> 00:39:45,880 So what do we see? 995 00:39:45,880 --> 00:39:47,970 So if this is the ace, king, queen game, 996 00:39:47,970 --> 00:39:50,040 we're going to map it to real poker this way. 997 00:39:50,040 --> 00:39:53,340 This is like our 99th percentile hand, the very best hand we 998 00:39:53,340 --> 00:39:55,260 can have in this spot, right? 999 00:39:55,260 --> 00:39:57,610 So on that board there were two kings on the board, 1000 00:39:57,610 --> 00:40:00,945 so a 99th percentile hand would be like quad kings, right? 1001 00:40:00,945 --> 00:40:02,620 Would be four of a kind. 1002 00:40:02,620 --> 00:40:05,086 This is our worst hand, the very worst hand we could have 1003 00:40:05,086 --> 00:40:06,211 in this spot, I don't know. 1004 00:40:06,211 --> 00:40:09,170 A four deuce. 1005 00:40:09,170 --> 00:40:11,460 And so what we're going to do-- so again, 1006 00:40:11,460 --> 00:40:14,120 these are the hands that are the very best at showdown, 1007 00:40:14,120 --> 00:40:16,020 very high EV. 1008 00:40:16,020 --> 00:40:19,540 Very worst at showdown, very low EV. 1009 00:40:19,540 --> 00:40:21,770 So we're going to be calling or raising 1 over 1 1010 00:40:21,770 --> 00:40:24,290 plus s of the time. 1011 00:40:24,290 --> 00:40:27,830 So the question is going to be, what is our distribution here? 1012 00:40:27,830 --> 00:40:31,520 What is 1 over 1 plus s? 1013 00:40:31,520 --> 00:40:33,550 Our bluffed value ratio is going to be s over 1 1014 00:40:33,550 --> 00:40:36,380 plus s of our worst hands, right? 1015 00:40:36,380 --> 00:40:39,420 These are the hands that gain the most value by bluffing, 1016 00:40:39,420 --> 00:40:39,920 right? 1017 00:40:39,920 --> 00:40:43,790 The ones that are going to do the worst at showdown. 1018 00:40:43,790 --> 00:40:46,422 Well, not for us in this spot. 1019 00:40:46,422 --> 00:40:47,880 I'm going to talk about that later. 1020 00:40:47,880 --> 00:40:50,430 Let's leave that for a second. 1021 00:40:50,430 --> 00:40:52,960 But those are the hands that my opponent should be bluffing, 1022 00:40:52,960 --> 00:40:53,460 right? 1023 00:40:56,080 --> 00:40:58,270 So if we think about our value betting range, 1024 00:40:58,270 --> 00:41:01,370 I might have a different value betting range than you. 1025 00:41:01,370 --> 00:41:04,600 And that has implications for how we play differently 1026 00:41:04,600 --> 00:41:05,610 than each other. 1027 00:41:05,610 --> 00:41:07,685 So the wider my value betting range 1028 00:41:07,685 --> 00:41:13,050 is, the more hands I need to be bluffing. 1029 00:41:13,050 --> 00:41:16,840 As this region expands, this region expands. 1030 00:41:16,840 --> 00:41:20,770 So if my opponent is value betting more hands, 1031 00:41:20,770 --> 00:41:23,040 they should also be bluffing more. 1032 00:41:23,040 --> 00:41:26,610 So when you see some of the very best no-limit players 1033 00:41:26,610 --> 00:41:29,230 play these guys who are just complete animals-- you're like, 1034 00:41:29,230 --> 00:41:31,610 how are they bluffing that there? 1035 00:41:31,610 --> 00:41:33,290 How are they calling that there? 1036 00:41:33,290 --> 00:41:37,290 How are they making this value bet so thin? 1037 00:41:37,290 --> 00:41:40,110 This how they do it, right? 1038 00:41:40,110 --> 00:41:43,380 If they're value betting a lot, they're also bluffing a lot. 1039 00:41:43,380 --> 00:41:45,010 So you have to call them more. 1040 00:41:45,010 --> 00:41:47,787 So the more they bluff, the more they have to value bet. 1041 00:41:47,787 --> 00:41:49,870 This is one of the places where a lot of beginners 1042 00:41:49,870 --> 00:41:54,110 just get way, way out of whack, because bluffing is-- 1043 00:41:54,110 --> 00:41:56,660 it starts scary and then it gets sexy, 1044 00:41:56,660 --> 00:42:01,210 and then it gets something in between. 1045 00:42:01,210 --> 00:42:04,330 So the whole idea, don't let this get out of whack. 1046 00:42:06,990 --> 00:42:11,060 And again, the larger amount that my opponent bets, 1047 00:42:11,060 --> 00:42:12,520 the less frequently I have to call. 1048 00:42:12,520 --> 00:42:15,290 The less they bet, the more frequently I have to call. 1049 00:42:15,290 --> 00:42:19,720 So we're about to our own hand. 1050 00:42:19,720 --> 00:42:22,450 Let's keep these couple of things in mind. 1051 00:42:22,450 --> 00:42:24,200 So again, I think reading your own hand is 1052 00:42:24,200 --> 00:42:25,700 the most important skill in poker, 1053 00:42:25,700 --> 00:42:28,330 and it's because what you do with part of your distribution 1054 00:42:28,330 --> 00:42:30,174 shapes what you do with the rest of it. 1055 00:42:30,174 --> 00:42:32,590 And so what we're about to do is we're going to go through 1056 00:42:32,590 --> 00:42:34,506 and we're going to sort of make some frequency 1057 00:42:34,506 --> 00:42:37,660 updates on each street. 1058 00:42:37,660 --> 00:42:39,320 So we're going to do two updates. 1059 00:42:39,320 --> 00:42:41,942 We're going to sort of update what our hands might be given 1060 00:42:41,942 --> 00:42:43,150 the cards that have come out. 1061 00:42:43,150 --> 00:42:46,030 So there's a card removal effect, right? 1062 00:42:46,030 --> 00:42:48,570 If an ace comes out, I'm a lot less likely 1063 00:42:48,570 --> 00:42:51,900 to have a pair of aces because there are fewer combinations. 1064 00:42:51,900 --> 00:42:55,540 And then we're also going to account for the actions 1065 00:42:55,540 --> 00:42:56,780 that we take. 1066 00:42:56,780 --> 00:42:58,720 So let's just do it. 1067 00:42:58,720 --> 00:42:59,350 It'll be clear. 1068 00:42:59,350 --> 00:42:59,850 So, OK. 1069 00:42:59,850 --> 00:43:01,266 So I've opened two off the button. 1070 00:43:01,266 --> 00:43:03,369 So here's some kind of reasonable range 1071 00:43:03,369 --> 00:43:04,660 for opening two off the button. 1072 00:43:04,660 --> 00:43:06,910 So we've gotten rid of all the hands that aren't here. 1073 00:43:06,910 --> 00:43:09,750 This is what I might have right now, OK? 1074 00:43:09,750 --> 00:43:11,940 So you don't really need to pay attention 1075 00:43:11,940 --> 00:43:15,360 to the specifics here, but flop comes, king, jack, eight. 1076 00:43:15,360 --> 00:43:18,170 So now I'm going to update for card removal. 1077 00:43:18,170 --> 00:43:20,469 So all the hands in orange are the frequencies 1078 00:43:20,469 --> 00:43:21,510 that have changed, right? 1079 00:43:21,510 --> 00:43:24,424 So eights, I could have had six of them 1080 00:43:24,424 --> 00:43:26,590 before the flop came, but now that there's an eight, 1081 00:43:26,590 --> 00:43:28,810 I only have three of them, et cetera. 1082 00:43:28,810 --> 00:43:31,080 So our total combination down the bottom 1083 00:43:31,080 --> 00:43:33,950 here has gone down, right? 1084 00:43:33,950 --> 00:43:35,630 So now what happens? 1085 00:43:35,630 --> 00:43:38,680 Well, they check, I bet. 1086 00:43:38,680 --> 00:43:41,270 So what hands am I betting here when my opponent checks? 1087 00:43:41,270 --> 00:43:42,440 Well, I'm getting rid of some of them. 1088 00:43:42,440 --> 00:43:44,356 I don't know if they're the right ones or not, 1089 00:43:44,356 --> 00:43:49,280 but I'm getting rid of some pairs, some bottom pairs, 1090 00:43:49,280 --> 00:43:50,590 some gut shots. 1091 00:43:50,590 --> 00:43:53,500 I might not be betting those here, right? 1092 00:43:53,500 --> 00:43:57,020 So the hands in white are all the hands I'm still betting. 1093 00:43:57,020 --> 00:43:59,520 And again, our frequency is coming down. 1094 00:43:59,520 --> 00:44:02,061 Our distribution is narrowing. 1095 00:44:02,061 --> 00:44:02,810 So the turn comes. 1096 00:44:02,810 --> 00:44:03,350 It's a five. 1097 00:44:03,350 --> 00:44:07,570 We get rid of some hands with fives in them. 1098 00:44:07,570 --> 00:44:08,756 I bet 2/3 of the pot. 1099 00:44:08,756 --> 00:44:11,130 So we get rid of all the hands in this distribution where 1100 00:44:11,130 --> 00:44:14,360 I'm not betting 2/3 of the pot. 1101 00:44:14,360 --> 00:44:17,960 And really quickly, when you're thinking 1102 00:44:17,960 --> 00:44:19,530 about reading your own hand-- and I'm 1103 00:44:19,530 --> 00:44:21,320 going to say that the most important time to be doing 1104 00:44:21,320 --> 00:44:23,930 it is probably off the table-- when you're thinking about it, 1105 00:44:23,930 --> 00:44:26,950 you should be really thinking about every street, OK? 1106 00:44:26,950 --> 00:44:27,450 So OK. 1107 00:44:27,450 --> 00:44:29,870 So these are the hands that I'm value betting. 1108 00:44:29,870 --> 00:44:34,190 Turns out I'm value betting about 94 combinations here. 1109 00:44:34,190 --> 00:44:36,130 How's my proportion of bluffs? 1110 00:44:36,130 --> 00:44:37,775 So I'm value betting 94 combinations. 1111 00:44:37,775 --> 00:44:39,990 I have a total of 120. 1112 00:44:39,990 --> 00:44:41,420 So that leaves what? 1113 00:44:41,420 --> 00:44:42,970 26 hands. 1114 00:44:42,970 --> 00:44:46,660 So how often should I be bluffing? 1115 00:44:46,660 --> 00:44:48,620 Or-- hm. 1116 00:44:48,620 --> 00:44:49,330 96. 1117 00:44:49,330 --> 00:44:52,354 I'm value betting 96 leaving 24 bluff hands. 1118 00:44:52,354 --> 00:44:53,770 So how often should I be bluffing? 1119 00:44:53,770 --> 00:44:57,590 OK, so 96 times-- what's that? 1120 00:44:57,590 --> 00:45:03,900 Is it like 1 over 1 plus s, s over 1 plus s, s over 1 plus s? 1121 00:45:03,900 --> 00:45:07,090 So times 0.4-- that's the amount I'm betting, 1122 00:45:07,090 --> 00:45:11,060 I'm betting 40% of the pot-- times 1 plus 0.4. 1123 00:45:11,060 --> 00:45:14,930 So 96 times 0.4. 1124 00:45:14,930 --> 00:45:15,610 Yeah. 1125 00:45:15,610 --> 00:45:17,980 96 times 0.4 over 1.4. 1126 00:45:17,980 --> 00:45:18,480 All right. 1127 00:45:18,480 --> 00:45:22,175 So I should be bluffing about 27 hands. 1128 00:45:22,175 --> 00:45:22,800 What do I have? 1129 00:45:22,800 --> 00:45:24,320 16, 24? 1130 00:45:24,320 --> 00:45:24,860 Huh. 1131 00:45:24,860 --> 00:45:25,526 Did pretty well. 1132 00:45:25,526 --> 00:45:26,500 I'm happy with that. 1133 00:45:26,500 --> 00:45:27,549 Pretty good shape. 1134 00:45:27,549 --> 00:45:28,090 I don't know. 1135 00:45:28,090 --> 00:45:29,030 I don't know about all the other actions. 1136 00:45:29,030 --> 00:45:30,863 We can argue about what I'm checking behind, 1137 00:45:30,863 --> 00:45:33,100 but we don't want to over think it. 1138 00:45:33,100 --> 00:45:36,020 So generally speaking, I want to be checking in on each street. 1139 00:45:36,020 --> 00:45:37,020 Like, ooh. 1140 00:45:37,020 --> 00:45:41,640 Am I balanced here in the way that I should be balanced? 1141 00:45:41,640 --> 00:45:46,680 So the river comes a king, and now we have fewer combinations. 1142 00:45:46,680 --> 00:45:49,110 So what do I do with my aces? 1143 00:45:49,110 --> 00:45:53,115 So again, s, the bet size, he bets $1,080,000 1144 00:45:53,115 --> 00:45:55,960 into a $720,000 chip pot. 1145 00:45:55,960 --> 00:45:57,670 So s is 1.5. 1146 00:45:57,670 --> 00:46:02,350 I should be calling 1.5 over 2.5, 40%. 1147 00:46:02,350 --> 00:46:05,440 That's 40% of hands that beat a bluff. 1148 00:46:05,440 --> 00:46:08,120 So what does that look like? 1149 00:46:08,120 --> 00:46:11,122 So if we're thinking about our calling region, 1150 00:46:11,122 --> 00:46:13,580 what I've done here is I've just sort of taken all my hands 1151 00:46:13,580 --> 00:46:19,150 and I've ranked them, and so kings represent my top 1%, king 1152 00:46:19,150 --> 00:46:20,260 jack. 1153 00:46:20,260 --> 00:46:21,085 Now we're at 9%. 1154 00:46:21,085 --> 00:46:23,585 This is like the cumulative sort of frequency distribution 1155 00:46:23,585 --> 00:46:24,460 with my hands ranked. 1156 00:46:28,590 --> 00:46:30,490 And I'm saying here in this distribution, 1157 00:46:30,490 --> 00:46:33,660 queen jack is the worst hand that still beats a bluff. 1158 00:46:33,660 --> 00:46:38,130 We can argue about that, but rough guess. 1159 00:46:38,130 --> 00:46:43,800 So first nothing in excess, calling 1 over 1 plus 1160 00:46:43,800 --> 00:46:46,730 s of a time. 1161 00:46:46,730 --> 00:46:47,637 Where are we? 1162 00:46:47,637 --> 00:46:48,890 Ooh. 1163 00:46:48,890 --> 00:46:50,542 This is surprising to me. 1164 00:46:50,542 --> 00:46:52,560 This felt like a tough decision, right? 1165 00:46:52,560 --> 00:46:55,480 So we're actually at the 62nd percentile here. 1166 00:46:55,480 --> 00:47:01,130 So one question is, so from this, what should I be doing? 1167 00:47:01,130 --> 00:47:03,400 Should I be calling or folding? 1168 00:47:03,400 --> 00:47:04,180 Folding. 1169 00:47:04,180 --> 00:47:05,540 Yeah. 1170 00:47:05,540 --> 00:47:07,540 So it looks like I'm calling with my king queen. 1171 00:47:07,540 --> 00:47:09,860 I might be folding king 10 maybe. 1172 00:47:09,860 --> 00:47:12,010 We can talk about that a little bit. 1173 00:47:12,010 --> 00:47:14,820 But aces seem like a pretty clear fold here. 1174 00:47:18,640 --> 00:47:22,890 Suppose my opponent thinks that I'll fold good hands like aces, 1175 00:47:22,890 --> 00:47:24,720 and so he's like, mm. 1176 00:47:24,720 --> 00:47:26,865 I'm going to bluff 90% of the time here. 1177 00:47:26,865 --> 00:47:28,250 Is he exploiting me? 1178 00:47:34,710 --> 00:47:37,756 Seeing head shakes. 1179 00:47:37,756 --> 00:47:39,110 He's not exploiting me, right? 1180 00:47:39,110 --> 00:47:39,800 So why not? 1181 00:47:43,252 --> 00:47:43,752 Yeah? 1182 00:47:43,752 --> 00:47:46,716 AUDIENCE: Because you win on his bluff. 1183 00:47:46,716 --> 00:47:49,383 Such a big question at the time, it makes up for the pot 1184 00:47:49,383 --> 00:47:50,174 that you're losing. 1185 00:47:50,174 --> 00:47:51,090 MATT HAWRILENKO: Yeah. 1186 00:47:51,090 --> 00:47:54,126 My distribution is really strong here, right? 1187 00:47:54,126 --> 00:48:00,479 Of the hands that beat a bluff, like half of them have trips. 1188 00:48:00,479 --> 00:48:01,270 That's crazy to me. 1189 00:48:04,190 --> 00:48:04,800 So no. 1190 00:48:04,800 --> 00:48:06,591 So he's not exploiting me, but we will talk 1191 00:48:06,591 --> 00:48:09,680 about exploitation in a minute. 1192 00:48:09,680 --> 00:48:11,830 So we solved it, right? 1193 00:48:11,830 --> 00:48:12,860 So we fold aces. 1194 00:48:12,860 --> 00:48:15,534 We even fold king 10. 1195 00:48:15,534 --> 00:48:16,950 So one question is, do we actually 1196 00:48:16,950 --> 00:48:18,220 want to have a distribution in the spot 1197 00:48:18,220 --> 00:48:19,386 where we have to fold trips? 1198 00:48:21,860 --> 00:48:27,160 And if that feels kind of bad, well, two possibilities. 1199 00:48:27,160 --> 00:48:29,460 One it just feels bad, or two, it 1200 00:48:29,460 --> 00:48:32,570 might mean we sort of screwed up on the way here. 1201 00:48:32,570 --> 00:48:34,050 It's not the worst. 1202 00:48:34,050 --> 00:48:36,000 It's not a four flush board. 1203 00:48:36,000 --> 00:48:37,860 There are no straights on it, right? 1204 00:48:37,860 --> 00:48:40,050 Some folding trips here, that feels kind of bad. 1205 00:48:40,050 --> 00:48:41,170 So what might that mean? 1206 00:48:41,170 --> 00:48:44,080 A couple of things, right? 1207 00:48:44,080 --> 00:48:48,000 So one thing we could do is I probably 1208 00:48:48,000 --> 00:48:50,692 want a distribution where I don't have to fold it. 1209 00:48:50,692 --> 00:48:52,650 And again, it depends a little bit on bet size, 1210 00:48:52,650 --> 00:48:54,714 but this is a pretty reasonable rule of thumb 1211 00:48:54,714 --> 00:48:56,130 when you're thinking about shaping 1212 00:48:56,130 --> 00:48:57,630 your play off the table. 1213 00:48:57,630 --> 00:49:00,490 So one thing that we can do, we can add some hands 1214 00:49:00,490 --> 00:49:01,370 in from earlier. 1215 00:49:01,370 --> 00:49:03,100 Ooh, maybe I should have played the turn a little bit 1216 00:49:03,100 --> 00:49:03,600 differently. 1217 00:49:03,600 --> 00:49:05,120 Maybe I should have played preflop, 1218 00:49:05,120 --> 00:49:07,203 maybe I should have played some more hands, right? 1219 00:49:07,203 --> 00:49:09,290 So we can start to expand our range. 1220 00:49:09,290 --> 00:49:10,190 Right? 1221 00:49:10,190 --> 00:49:12,440 Now we're calling with most all of our kings. 1222 00:49:14,944 --> 00:49:16,860 We can actually construct a distribution where 1223 00:49:16,860 --> 00:49:19,690 we have to call it aces, right? 1224 00:49:19,690 --> 00:49:22,430 If we're playing way more hands and if we're 1225 00:49:22,430 --> 00:49:26,790 value betting way more hands throughout, all of a sudden 1226 00:49:26,790 --> 00:49:29,240 our distribution is wider, right? 1227 00:49:29,240 --> 00:49:32,780 And now I should be in the same spot with the same hand 1228 00:49:32,780 --> 00:49:36,320 and do something differently because my strategy to get here 1229 00:49:36,320 --> 00:49:37,830 was different. 1230 00:49:37,830 --> 00:49:39,390 And again, that's the same idea. 1231 00:49:39,390 --> 00:49:41,630 You see these really good players 1232 00:49:41,630 --> 00:49:45,980 making these crazily thin value bets, and this is why. 1233 00:49:45,980 --> 00:49:50,339 They're bluffing a lot so they value bet a lot. 1234 00:49:50,339 --> 00:49:52,130 The main idea that I want you to take away, 1235 00:49:52,130 --> 00:49:54,020 if we sort of think of a principle, 1236 00:49:54,020 --> 00:49:56,640 if I find myself on the river and I have more medium strength 1237 00:49:56,640 --> 00:49:59,810 hands, I have to call more with medium strength hands, 1238 00:49:59,810 --> 00:50:02,890 otherwise I can get exploited. 1239 00:50:02,890 --> 00:50:06,399 Suppose we were deeper and our opponent bets into us, 1240 00:50:06,399 --> 00:50:07,690 and we have a bunch more chips. 1241 00:50:07,690 --> 00:50:11,080 Which hands should we be bluff raising from this distribution? 1242 00:50:11,080 --> 00:50:14,920 So most the time, if I'm just straight bluffing, 1243 00:50:14,920 --> 00:50:18,170 I want to be bluffing with the very bottom of my distribution 1244 00:50:18,170 --> 00:50:20,110 because that's the part the gains the most 1245 00:50:20,110 --> 00:50:21,470 when my opponent folds. 1246 00:50:21,470 --> 00:50:25,740 If I'm bluff raising, it's a little different. 1247 00:50:25,740 --> 00:50:28,450 If I'm bluff raising, I want to think about, OK, 1248 00:50:28,450 --> 00:50:30,980 so what is the set of hands I would fold? 1249 00:50:30,980 --> 00:50:35,270 What are the very best hands in that set that I would fold? 1250 00:50:35,270 --> 00:50:37,230 And I may as well choose those, right? 1251 00:50:37,230 --> 00:50:40,610 Because it seems like those hands have more value, so 1252 00:50:40,610 --> 00:50:42,190 if I'm going to fold them anyway, 1253 00:50:42,190 --> 00:50:45,320 it's a dominated strategy to bluff raise 1254 00:50:45,320 --> 00:50:48,917 with hands that are weaker than that, right? 1255 00:50:48,917 --> 00:50:50,750 So if I'm bluff raising, it should be really 1256 00:50:50,750 --> 00:50:53,050 with the very best hands that I would otherwise 1257 00:50:53,050 --> 00:50:55,345 fold, not with the very bottom of my distribution. 1258 00:51:00,590 --> 00:51:02,060 So what do we see here? 1259 00:51:02,060 --> 00:51:05,034 So first off, we want to check for balance on all streets. 1260 00:51:05,034 --> 00:51:06,450 That's the big thing we take away. 1261 00:51:06,450 --> 00:51:11,050 We can argue about little bits of distributions, 1262 00:51:11,050 --> 00:51:14,280 but really, we're not solving to the second decimal point 1263 00:51:14,280 --> 00:51:16,060 here, right? 1264 00:51:16,060 --> 00:51:18,800 Second, we can look at this board all day. 1265 00:51:18,800 --> 00:51:23,419 We can look at this king jack eight five king board all day. 1266 00:51:23,419 --> 00:51:25,585 Unfortunately, that's not going to be the board that 1267 00:51:25,585 --> 00:51:28,940 comes every time, and if we just look at this board all day, 1268 00:51:28,940 --> 00:51:31,720 we're going to start to overfit our strategy a little bit 1269 00:51:31,720 --> 00:51:33,040 to this board. 1270 00:51:33,040 --> 00:51:40,550 So what I suggest you focus on is fixing the glaring errors, 1271 00:51:40,550 --> 00:51:43,400 and there will be glaring errors, places 1272 00:51:43,400 --> 00:51:45,730 where your distribution is way, way imbalanced. 1273 00:51:48,529 --> 00:51:50,445 I still find glaring errors when I play poker, 1274 00:51:50,445 --> 00:51:54,540 and I've been trying to do this for a little while now. 1275 00:51:54,540 --> 00:51:57,370 Another thought which is not quite so obvious from what I've 1276 00:51:57,370 --> 00:51:59,950 said so far is, you don't want to needlessly bifurcate 1277 00:51:59,950 --> 00:52:00,710 your distribution. 1278 00:52:00,710 --> 00:52:02,340 How do you bifurcate your distribution? 1279 00:52:02,340 --> 00:52:07,790 Well, suppose preflop, I raise some amount 1280 00:52:07,790 --> 00:52:10,750 with some set of hands and in a different amount 1281 00:52:10,750 --> 00:52:12,970 with a different set of hands. 1282 00:52:12,970 --> 00:52:15,370 Ooh, right? 1283 00:52:15,370 --> 00:52:18,730 All of a sudden I started off here with 310 combinations, 1284 00:52:18,730 --> 00:52:22,326 and I got down to, I don't know, 60 or something. 1285 00:52:22,326 --> 00:52:24,700 But now all of a sudden, I'm starting off with half that. 1286 00:52:24,700 --> 00:52:29,050 I'm starting off with 155, in this game tree gets smaller 1287 00:52:29,050 --> 00:52:30,720 really, really quickly. 1288 00:52:30,720 --> 00:52:32,590 So I'm not saying don't do it. 1289 00:52:32,590 --> 00:52:36,070 But I'm saying if you do it, A, have a really good reason 1290 00:52:36,070 --> 00:52:37,190 for doing it. 1291 00:52:37,190 --> 00:52:40,060 B, be really careful. 1292 00:52:40,060 --> 00:52:42,420 Be really careful of betting different amounts 1293 00:52:42,420 --> 00:52:43,740 with different hand types. 1294 00:52:43,740 --> 00:52:45,750 I basically don't. 1295 00:52:45,750 --> 00:52:47,470 I will bet different amounts based 1296 00:52:47,470 --> 00:52:48,990 on the texture of the board. 1297 00:52:48,990 --> 00:52:50,470 So if boards are more [? drawy ?] 1298 00:52:50,470 --> 00:52:54,590 I might tend to make my bet sizes larger earlier. 1299 00:52:54,590 --> 00:52:57,350 But I won't bet different amounts with different hand 1300 00:52:57,350 --> 00:53:01,700 types because I think it the possible gain is so small 1301 00:53:01,700 --> 00:53:05,881 and the possible loss is so big. 1302 00:53:05,881 --> 00:53:08,130 And the last thing that I found pretty cool about this 1303 00:53:08,130 --> 00:53:10,840 was when I started really, really spending 1304 00:53:10,840 --> 00:53:12,490 time trying to read my own hand, I'd 1305 00:53:12,490 --> 00:53:14,700 start to find these consistent situations where 1306 00:53:14,700 --> 00:53:17,047 I would get really imbalanced. 1307 00:53:17,047 --> 00:53:19,380 And then when you want to start to think about moving on 1308 00:53:19,380 --> 00:53:21,335 to exploitive play after you have paid off 1309 00:53:21,335 --> 00:53:24,220 a house with your poker winnings, 1310 00:53:24,220 --> 00:53:28,400 you want to maybe identify those spots in your own opponents, 1311 00:53:28,400 --> 00:53:28,910 right? 1312 00:53:28,910 --> 00:53:30,368 If you're getting imbalanced there, 1313 00:53:30,368 --> 00:53:35,100 other people probably are too, so be ready for that. 1314 00:53:35,100 --> 00:53:40,660 So what do I want to say here? 1315 00:53:40,660 --> 00:53:43,950 So I guess we've ignored a few assumptions of this model, 1316 00:53:43,950 --> 00:53:45,180 right? 1317 00:53:45,180 --> 00:53:47,920 The biggest assumption in a toy game like the ace king queen 1318 00:53:47,920 --> 00:53:50,340 game or the Coin Flip Clairvoyance game 1319 00:53:50,340 --> 00:53:54,450 is that distributions are symmetric. 1320 00:53:54,450 --> 00:53:58,970 If I'm applying the ace king queen game to my river 1321 00:53:58,970 --> 00:54:02,220 situation here, I'm implicitly assuming 1322 00:54:02,220 --> 00:54:04,780 that my opponents and I essentially 1323 00:54:04,780 --> 00:54:08,450 have an equivalent distribution of aces, kings, and queens. 1324 00:54:08,450 --> 00:54:11,010 That's not always true in poker. 1325 00:54:11,010 --> 00:54:18,160 So generally I'd say that this sort this mapping is actually 1326 00:54:18,160 --> 00:54:21,220 fairly robust, but at the same time, 1327 00:54:21,220 --> 00:54:22,949 you have to be aware of situations 1328 00:54:22,949 --> 00:54:24,990 where your distributions aren't symmetric, right? 1329 00:54:24,990 --> 00:54:27,980 Like if you raise under the gun at a ten handed table 1330 00:54:27,980 --> 00:54:30,450 and the big blind calls, your distribution 1331 00:54:30,450 --> 00:54:31,600 is way, way stronger. 1332 00:54:31,600 --> 00:54:32,520 It's not symmetric. 1333 00:54:32,520 --> 00:54:34,730 So you're going to have a different set of actions. 1334 00:54:34,730 --> 00:54:38,360 However, as you progress throughout the hand, 1335 00:54:38,360 --> 00:54:42,700 distributions sort of tend to become more and more symmetric. 1336 00:54:42,700 --> 00:54:46,550 So generally speaking, it's a model with some assumptions 1337 00:54:46,550 --> 00:54:49,140 which are meh. 1338 00:54:49,140 --> 00:54:51,650 But in my experience, it holds pretty well. 1339 00:54:55,005 --> 00:54:56,880 So another thing I haven't talked about today 1340 00:54:56,880 --> 00:54:59,850 is I haven't told you which hands to value bet, right? 1341 00:54:59,850 --> 00:55:01,800 So I've told you the calling proportion, 1342 00:55:01,800 --> 00:55:02,930 bluffing proportion. 1343 00:55:02,930 --> 00:55:05,750 I haven't said anything about, how do you choose what to bet? 1344 00:55:05,750 --> 00:55:08,931 And there are game theory games that can kind of give you 1345 00:55:08,931 --> 00:55:09,680 insight into that. 1346 00:55:09,680 --> 00:55:12,280 You can get insight into that from Bill and Jared's book. 1347 00:55:12,280 --> 00:55:18,890 But I think that what's most important 1348 00:55:18,890 --> 00:55:21,410 here is reading your own hand is the thing that I 1349 00:55:21,410 --> 00:55:24,480 think can integrate into everybody's game. 1350 00:55:24,480 --> 00:55:27,720 Whatever hands you currently value bet, it can work for you. 1351 00:55:27,720 --> 00:55:28,220 Right? 1352 00:55:28,220 --> 00:55:31,185 And it can sort of work equally well for the right player 1353 00:55:31,185 --> 00:55:33,440 as it can for the very loose player. 1354 00:55:33,440 --> 00:55:36,290 So the reason I've decided to talk about the reading 1355 00:55:36,290 --> 00:55:38,910 your own hand approach is this is a very flexible approach 1356 00:55:38,910 --> 00:55:41,380 that can work for a lot of people in a lot of situations. 1357 00:55:44,164 --> 00:55:45,830 And, you know, as you get better and you 1358 00:55:45,830 --> 00:55:48,650 start to play more and more hands-- or fewer and fewer, 1359 00:55:48,650 --> 00:55:50,400 depending where you fall on the spectrum-- 1360 00:55:50,400 --> 00:55:52,320 but generally as you start to play more and more hands, what 1361 00:55:52,320 --> 00:55:54,860 you're doing here, thinking from sort of like this game 1362 00:55:54,860 --> 00:55:57,790 theoretic perspective is you're moving 1363 00:55:57,790 --> 00:56:02,130 towards hands that are closer to threshold hands, closer to zero 1364 00:56:02,130 --> 00:56:02,860 easy. 1365 00:56:02,860 --> 00:56:07,350 So adding in the nth hand has a much smaller effect 1366 00:56:07,350 --> 00:56:11,100 than adding in that, like, fifth hand, right? 1367 00:56:11,100 --> 00:56:14,080 Or if you think about all the good hands in poker, right? 1368 00:56:14,080 --> 00:56:17,027 So you're always going to play your jacks, 1369 00:56:17,027 --> 00:56:18,860 you're always going to play your 10s, right? 1370 00:56:18,860 --> 00:56:24,350 Adding in that nine six suited has a much smaller impact 1371 00:56:24,350 --> 00:56:28,510 on your EV than adding in the 10s, the nines, the eights. 1372 00:56:31,040 --> 00:56:32,876 Yeah, that's all I want to say there. 1373 00:56:32,876 --> 00:56:35,000 So in the last few minutes I'm going to talk really 1374 00:56:35,000 --> 00:56:36,680 briefly about exploitive play. 1375 00:56:36,680 --> 00:56:38,700 So exploitive play. 1376 00:56:38,700 --> 00:56:41,670 So if we're looking at the top, our best hand's at showdown, 1377 00:56:41,670 --> 00:56:42,880 our worst hand's at showdown. 1378 00:56:42,880 --> 00:56:45,171 And this is about where our value betting threshold is. 1379 00:56:47,710 --> 00:56:50,650 The way to exploit from a game theoretic perspective 1380 00:56:50,650 --> 00:56:53,780 isn't to say, ah, I know he's bluffing! 1381 00:56:53,780 --> 00:56:55,300 I call a blind! 1382 00:56:55,300 --> 00:56:58,800 Although apparently that can work pretty well sometimes. 1383 00:56:58,800 --> 00:57:01,370 The way you do it is you expand to the margins. 1384 00:57:01,370 --> 00:57:05,210 So if normally I'm value betting here and my opponent-- 1385 00:57:05,210 --> 00:57:08,180 or normally I'm calling here and my opponent bluffs 1386 00:57:08,180 --> 00:57:10,480 way too much, I might expand to the marginal calls. 1387 00:57:10,480 --> 00:57:12,516 That's one thing I might do. 1388 00:57:12,516 --> 00:57:13,890 If they don't value bet enough, I 1389 00:57:13,890 --> 00:57:16,910 might contract the marginal calls, right? 1390 00:57:16,910 --> 00:57:21,190 But again, the ones that are very close to zero EV, 1391 00:57:21,190 --> 00:57:23,880 I'm never making the big fold here. 1392 00:57:23,880 --> 00:57:25,510 If they fold too much, I might expand 1393 00:57:25,510 --> 00:57:26,968 to the marginal bluffs a little bit 1394 00:57:26,968 --> 00:57:31,100 and contract the marginal bets a little bit. 1395 00:57:31,100 --> 00:57:34,100 If they call too much, I'm going to expand the marginal bets 1396 00:57:34,100 --> 00:57:35,870 and contract the marginal bluffs. 1397 00:57:35,870 --> 00:57:38,370 So what that means is you get away 1398 00:57:38,370 --> 00:57:45,060 from, I think he's bluffing 80% of the time in this situation, 1399 00:57:45,060 --> 00:57:46,920 to-- in this exact situation, and I'm 1400 00:57:46,920 --> 00:57:50,590 going to catch him-- to, hm. 1401 00:57:50,590 --> 00:57:52,650 This person seems a little bluffy, 1402 00:57:52,650 --> 00:57:54,600 so I'm going to shape my distribution 1403 00:57:54,600 --> 00:57:56,450 just a little bit around that. 1404 00:57:59,380 --> 00:57:59,880 OK. 1405 00:58:03,800 --> 00:58:06,260 So the other idea about exploitive play 1406 00:58:06,260 --> 00:58:08,940 is as your read grows stronger, as you have more confidence, 1407 00:58:08,940 --> 00:58:10,680 you can expand to the margins, right? 1408 00:58:10,680 --> 00:58:13,720 So a little read, you move the margins a little. 1409 00:58:13,720 --> 00:58:17,460 Big read, you move the margins more. 1410 00:58:17,460 --> 00:58:21,520 For example, well, OK. 1411 00:58:21,520 --> 00:58:26,360 So with our example hand, we have a margin right about here, 1412 00:58:26,360 --> 00:58:28,220 but we can start to move it wider 1413 00:58:28,220 --> 00:58:30,830 as our read grow stronger that our opponent might be bluffing. 1414 00:58:30,830 --> 00:58:32,990 But again, we don't want to move it 1415 00:58:32,990 --> 00:58:36,170 wider with just the hand that I happen to be holding right now. 1416 00:58:36,170 --> 00:58:37,974 We need to be thinking, how strong is it, 1417 00:58:37,974 --> 00:58:39,640 and how wide am I comfortable moving it? 1418 00:58:42,944 --> 00:58:45,079 Yeah. 1419 00:58:45,079 --> 00:58:46,620 So if we're thinking about exploiting 1420 00:58:46,620 --> 00:58:48,703 with my sort of, like, shamefully exploitive hand, 1421 00:58:48,703 --> 00:58:49,400 what did I do? 1422 00:58:49,400 --> 00:58:52,335 Well, it wasn't quite a 1 over 1 plus s situation. 1423 00:58:52,335 --> 00:58:53,710 We're in this situation where I'm 1424 00:58:53,710 --> 00:58:58,190 going to be shoving in the top hands and folding the worst. 1425 00:58:58,190 --> 00:59:04,410 So if my margin was here, if my margin was, I don't know, 1426 00:59:04,410 --> 00:59:06,410 eight six suited or something, maybe I'd 1427 00:59:06,410 --> 00:59:08,340 go, like, eight five suited. 1428 00:59:08,340 --> 00:59:12,330 Maybe I'd go king deuce off suit, something like that. 1429 00:59:12,330 --> 00:59:14,560 Instead what I did was I went all the way 1430 00:59:14,560 --> 00:59:16,730 to the very bottom of my distribution 1431 00:59:16,730 --> 00:59:18,720 and got suitably punished. 1432 00:59:22,050 --> 00:59:22,550 Yeah. 1433 00:59:22,550 --> 00:59:26,760 So however confident you think you are in your read, 1434 00:59:26,760 --> 00:59:29,351 you are probably overestimating it. 1435 00:59:29,351 --> 00:59:29,850 So, yeah. 1436 00:59:29,850 --> 00:59:31,940 That's where I was. 1437 00:59:31,940 --> 00:59:34,720 One other thought here before I wrap up, 1438 00:59:34,720 --> 00:59:37,510 and that's this idea of advanced exploitive play, 1439 00:59:37,510 --> 00:59:39,580 and this is fun. 1440 00:59:39,580 --> 00:59:41,990 So we think about expanding the margins. 1441 00:59:41,990 --> 00:59:44,320 We think, oh, in this spot he's bluffing. 1442 00:59:44,320 --> 00:59:46,220 I should call more. 1443 00:59:46,220 --> 00:59:50,140 But now if you start to make slightly more subtle reads, 1444 00:59:50,140 --> 00:59:55,464 this is an opponent who bluffs a little too much on the river, 1445 00:59:55,464 --> 00:59:57,255 I could punish him on the river by calling, 1446 00:59:57,255 --> 00:59:59,546 or this is an opponent who folds too much on the river. 1447 00:59:59,546 --> 01:00:01,490 I could punish them, or I could punish her 1448 01:00:01,490 --> 01:00:03,067 by betting the river. 1449 01:00:03,067 --> 01:00:04,650 But they're going to get that feedback 1450 01:00:04,650 --> 01:00:07,067 pretty soon if you're just starting to hammer every river. 1451 01:00:07,067 --> 01:00:08,524 Another thing you can do is you can 1452 01:00:08,524 --> 01:00:10,335 make the pot a little bit bigger, right? 1453 01:00:10,335 --> 01:00:11,460 So don't forget about this. 1454 01:00:11,460 --> 01:00:12,750 This is the pot. 1455 01:00:12,750 --> 01:00:15,810 If you start making this bigger on earlier streets, 1456 01:00:15,810 --> 01:00:17,580 maybe against this particular player, 1457 01:00:17,580 --> 01:00:19,830 I raise a little bit more preflop. 1458 01:00:19,830 --> 01:00:22,570 I bet a little bit more on the flop. 1459 01:00:22,570 --> 01:00:23,070 Right? 1460 01:00:23,070 --> 01:00:25,940 The pot's bigger on the turn, so now I'm betting on the turn. 1461 01:00:25,940 --> 01:00:28,910 And now with the river I take all my normal actions 1462 01:00:28,910 --> 01:00:31,790 except I know that I'm winning a few too many pots 1463 01:00:31,790 --> 01:00:33,470 because they're folding too much, 1464 01:00:33,470 --> 01:00:35,800 and now the few too many parts that I'm winning 1465 01:00:35,800 --> 01:00:37,906 are proportionally larger. 1466 01:00:37,906 --> 01:00:42,110 So this is this idea of we can exploit downstream. 1467 01:00:42,110 --> 01:00:44,232 We can anticipate where they're weak. 1468 01:00:44,232 --> 01:00:47,660 We cannot change our play in that spot and tip them off, 1469 01:00:47,660 --> 01:00:49,810 but we can change it earlier. 1470 01:00:49,810 --> 01:00:54,470 So to wrap up, so you want to know yourself. 1471 01:00:54,470 --> 01:00:56,370 You want know your own hand, right? 1472 01:00:56,370 --> 01:00:57,695 That's the first key. 1473 01:00:57,695 --> 01:01:00,680 The second key is to keep it balanced, 1474 01:01:00,680 --> 01:01:02,390 and you want to exploit the margins. 1475 01:01:02,390 --> 01:01:03,960 And so as we think about Cepheus, 1476 01:01:03,960 --> 01:01:05,760 as we think about these algorithms coming 1477 01:01:05,760 --> 01:01:09,834 and exploiting players, so even in 20 years, computing power-- 1478 01:01:09,834 --> 01:01:10,500 oh, what's that? 1479 01:01:10,500 --> 01:01:12,680 Like 1,000 times greater or something? 1480 01:01:12,680 --> 01:01:14,160 Is that right? 1481 01:01:14,160 --> 01:01:14,755 Wrong? 1482 01:01:14,755 --> 01:01:15,880 AUDIENCE: Sounds all right. 1483 01:01:15,880 --> 01:01:16,610 MATT HAWRILENKO: Depending. 1484 01:01:16,610 --> 01:01:17,820 Depending if you believe Moore's law, I guess. 1485 01:01:17,820 --> 01:01:18,430 OK. 1486 01:01:18,430 --> 01:01:23,430 So even then, even when more poker games are tractable, 1487 01:01:23,430 --> 01:01:26,670 you're going to need toy games to draw insights 1488 01:01:26,670 --> 01:01:28,450 on what's going on. 1489 01:01:28,450 --> 01:01:31,160 As these strategies come out of the black boxes, if you 1490 01:01:31,160 --> 01:01:33,990 hope to grasp them, if you hope to hold onto them, 1491 01:01:33,990 --> 01:01:36,940 you need these kind of insights to be 1492 01:01:36,940 --> 01:01:40,680 able to have some scaffolding to start to put them on. 1493 01:01:40,680 --> 01:01:45,020 So I think I'm done, but if I were to summarize this talk one 1494 01:01:45,020 --> 01:01:46,820 way, don't be this guy. 1495 01:01:46,820 --> 01:01:48,630 Be this guy. 1496 01:01:48,630 --> 01:01:51,460 OK, we're done. 1497 01:01:51,460 --> 01:01:52,115 Any questions? 1498 01:01:55,930 --> 01:01:56,942 Ooh, wait. 1499 01:01:56,942 --> 01:01:59,400 AUDIENCE: So if you're doing, like, Nash equilibrium, well, 1500 01:01:59,400 --> 01:02:01,135 that guarantees you a positive EV. 1501 01:02:01,135 --> 01:02:03,173 But [INAUDIBLE] that's always enough. 1502 01:02:03,173 --> 01:02:05,770 Like, if you're in tournament having a positive EV, 1503 01:02:05,770 --> 01:02:08,210 your chips will grow a little but [? maybe blinds ?] 1504 01:02:08,210 --> 01:02:09,910 are growing faster. 1505 01:02:09,910 --> 01:02:12,139 Is that an [INAUDIBLE] Nash equilibrium strategy, 1506 01:02:12,139 --> 01:02:13,680 or do you have to deviate if you want 1507 01:02:13,680 --> 01:02:15,110 a higher variance [INAUDIBLE]? 1508 01:02:15,110 --> 01:02:16,776 MATT HAWRILENKO: Yeah, so good question. 1509 01:02:16,776 --> 01:02:20,840 So the question-- and tell me-- let me make sure we answer it-- 1510 01:02:20,840 --> 01:02:23,590 the question is, OK, well, you can try to play an equilibrium 1511 01:02:23,590 --> 01:02:25,694 strategy and that's fine. 1512 01:02:25,694 --> 01:02:27,610 But if you're exploiting, you're winning more. 1513 01:02:27,610 --> 01:02:29,235 And so if you're playing in tournaments 1514 01:02:29,235 --> 01:02:31,510 or these situations, you really need 1515 01:02:31,510 --> 01:02:33,240 to exploit to win more money. 1516 01:02:33,240 --> 01:02:35,250 Is that kind of-- yeah? 1517 01:02:35,250 --> 01:02:36,230 So yeah. 1518 01:02:36,230 --> 01:02:38,440 That idea has been around for a long time, 1519 01:02:38,440 --> 01:02:42,610 and I think that that idea is driven 1520 01:02:42,610 --> 01:02:48,010 by people not really knowing just how strong game theory 1521 01:02:48,010 --> 01:02:51,170 strategies might be, and just how strong sort of like, OK. 1522 01:02:51,170 --> 01:02:53,237 So what is a Nash equilibria here? 1523 01:02:53,237 --> 01:02:54,820 When you're playing a Nash equilibria, 1524 01:02:54,820 --> 01:02:57,403 the idea is that your opponents are going to impale themselves 1525 01:02:57,403 --> 01:02:59,680 on their own mistakes, and you're 1526 01:02:59,680 --> 01:03:02,130 trying to make as few mistakes as possible. 1527 01:03:02,130 --> 01:03:06,270 And how big is that, right? 1528 01:03:06,270 --> 01:03:08,220 It's kind of an empirical question. 1529 01:03:08,220 --> 01:03:13,392 In my experience, it can be a lot bigger 1530 01:03:13,392 --> 01:03:14,350 than most people think. 1531 01:03:14,350 --> 01:03:15,766 Because when you start exploiting, 1532 01:03:15,766 --> 01:03:17,480 you start making mistakes. 1533 01:03:17,480 --> 01:03:20,180 And you start sort of getting impaled a little bit 1534 01:03:20,180 --> 01:03:21,920 on your own mistakes too. 1535 01:03:21,920 --> 01:03:28,150 And my guess is for most of us, for 99% of us, 1536 01:03:28,150 --> 01:03:30,840 we're going to make a lot more mistakes than we think we do. 1537 01:03:30,840 --> 01:03:32,510 So we think we're exploiting. 1538 01:03:32,510 --> 01:03:34,760 At the same time we're getting exploited. 1539 01:03:34,760 --> 01:03:41,601 So actually, thinking about that is an empirical question, 1540 01:03:41,601 --> 01:03:42,100 right? 1541 01:03:42,100 --> 01:03:47,030 Like, how do human players do right now against Cepheus? 1542 01:03:47,030 --> 01:03:49,340 My guess is not very well. 1543 01:03:49,340 --> 01:03:50,840 In fact, my guess is that they're 1544 01:03:50,840 --> 01:03:55,820 losing more than the top players, 1545 01:03:55,820 --> 01:03:57,450 the top human players are winning 1546 01:03:57,450 --> 01:03:58,960 from other human players. 1547 01:03:58,960 --> 01:04:02,450 So that was certainly kind of my experience a few years ago. 1548 01:04:02,450 --> 01:04:06,354 So it's one of these things where you'd see it, right? 1549 01:04:06,354 --> 01:04:07,520 Like I think-- I don't know. 1550 01:04:07,520 --> 01:04:10,020 I feel like I saw some stat where Cepheus was beating 1551 01:04:10,020 --> 01:04:14,020 really good professionals for four bets per hundred 1552 01:04:14,020 --> 01:04:16,010 hands, which is a lot. 1553 01:04:16,010 --> 01:04:17,230 Which is a lot. 1554 01:04:17,230 --> 01:04:20,720 Like, most top players are winning less than half of that. 1555 01:04:20,720 --> 01:04:22,372 So Nash equilibria, yeah. 1556 01:04:22,372 --> 01:04:23,080 Pretty darn good. 1557 01:04:23,080 --> 01:04:25,804 Maybe one day when human players are better, 1558 01:04:25,804 --> 01:04:27,220 you need to start exploiting more. 1559 01:04:27,220 --> 01:04:29,730 I don't think we're anywhere close. 1560 01:04:29,730 --> 01:04:31,696 Other questions? 1561 01:04:31,696 --> 01:04:34,301 Anything else? 1562 01:04:34,301 --> 01:04:35,550 All right, I guess we're done. 1563 01:04:35,550 --> 01:04:36,049 Thanks guys. 1564 01:04:36,049 --> 01:04:38,590 I'll stick around for a little bit if anyone wants to chat. 1565 01:04:38,590 --> 01:04:41,640 [APPLAUSE]