1 00:00:00,080 --> 00:00:02,579 NARRATOR: The following content is provided under a Creative 2 00:00:02,579 --> 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 --> 00:00:17,260 at ocw.mit.edu. 8 00:00:21,967 --> 00:00:23,300 PROFESSOR: So let's get started. 9 00:00:23,300 --> 00:00:24,980 Today we're going to be talking about preflop, which 10 00:00:24,980 --> 00:00:26,570 is the last thing I definitely want 11 00:00:26,570 --> 00:00:29,350 to cover before the [? Sakuna ?] tournament. 12 00:00:29,350 --> 00:00:31,892 As you know, this is going to be one of my last lectures. 13 00:00:31,892 --> 00:00:33,850 I'm teaching one or to over the next two weeks, 14 00:00:33,850 --> 00:00:35,224 but we're primarily going to have 15 00:00:35,224 --> 00:00:37,970 guest speakers talking about more the macro poker 16 00:00:37,970 --> 00:00:39,280 environment. 17 00:00:39,280 --> 00:00:41,490 So why are we doing preflop? 18 00:00:41,490 --> 00:00:43,215 So in tournaments, most of your value 19 00:00:43,215 --> 00:00:45,940 is going to come from what you do preflop-- 20 00:00:45,940 --> 00:00:47,400 playing it close to optimally. 21 00:00:47,400 --> 00:00:49,430 And the reason is because a lot of people 22 00:00:49,430 --> 00:00:51,220 don't do this good at all. 23 00:00:51,220 --> 00:00:52,990 Like they really, really play preflop 24 00:00:52,990 --> 00:00:55,910 badly because it's very counter intuitive. 25 00:00:55,910 --> 00:00:57,050 Especially live. 26 00:00:57,050 --> 00:00:59,320 Like people have a much tougher time 27 00:00:59,320 --> 00:01:02,300 doing this because either they're 28 00:01:02,300 --> 00:01:04,390 afraid of getting knocked down on a bad hand, 29 00:01:04,390 --> 00:01:06,610 or their afraid of showing down a bad hand, 30 00:01:06,610 --> 00:01:10,400 or live players are just worse in general. 31 00:01:10,400 --> 00:01:12,800 So for whatever reason, people screw this up online. 32 00:01:12,800 --> 00:01:14,911 A little bit on live a lot. 33 00:01:14,911 --> 00:01:16,660 In addition, one of the reasons that we're 34 00:01:16,660 --> 00:01:19,720 spending an entire day on it is it's relatively easier to solve 35 00:01:19,720 --> 00:01:21,340 from a mathematical standpoint. 36 00:01:21,340 --> 00:01:24,190 Like we get close to a Nash equilibrium 37 00:01:24,190 --> 00:01:26,130 because there aren't that many variables. 38 00:01:26,130 --> 00:01:28,365 Whereas postflop, there are a million variables. 39 00:01:28,365 --> 00:01:30,740 It's more related to kind of putting things into patterns 40 00:01:30,740 --> 00:01:32,812 that you might be close to. 41 00:01:32,812 --> 00:01:34,020 So that's why I'm doing this. 42 00:01:34,020 --> 00:01:35,680 And then let's start with a scenario 43 00:01:35,680 --> 00:01:38,138 that we're going to be analyzing for the rest of the class. 44 00:01:42,260 --> 00:01:42,922 There we go. 45 00:01:42,922 --> 00:01:43,880 So here's our scenario. 46 00:01:43,880 --> 00:01:47,680 So I'm-- how it works heads up is the dealer button is a small 47 00:01:47,680 --> 00:01:48,360 blind. 48 00:01:48,360 --> 00:01:50,560 That's a slight break in the rules 49 00:01:50,560 --> 00:01:53,276 because you assume I'm button, he's small blind, 50 00:01:53,276 --> 00:01:55,400 I'm big blind, but they change around a little bit. 51 00:01:55,400 --> 00:01:58,860 This way, the button isn't the last one to act every round. 52 00:01:58,860 --> 00:02:01,280 So here, I'm first one to act preflop and then last 53 00:02:01,280 --> 00:02:03,240 to act every round thereafter. 54 00:02:03,240 --> 00:02:05,710 If I were big blind, I'd be less every single round. 55 00:02:05,710 --> 00:02:10,039 So it's a minor variation that you guys should just know. 56 00:02:10,039 --> 00:02:13,800 So situation-- I'm small blind for 125, 57 00:02:13,800 --> 00:02:15,470 he's big blind for 150, and there's 58 00:02:15,470 --> 00:02:17,840 a 25 ante, which is why there's 50 in the pot. 59 00:02:17,840 --> 00:02:19,790 And the question is what do we do here? 60 00:02:19,790 --> 00:02:24,581 OK, so we have 9-6 offsuit with 2 1/2 m. 61 00:02:24,581 --> 00:02:26,330 We're in the small blind, and we're trying 62 00:02:26,330 --> 00:02:27,780 to figure out what do we do. 63 00:02:27,780 --> 00:02:29,920 So the answer here might not be that intuitive, 64 00:02:29,920 --> 00:02:32,730 and I don't think I'd give it to you right away. 65 00:02:32,730 --> 00:02:36,120 But how we figure it out is just with a normal semi-bluffing 66 00:02:36,120 --> 00:02:37,050 equation. 67 00:02:37,050 --> 00:02:41,000 We take a look at-- OK, so everything preflop 68 00:02:41,000 --> 00:02:43,880 is a semi-bluff because we have some chance of winning, 69 00:02:43,880 --> 00:02:46,680 and we're virtually never less than 30%. 70 00:02:46,680 --> 00:02:49,710 So we just use this semi-bluffing formula 71 00:02:49,710 --> 00:02:52,900 that we've seen before where our EV is just 72 00:02:52,900 --> 00:02:55,770 going to be the pot times the chance he folds, 73 00:02:55,770 --> 00:03:00,029 plus the chance he doesn't fold times our EV when he calls. 74 00:03:00,029 --> 00:03:02,070 We need to figure out some sort of calling range. 75 00:03:02,070 --> 00:03:04,700 I just made up one here that seemed 76 00:03:04,700 --> 00:03:08,020 like about at the pro level, and this is pretty wide. 77 00:03:08,020 --> 00:03:12,220 Like him calling with like Ace-2 or Jack-10 or 2-2. 78 00:03:12,220 --> 00:03:13,701 This is a wideish range. 79 00:03:13,701 --> 00:03:15,700 I think a lot of players for the tournament life 80 00:03:15,700 --> 00:03:17,830 might not call this wide, but it ends up 81 00:03:17,830 --> 00:03:21,715 being like 27.6% of hands he's calling. 82 00:03:21,715 --> 00:03:23,340 So we're going to use it as a baseline, 83 00:03:23,340 --> 00:03:26,260 and then later we'll show why that doesn't matter. 84 00:03:26,260 --> 00:03:31,090 So our question is, what's our equity versus range here? 85 00:03:31,090 --> 00:03:34,580 And what we can do there is just plug into PokerTracker. 86 00:03:34,580 --> 00:03:36,120 So the idea is we don't know what 87 00:03:36,120 --> 00:03:38,144 hand he has and we don't care. 88 00:03:38,144 --> 00:03:40,060 It's unrealistic to think that we can get down 89 00:03:40,060 --> 00:03:41,950 to any sort of hand he'll be calling with, 90 00:03:41,950 --> 00:03:43,241 but we can get down to a range. 91 00:03:43,241 --> 00:03:45,970 We can say he's equally likely to have 92 00:03:45,970 --> 00:03:50,200 any assortment of the hands in that range because if he calls, 93 00:03:50,200 --> 00:03:52,050 that means that he has one of those hands. 94 00:03:52,050 --> 00:03:54,850 So we can compare our equity versus any one of those hands 95 00:03:54,850 --> 00:03:57,100 to get our equity versus range, and we 96 00:03:57,100 --> 00:03:58,930 can do that in PokerTracker. 97 00:03:58,930 --> 00:04:01,138 So what you're going to do is you're going to open up 98 00:04:01,138 --> 00:04:04,290 the equity calculator, you're going to put in 9-6 off, 99 00:04:04,290 --> 00:04:06,160 and then you're going to put in this. 100 00:04:06,160 --> 00:04:07,750 I actually just drew it in there, 101 00:04:07,750 --> 00:04:09,500 but that's the same thing I showed before, 102 00:04:09,500 --> 00:04:11,850 which is pocket 2s are better. 103 00:04:11,850 --> 00:04:13,990 Ace-2, King-2 , Queen-- sorry. 104 00:04:13,990 --> 00:04:16,500 King-10, Queen-10, Jack-10, and then the same 105 00:04:16,500 --> 00:04:20,279 for offsuit, which is the representation 106 00:04:20,279 --> 00:04:21,200 of this entire thing. 107 00:04:21,200 --> 00:04:25,470 I just need to separate offsuit or suited, 108 00:04:25,470 --> 00:04:29,470 and then I assumed by jack-10, it meant that entire corner, 109 00:04:29,470 --> 00:04:31,480 although PokerTracker likes specifying. 110 00:04:31,480 --> 00:04:33,350 Anyway, so this is our equity versus. 111 00:04:33,350 --> 00:04:36,382 This is saying that if we go in with 9-6 112 00:04:36,382 --> 00:04:40,070 and he calls with anything in that range, 113 00:04:40,070 --> 00:04:42,310 we are 34% to win this hand. 114 00:04:42,310 --> 00:04:45,090 So I don't know if that's about what you'd expect. 115 00:04:45,090 --> 00:04:47,450 It seems higher than I would have thought initially, 116 00:04:47,450 --> 00:04:49,940 but that's our equity verses range. 117 00:04:49,940 --> 00:04:52,280 If we go all in and he calls, we can 118 00:04:52,280 --> 00:04:55,650 assume we're a 35-65 underdog without even 119 00:04:55,650 --> 00:04:56,610 knowing what he has. 120 00:04:56,610 --> 00:04:57,940 And then once we find out what he has, 121 00:04:57,940 --> 00:05:00,273 we will find out whether we're slightly better or worse, 122 00:05:00,273 --> 00:05:02,900 but that doesn't really matter. 123 00:05:02,900 --> 00:05:09,230 So we can calculate our EV in this hand in the same way 124 00:05:09,230 --> 00:05:11,730 that we're used to calculating semi-bluffing. 125 00:05:11,730 --> 00:05:15,770 The EV of the push is going to be this. 126 00:05:15,770 --> 00:05:18,700 The chance of him folding times 425. 127 00:05:18,700 --> 00:05:20,410 If he calls 27% of the time, that 128 00:05:20,410 --> 00:05:25,200 means he folds whatever this is like 73% of the time. 129 00:05:25,200 --> 00:05:28,920 So that's our value from him folding-- the fold equity. 130 00:05:28,920 --> 00:05:31,770 And then 20% of the time we're in a showdown situation 131 00:05:31,770 --> 00:05:35,460 where of that [? push ?] time that he calls, 132 00:05:35,460 --> 00:05:39,260 we're 35 to win 1250 and we're 65 to lose 950, 133 00:05:39,260 --> 00:05:43,170 resulting in a total equity of 253. 134 00:05:43,170 --> 00:05:46,130 So that's a lot of chips for what might 135 00:05:46,130 --> 00:05:47,729 seem like a very marginal move. 136 00:05:47,729 --> 00:05:49,270 By going all in here, you're actually 137 00:05:49,270 --> 00:05:50,750 making that many chips. 138 00:05:50,750 --> 00:05:55,410 And in fact, a more provocative way 139 00:05:55,410 --> 00:05:57,480 to describe it is if you don't do this, 140 00:05:57,480 --> 00:06:00,570 you are losing 250 chips. 141 00:06:00,570 --> 00:06:03,750 You only need 1,000 to win this whole tournament, 142 00:06:03,750 --> 00:06:06,920 and by folding what seems like a very weak hand 143 00:06:06,920 --> 00:06:10,800 in this position, you are just giving him 250 chips of value. 144 00:06:10,800 --> 00:06:14,400 So that's a lot, and that shows how counterintuitive this is. 145 00:06:14,400 --> 00:06:16,970 That a situation where you have really bad cards, 146 00:06:16,970 --> 00:06:19,030 you don't realize that these are actually really, 147 00:06:19,030 --> 00:06:21,090 really good cards in the situation. 148 00:06:21,090 --> 00:06:22,660 In fact, no matter what, your cards 149 00:06:22,660 --> 00:06:25,040 are basically good in this situation. 150 00:06:25,040 --> 00:06:30,980 Because this situation makes any two cards good enough. 151 00:06:30,980 --> 00:06:33,907 So let's talk about-- so we made one assumption, which 152 00:06:33,907 --> 00:06:34,990 is what his call range is. 153 00:06:34,990 --> 00:06:36,662 Did you have a question? 154 00:06:36,662 --> 00:06:38,020 Oh, OK. 155 00:06:38,020 --> 00:06:40,890 So we made some assumption about what his call range is, and I 156 00:06:40,890 --> 00:06:41,990 said it didn't matter. 157 00:06:41,990 --> 00:06:42,590 Why? 158 00:06:42,590 --> 00:06:48,130 Because what we can do here is make the call range a variable. 159 00:06:48,130 --> 00:06:50,560 So this fold percent is a variable, 160 00:06:50,560 --> 00:06:53,900 and then our win percent is related to the percent 161 00:06:53,900 --> 00:06:55,610 that he folds. 162 00:06:55,610 --> 00:06:58,859 Because if he calls a small range of hands when we get 163 00:06:58,859 --> 00:07:00,400 called, he's going to be crushing us. 164 00:07:00,400 --> 00:07:02,880 Whereas if he calls like 90% of the time, 165 00:07:02,880 --> 00:07:04,870 we're probably ahead of his range 166 00:07:04,870 --> 00:07:07,200 because he calls a lot of worse hands. 167 00:07:07,200 --> 00:07:09,560 Anyway, so you can take a graph and just 168 00:07:09,560 --> 00:07:12,700 look, OK, he calls somewhere between 0% of the time 169 00:07:12,700 --> 00:07:17,560 in 100% of the time, and then we can do this EV equation for all 170 00:07:17,560 --> 00:07:20,140 those hands by calculating OK, so what's 171 00:07:20,140 --> 00:07:22,820 our equity versus calling range? 172 00:07:22,820 --> 00:07:23,840 This doesn't change. 173 00:07:23,840 --> 00:07:27,010 We still win or lose the same amount every time. 174 00:07:27,010 --> 00:07:32,570 And say so if we were always pushing here, 175 00:07:32,570 --> 00:07:35,049 if he calls with whatever range, this is our EV. 176 00:07:35,049 --> 00:07:36,590 And then one thing that's interesting 177 00:07:36,590 --> 00:07:40,070 about this graph is what? 178 00:07:40,070 --> 00:07:41,730 It's always positive, which means 179 00:07:41,730 --> 00:07:46,060 that no matter what his calling range is, this push is good. 180 00:07:46,060 --> 00:07:47,600 It might be more intuitive this way. 181 00:07:47,600 --> 00:07:50,490 Like if he folds 100% of the time-- 182 00:07:50,490 --> 00:07:53,140 if he only calls 0% of the time, we trend up 183 00:07:53,140 --> 00:07:54,580 to a number around here. 184 00:07:54,580 --> 00:07:57,710 And what number's around here? 185 00:07:57,710 --> 00:07:58,560 That's just this. 186 00:07:58,560 --> 00:08:00,760 It's the pot before we do anything. 187 00:08:00,760 --> 00:08:04,160 So if he folds 100% of the time, we just win the pot. 188 00:08:04,160 --> 00:08:06,610 Like that's our EV every hand, and it just trends 189 00:08:06,610 --> 00:08:07,700 based on this. 190 00:08:07,700 --> 00:08:11,440 Where the more he calls, typically the better the worse 191 00:08:11,440 --> 00:08:12,410 our EVs going to be. 192 00:08:12,410 --> 00:08:12,910 Yes? 193 00:08:17,430 --> 00:08:23,350 [? Yes. ?] We'll get to that. 194 00:08:23,350 --> 00:08:26,380 And that's a good question, although it's 195 00:08:26,380 --> 00:08:28,960 going to take us half the class to answer that. 196 00:08:28,960 --> 00:08:30,460 Anyway, so that's a cool thing here. 197 00:08:30,460 --> 00:08:33,400 So it's always positive, which means 198 00:08:33,400 --> 00:08:40,740 I'm saying-- no matter what his-- the villain does, always, 199 00:08:40,740 --> 00:08:44,850 always push all in with 9-6 offsuit in this position. 200 00:08:44,850 --> 00:08:46,980 So let's break it down into components. 201 00:08:46,980 --> 00:08:49,420 So to explain intuitively what drives 202 00:08:49,420 --> 00:08:52,837 this graph is your equity there is split into two parts 203 00:08:52,837 --> 00:08:53,920 because it's a semi-bluff. 204 00:08:53,920 --> 00:08:56,820 It's your fold equity and your showdown equity. 205 00:08:56,820 --> 00:08:58,840 So let's turn this into lines. 206 00:08:58,840 --> 00:09:01,530 So you see your fold equity just decreases the more 207 00:09:01,530 --> 00:09:03,810 he calls in a linear fashion. 208 00:09:03,810 --> 00:09:06,250 So that should be fairly intuitive. 209 00:09:06,250 --> 00:09:09,080 The proportion he calls reduces your fold equity 210 00:09:09,080 --> 00:09:11,860 by that amount, and then your showdown equity 211 00:09:11,860 --> 00:09:15,010 has a little curve here where you 212 00:09:15,010 --> 00:09:19,859 get more value from the showdown on average the more he calls. 213 00:09:19,859 --> 00:09:21,900 The only reason there's a little bit of curvature 214 00:09:21,900 --> 00:09:23,899 is because it's multiplied by the chances of him 215 00:09:23,899 --> 00:09:25,220 calling in the first plAce. 216 00:09:25,220 --> 00:09:29,730 So it's tilting in some direction. 217 00:09:29,730 --> 00:09:33,020 But anyway, these are curved. 218 00:09:33,020 --> 00:09:35,700 Makes this a very interesting optimization puzzle. 219 00:09:35,700 --> 00:09:39,820 And the reason we're positive at the end is for this reason. 220 00:09:39,820 --> 00:09:42,330 We're basically-- so this line, the total equity, 221 00:09:42,330 --> 00:09:44,186 is just the sum of these two. 222 00:09:44,186 --> 00:09:45,560 Where our showdown value is going 223 00:09:45,560 --> 00:09:50,900 to be negative over basically this entire range. 224 00:09:50,900 --> 00:09:53,320 Even when our fold equity reaches zero, 225 00:09:53,320 --> 00:09:57,080 that's when our showdown equity creeps just above zero. 226 00:09:57,080 --> 00:10:01,260 Regardless of what his calling range is, 227 00:10:01,260 --> 00:10:03,840 your average is like 175 chips of EV. 228 00:10:03,840 --> 00:10:07,060 Like the 20% call-- or whatever we said. 229 00:10:07,060 --> 00:10:10,020 The 27% calling range isn't necessarily optimal. 230 00:10:10,020 --> 00:10:12,110 He knows you have these cards. 231 00:10:12,110 --> 00:10:14,230 But on average, you're getting-- whatever, 232 00:10:14,230 --> 00:10:16,060 like 100 and something chips. 233 00:10:16,060 --> 00:10:18,500 And just to show how bad is folding, 234 00:10:18,500 --> 00:10:21,160 if you just open fold this for some reason, 235 00:10:21,160 --> 00:10:23,890 that's as bad as purposely calling it all 236 00:10:23,890 --> 00:10:26,010 in with 3-4 versus Ace-King. 237 00:10:26,010 --> 00:10:28,900 Like that's an equivalent amount of EV loss 238 00:10:28,900 --> 00:10:31,850 as folding this hand. 239 00:10:31,850 --> 00:10:34,540 So now let's talk about how hard this is going to be. 240 00:10:34,540 --> 00:10:37,770 So push/fold decisions are really 241 00:10:37,770 --> 00:10:40,220 hard to kind of intuitively figure out 242 00:10:40,220 --> 00:10:44,050 just because of the curvature and the steepness of those 243 00:10:44,050 --> 00:10:46,670 graphs are moving in weird directions 244 00:10:46,670 --> 00:10:49,220 and they're both moving at the same time with regard 245 00:10:49,220 --> 00:10:50,780 to all the other variables. 246 00:10:50,780 --> 00:10:53,720 So it makes it so that it's very hard to come up 247 00:10:53,720 --> 00:10:55,950 with very quick rules. 248 00:10:55,950 --> 00:10:58,180 Some variables are going to affect our decision, 249 00:10:58,180 --> 00:11:00,440 and the result is either push or fold. 250 00:11:00,440 --> 00:11:02,350 Our result isn't even as complicated 251 00:11:02,350 --> 00:11:04,670 as betting a certain amount, but the variables 252 00:11:04,670 --> 00:11:08,540 you have to consider are our cards, our position, our stack, 253 00:11:08,540 --> 00:11:11,100 and the villain's call range, which 254 00:11:11,100 --> 00:11:13,570 results in this five-dimensional ray that we 255 00:11:13,570 --> 00:11:18,500 have to slice and dice so that we have our push/fold decision 256 00:11:18,500 --> 00:11:19,780 range. 257 00:11:19,780 --> 00:11:23,280 So what we want to do is isolate for specific things. 258 00:11:23,280 --> 00:11:30,150 We want to say OK, let's take-- let's make this and this static 259 00:11:30,150 --> 00:11:31,850 so that we can solve for these two, 260 00:11:31,850 --> 00:11:34,570 or let's make these two static so we can solve for these two. 261 00:11:34,570 --> 00:11:36,740 So we can end up with a chart that looks something like this. 262 00:11:36,740 --> 00:11:38,448 And this is a little bit more manageable. 263 00:11:38,448 --> 00:11:41,570 We can just say this green area is when you should push 264 00:11:41,570 --> 00:11:44,240 and this yellow area is when you should fold. 265 00:11:44,240 --> 00:11:45,410 That's our goal here. 266 00:11:45,410 --> 00:11:47,880 To be able to develop that sort of chart. 267 00:11:47,880 --> 00:11:51,770 And then figure out what's the best thing to isolate. 268 00:11:51,770 --> 00:11:54,220 So let's get to it. 269 00:11:54,220 --> 00:11:55,739 So range is the postset of hands. 270 00:11:55,739 --> 00:11:56,780 This is how you write it. 271 00:11:59,262 --> 00:12:00,970 This is the assumption that we're making. 272 00:12:00,970 --> 00:12:02,850 So we're doing it for two reasons. 273 00:12:02,850 --> 00:12:04,680 Analyzing our opponent, which we're not going to be doing. 274 00:12:04,680 --> 00:12:06,930 We're going to assume we have no information about him 275 00:12:06,930 --> 00:12:10,430 because it's preflop, and a lot of it-- one of our assumptions 276 00:12:10,430 --> 00:12:12,220 is that he hasn't even acted yet, so we 277 00:12:12,220 --> 00:12:14,550 have no information at all. 278 00:12:14,550 --> 00:12:16,860 But we're going to be using it to determine our plays. 279 00:12:16,860 --> 00:12:19,350 Basically we're saying we have some sort of decision 280 00:12:19,350 --> 00:12:20,620 [INAUDIBLE] for our range. 281 00:12:20,620 --> 00:12:22,954 Like we certainly can't solve this for every single hand 282 00:12:22,954 --> 00:12:25,411 or at least we can't remember it, so what we're going to do 283 00:12:25,411 --> 00:12:27,630 is come up with a line where we say every hand 284 00:12:27,630 --> 00:12:29,540 above that certain line, i.e. 285 00:12:29,540 --> 00:12:31,640 That range above that line, is going 286 00:12:31,640 --> 00:12:34,790 to be good for our specific decision. 287 00:12:34,790 --> 00:12:36,540 And we're bringing these into percentiles, 288 00:12:36,540 --> 00:12:38,373 and that's how we're going to describe them. 289 00:12:38,373 --> 00:12:40,620 And we're using Sklansky-Carlson. 290 00:12:40,620 --> 00:12:44,880 His rankings for our breakdown of percentiles. 291 00:12:44,880 --> 00:12:46,710 But here's his original question, 292 00:12:46,710 --> 00:12:48,780 and this is just to explain where these come from 293 00:12:48,780 --> 00:12:51,470 and why this is particularly relevant to what we're doing. 294 00:12:51,470 --> 00:12:53,460 So his question is you're the small blind 295 00:12:53,460 --> 00:12:55,520 and you have a choice between either folding 296 00:12:55,520 --> 00:12:59,030 or open pushing a hand, or open pushing here means you push 297 00:12:59,030 --> 00:13:01,540 and you show your hand before he makes a call. 298 00:13:01,540 --> 00:13:05,210 And the question is how many chips is this good for? 299 00:13:05,210 --> 00:13:07,820 If you have one chip, or I guess we have two chips, 300 00:13:07,820 --> 00:13:11,320 you have since they're 1-2 blinds, if you have two chips 301 00:13:11,320 --> 00:13:14,950 and one is already in the small blind, your pot odds are 25%. 302 00:13:14,950 --> 00:13:16,800 So even if he knows-- he's going to call 303 00:13:16,800 --> 00:13:18,940 if he's anything more than a 50% favorite, 304 00:13:18,940 --> 00:13:23,350 so you have the odds to do that with at least a pretty bad hand 305 00:13:23,350 --> 00:13:24,690 and a lot of good hands. 306 00:13:24,690 --> 00:13:27,570 So x here is how big can your stack 307 00:13:27,570 --> 00:13:30,560 be before this starts becoming unprofitable? 308 00:13:30,560 --> 00:13:34,590 And the answer for Ace-Ace offsuit is about 70, 309 00:13:34,590 --> 00:13:36,502 and to explain how we got to that, 310 00:13:36,502 --> 00:13:38,210 we're going to make a couple assumptions. 311 00:13:38,210 --> 00:13:40,820 And you can see the clear relation 312 00:13:40,820 --> 00:13:43,790 between this methodology and what we're doing. 313 00:13:43,790 --> 00:13:46,620 So 1-2 blinds-- here a small blind with whatever. 314 00:13:46,620 --> 00:13:47,834 Here are bets x all in. 315 00:13:47,834 --> 00:13:49,500 And we're going to say big blind's going 316 00:13:49,500 --> 00:13:52,410 to call when EV's more than 50. 317 00:13:52,410 --> 00:13:55,082 Which he might do pot odds, which we're just going 318 00:13:55,082 --> 00:13:56,290 to ignore now for simplicity. 319 00:13:56,290 --> 00:13:58,123 We're just going to say big blind is calling 320 00:13:58,123 --> 00:14:00,230 when he's more than 50% to win. 321 00:14:00,230 --> 00:14:03,105 It's actually zero when he has the pot odds, which 322 00:14:03,105 --> 00:14:05,547 is this equation, but we're going to forget about that. 323 00:14:05,547 --> 00:14:07,130 Let's just say he's going to only call 324 00:14:07,130 --> 00:14:08,880 with literal better hands. 325 00:14:08,880 --> 00:14:12,060 So here he's going to call with Ace-8 326 00:14:12,060 --> 00:14:14,210 or pocket 2's because we have Ace-8. 327 00:14:14,210 --> 00:14:16,460 He's going to call with a pocket pair, which is always 328 00:14:16,460 --> 00:14:17,960 going to be better, and Ace-8, which 329 00:14:17,960 --> 00:14:19,730 is going to be equal or better. 330 00:14:19,730 --> 00:14:22,290 So that's his calling range 13% of the time. 331 00:14:22,290 --> 00:14:25,030 So we win 33% for this range, which 332 00:14:25,030 --> 00:14:29,020 is you just plug-in to the PokerTracker 333 00:14:29,020 --> 00:14:33,290 and it'll give you that you're a 30% underdog, which 334 00:14:33,290 --> 00:14:34,650 is what I did here. 335 00:14:34,650 --> 00:14:35,540 That's how you do it. 336 00:14:38,290 --> 00:14:40,580 And we get our EV from the situation, 337 00:14:40,580 --> 00:14:42,160 and we have to solve for x. 338 00:14:42,160 --> 00:14:45,610 So we want EV to be 0 because we're finding the marginal EV, 339 00:14:45,610 --> 00:14:47,820 and this is what we get. 340 00:14:47,820 --> 00:14:53,130 We get x, which is all the chips we 341 00:14:53,130 --> 00:14:56,190 had before we paid the big blind, 342 00:14:56,190 --> 00:15:00,080 and we lose x minus 1, which is all the chips we have 343 00:15:00,080 --> 00:15:02,154 after paying the small blind. 344 00:15:02,154 --> 00:15:03,820 So a little bit of nuance there and only 345 00:15:03,820 --> 00:15:07,030 changes our number by one, but that gives us our break even. 346 00:15:07,030 --> 00:15:08,829 And our break even here is like 62x. 347 00:15:08,829 --> 00:15:10,370 So the reason it's a little bit lower 348 00:15:10,370 --> 00:15:13,390 is it doesn't factor in the big blind doing pot odds, 349 00:15:13,390 --> 00:15:14,600 but that's the idea. 350 00:15:14,600 --> 00:15:17,162 So what we're going to do is we're going to solve this 351 00:15:17,162 --> 00:15:18,370 and we're not going to do it. 352 00:15:18,370 --> 00:15:20,441 Someone else did it. 353 00:15:20,441 --> 00:15:22,440 We're going to solve this for every single hand, 354 00:15:22,440 --> 00:15:23,960 and this is what Sklansky did. 355 00:15:23,960 --> 00:15:27,620 So he figured what your number here is going to be two things. 356 00:15:27,620 --> 00:15:30,190 The number of hands you are slightly better than, 357 00:15:30,190 --> 00:15:33,201 and why is this factor important? 358 00:15:33,201 --> 00:15:35,700 What's he going to do it if you have a better hand than him? 359 00:15:38,910 --> 00:15:40,020 He's going to fold. 360 00:15:40,020 --> 00:15:43,050 So this determines our fold equity, 361 00:15:43,050 --> 00:15:45,140 and then chance of winning when you're behind 362 00:15:45,140 --> 00:15:47,370 determines our equity when he actually does call. 363 00:15:47,370 --> 00:15:49,110 He just has perfect information which 364 00:15:49,110 --> 00:15:51,600 is why it's a little bit of a change 365 00:15:51,600 --> 00:15:57,310 and we're able to solve it out perfectly here. 366 00:15:57,310 --> 00:15:59,380 So Sklansky didn't know how to program, 367 00:15:59,380 --> 00:16:03,410 which is why Scott Carlson, or Victor Chubukov a couple days 368 00:16:03,410 --> 00:16:06,440 later-- apparently later the same day- 369 00:16:06,440 --> 00:16:07,440 came up with the answer. 370 00:16:07,440 --> 00:16:12,310 Where he said Aces have infinity value here 371 00:16:12,310 --> 00:16:15,040 where you can have an unlimited amount of chips 372 00:16:15,040 --> 00:16:18,430 and then show Aces and push them, and it's plus EV. 373 00:16:18,430 --> 00:16:20,430 We're not saying it's the most optimal decision, 374 00:16:20,430 --> 00:16:23,090 but you won't actually lose chips on average even if you 375 00:16:23,090 --> 00:16:25,050 have an unlimited chip stack. 376 00:16:25,050 --> 00:16:28,880 Whereas King, it only works for 1,290 chips. 377 00:16:28,880 --> 00:16:31,800 So we can solve it for every hand to get down to, 378 00:16:31,800 --> 00:16:35,210 you could do this with 3-2 off with 1.8 chips and so on. 379 00:16:35,210 --> 00:16:38,620 So this is our primary way to rank hands, 380 00:16:38,620 --> 00:16:41,740 and we're assuming that at least in a heads-up situation, 381 00:16:41,740 --> 00:16:44,899 this is a pretty good idea of what hands 382 00:16:44,899 --> 00:16:46,690 will have the most value especially when it 383 00:16:46,690 --> 00:16:48,000 comes to going all in. 384 00:16:48,000 --> 00:16:52,100 One other method is going to be equity versus three randoms, 385 00:16:52,100 --> 00:16:55,000 and it might be more relevant for multi-way pots. 386 00:16:55,000 --> 00:16:57,150 You just rank them by their expectation 387 00:16:57,150 --> 00:17:00,759 against three callers who haven't looked at their hand. 388 00:17:00,759 --> 00:17:03,050 But we're not going to do that especially because we're 389 00:17:03,050 --> 00:17:06,240 assuming generally we're going to get one caller, especially 390 00:17:06,240 --> 00:17:07,819 heads-up where you can only get one. 391 00:17:07,819 --> 00:17:11,419 But we're going to expand it out later. 392 00:17:11,419 --> 00:17:12,960 So just an example of what these are. 393 00:17:12,960 --> 00:17:16,560 Top 1% is Aces, top 5% is 10s and Ace-Queens. 394 00:17:16,560 --> 00:17:18,109 30% is this. 395 00:17:18,109 --> 00:17:20,589 And sorry to break it to you guys, 396 00:17:20,589 --> 00:17:22,990 but you're going to have to memorize these. 397 00:17:22,990 --> 00:17:25,916 So 5% you just remember their premium hands, just ten 398 00:17:25,916 --> 00:17:28,260 or Ace Queens, and I'm giving you little mnemonics 399 00:17:28,260 --> 00:17:29,690 to help you remember it. 400 00:17:29,690 --> 00:17:32,796 Like Ace-10 or better is 10%, and then 401 00:17:32,796 --> 00:17:35,420 like some sort of pocket pairs-- it's not even that big of deal 402 00:17:35,420 --> 00:17:37,690 if you go down to 2s here. 403 00:17:37,690 --> 00:17:41,000 20% is Ace-2 or pocket 2's. 404 00:17:41,000 --> 00:17:42,730 That's how you're going to remember it. 405 00:17:42,730 --> 00:17:46,510 And then 30% is Broadway, so Broadway is any two fAce cards. 406 00:17:46,510 --> 00:17:50,580 And an intuitive way to think about it is based on this. 407 00:17:50,580 --> 00:17:56,260 Broadway is just this corner here, which is about 1/3 408 00:17:56,260 --> 00:17:58,750 of the graph when you count in pocket pairs. 409 00:17:58,750 --> 00:18:01,565 So that's how you just remember 30%-- it's that corner. 410 00:18:01,565 --> 00:18:02,440 So it's not that bad. 411 00:18:02,440 --> 00:18:05,870 Just remember top 20% is Ace-2 and 2s. 412 00:18:05,870 --> 00:18:10,990 30% is Broadway, and then 10% is Ace-10-- not that bad. 413 00:18:10,990 --> 00:18:14,330 So 50% is just going to be the diagonal on the graph. 414 00:18:14,330 --> 00:18:18,560 It's any two cards adding up to 15. 415 00:18:18,560 --> 00:18:20,060 This is what I mean by the diagonal. 416 00:18:20,060 --> 00:18:23,930 Like this is your 13-by-13 graph where these are offsuit 417 00:18:23,930 --> 00:18:27,240 and these are suited, which is why we double count them. 418 00:18:27,240 --> 00:18:30,300 And then this hand adds up to 15. 419 00:18:30,300 --> 00:18:33,130 Ace-two and so does King-3 and so does Queen-4. 420 00:18:33,130 --> 00:18:35,160 So this is your 50th percentile hand. 421 00:18:35,160 --> 00:18:37,946 So that's how you're going to remember that. 422 00:18:37,946 --> 00:18:40,070 And then you don't really need to remember anything 423 00:18:40,070 --> 00:18:40,810 more than that. 424 00:18:40,810 --> 00:18:44,190 So 100% is going to be any two cards. 425 00:18:44,190 --> 00:18:46,430 It's going to be the entire graph here. 426 00:18:46,430 --> 00:18:50,170 So we're going to be talking about-- yeah? 427 00:18:50,170 --> 00:18:53,150 Percentage is the percent of hands 428 00:18:53,150 --> 00:18:55,150 that that range represents. 429 00:18:55,150 --> 00:18:58,270 So like this is the top 10% of hands. 430 00:18:58,270 --> 00:19:00,200 So if he calls-- if we assume he's 431 00:19:00,200 --> 00:19:02,440 going to call 10% of the time, we 432 00:19:02,440 --> 00:19:04,410 are saying that he will call with these cards 433 00:19:04,410 --> 00:19:05,710 and these cards only. 434 00:19:05,710 --> 00:19:08,120 And we're going to be talking about ranges 435 00:19:08,120 --> 00:19:16,490 from now on because it helps us understand what cards he has, 436 00:19:16,490 --> 00:19:18,980 to some extent, but also lets us use it 437 00:19:18,980 --> 00:19:22,430 as an idea to get-- to figure out exactly how often he's 438 00:19:22,430 --> 00:19:23,252 going to call. 439 00:19:23,252 --> 00:19:25,210 So we're just going to be talking about ranges, 440 00:19:25,210 --> 00:19:27,190 and this is what I mean when I say ranges. 441 00:19:27,190 --> 00:19:29,930 And to the extent that you're just doing this at the table, 442 00:19:29,930 --> 00:19:32,962 you just have to memorize these three numbers. 443 00:19:32,962 --> 00:19:34,420 Because this is easy, this is easy, 444 00:19:34,420 --> 00:19:36,475 and then just remember that tens are our 5%. 445 00:19:41,670 --> 00:19:43,810 When we're talking about ranges in general, 446 00:19:43,810 --> 00:19:47,460 a plus EV range-- a decision that's 447 00:19:47,460 --> 00:19:51,380 good for a range means that on average, your decision is 448 00:19:51,380 --> 00:19:55,230 profitable for every hand for that range in general. 449 00:19:55,230 --> 00:19:57,690 But an optimal range is profitable for literally 450 00:19:57,690 --> 00:19:58,654 every hand. 451 00:19:58,654 --> 00:20:00,070 So you can do a lot of things that 452 00:20:00,070 --> 00:20:01,970 are profitable for any two cards, 453 00:20:01,970 --> 00:20:05,390 but 3-2 off might actually not be profitable. 454 00:20:05,390 --> 00:20:06,740 So it's not necessarily optimal. 455 00:20:06,740 --> 00:20:09,320 You want to make sure that every [INAUDIBLE] you can, 456 00:20:09,320 --> 00:20:12,090 every single card in that range is optimal 457 00:20:12,090 --> 00:20:15,370 and is profitable, which gives you the optimal range. 458 00:20:15,370 --> 00:20:20,100 It's the most plus EV range for that type of decision. 459 00:20:20,100 --> 00:20:22,620 An example of this is-- so say you're 460 00:20:22,620 --> 00:20:27,780 playing against Ace-Queen and you call with this range. 461 00:20:27,780 --> 00:20:30,240 Pocket 5's and Ace-10 or better. 462 00:20:30,240 --> 00:20:33,630 So you are ahead of this [INAUDIBLE] Queen 463 00:20:33,630 --> 00:20:36,856 because you're 53% to win the hand with this range. 464 00:20:36,856 --> 00:20:38,230 However, we know it's not optimal 465 00:20:38,230 --> 00:20:40,570 because we're calling with two losing hands-- 466 00:20:40,570 --> 00:20:42,000 Ace-10 and Ace-jack. 467 00:20:42,000 --> 00:20:44,370 So a more realistic, more optimal 468 00:20:44,370 --> 00:20:49,529 range is going to be pocket 2s and Ace-King or better. 469 00:20:49,529 --> 00:20:51,320 So that's going to be the difference there. 470 00:20:51,320 --> 00:20:54,200 So I want to make sure we're not solving for something that's 471 00:20:54,200 --> 00:20:57,490 a slight favorite when actually missing out on something 472 00:20:57,490 --> 00:20:59,450 a little bit more optimal. 473 00:20:59,450 --> 00:21:01,830 Here we go, so this is a better range. 474 00:21:01,830 --> 00:21:04,420 5-5 or Ace-Queen, actually 2s or Ace-Queen 475 00:21:04,420 --> 00:21:09,530 would be a little bit better, and we win 60% of the time. 476 00:21:09,530 --> 00:21:11,720 And then if a range is optimal, then 477 00:21:11,720 --> 00:21:15,420 we know for every hand in that range, 478 00:21:15,420 --> 00:21:17,010 we have a plus EV decision. 479 00:21:17,010 --> 00:21:19,240 And that's why this is the action we're 480 00:21:19,240 --> 00:21:24,550 going to use to prove that if we solve for a range, 481 00:21:24,550 --> 00:21:27,520 then we know that if you have any card in that range, 482 00:21:27,520 --> 00:21:28,982 our rule is still good for it. 483 00:21:28,982 --> 00:21:30,440 So that's why I'm showing you that. 484 00:21:30,440 --> 00:21:31,273 Right, so that's it. 485 00:21:31,273 --> 00:21:33,430 So that's all we're going to do in terms 486 00:21:33,430 --> 00:21:36,170 of defining what ranges are and how we got those numbers. 487 00:21:36,170 --> 00:21:39,810 And from now, we're going to talk about making decisions 488 00:21:39,810 --> 00:21:41,540 based on a range. 489 00:21:41,540 --> 00:21:42,750 So let's talk about preflops. 490 00:21:42,750 --> 00:21:45,527 Our assumption is hero has M less than 10. 491 00:21:45,527 --> 00:21:47,110 We're in that period of the tournament 492 00:21:47,110 --> 00:21:50,110 where your M is not going to be that high. 493 00:21:50,110 --> 00:21:52,570 The villain is calling some percentage 494 00:21:52,570 --> 00:21:56,260 of hands that are presumably the top whatever of hands. 495 00:21:56,260 --> 00:21:58,800 We're guessing he's not calling with a worse hand 496 00:21:58,800 --> 00:22:01,930 then-- and folding better hands. 497 00:22:01,930 --> 00:22:03,470 [INAUDIBLE] 498 00:22:03,470 --> 00:22:06,124 He might be a little bit-- his view of what 499 00:22:06,124 --> 00:22:07,540 are good hands and bad hands might 500 00:22:07,540 --> 00:22:09,490 be a little bit off of ours, but we're just 501 00:22:09,490 --> 00:22:11,440 assuming everyone has the same. 502 00:22:11,440 --> 00:22:13,300 [? ICM ?] doesn't matter, so we don't care 503 00:22:13,300 --> 00:22:15,420 about payout in tournaments. 504 00:22:15,420 --> 00:22:19,990 We're just trying to maximize our chip-- our chip EV, 505 00:22:19,990 --> 00:22:22,462 and we only have two decisions-- push or call. 506 00:22:22,462 --> 00:22:24,670 So the way that we're going to come up with this rule 507 00:22:24,670 --> 00:22:27,540 here for heads-up is-- so what we're doing 508 00:22:27,540 --> 00:22:31,140 is we want to figure out what our push/fold range is 509 00:22:31,140 --> 00:22:33,400 for heads-up in every scenario. 510 00:22:33,400 --> 00:22:37,290 And the way that we're going to do this is first, 511 00:22:37,290 --> 00:22:40,970 we need an equation that tells us range for range equities. 512 00:22:40,970 --> 00:22:46,640 So everyone can figure out Aces versus whatever is like 80-20, 513 00:22:46,640 --> 00:22:50,960 and then 2 over cards with a pocket pair is 50-50ish. 514 00:22:50,960 --> 00:22:53,540 But we want to know what's a range versus a range. 515 00:22:53,540 --> 00:22:56,550 Like if we push 70% of the time and he 516 00:22:56,550 --> 00:23:00,290 calls 30% of the time, what does that translate to 517 00:23:00,290 --> 00:23:01,440 in terms of our equity? 518 00:23:01,440 --> 00:23:03,617 And it ends up being like 60/40, but we 519 00:23:03,617 --> 00:23:05,950 want to get an idea of what that trend is because that's 520 00:23:05,950 --> 00:23:10,640 going to materially change our ability to come up 521 00:23:10,640 --> 00:23:13,200 with an optimal solution here. 522 00:23:13,200 --> 00:23:16,030 So we want to build a table of range versus range, 523 00:23:16,030 --> 00:23:18,020 and then we come up with a formula that 524 00:23:18,020 --> 00:23:21,440 will let us put in two ranges and come up 525 00:23:21,440 --> 00:23:24,536 with an equity calculation for both of those ranges. 526 00:23:24,536 --> 00:23:25,910 Then we're going to develop an EV 527 00:23:25,910 --> 00:23:28,090 model for semi-bluffs, which we already did, 528 00:23:28,090 --> 00:23:30,470 so that should be quick. 529 00:23:30,470 --> 00:23:34,600 For each m, find Nash equilibrium if one exists. 530 00:23:34,600 --> 00:23:37,490 So a lot of people-- if you Google "Nash equilibrium" 531 00:23:37,490 --> 00:23:40,200 for a preflop, you'll find something, it's wrong, 532 00:23:40,200 --> 00:23:42,240 and later I'll show you why. 533 00:23:42,240 --> 00:23:44,760 And therefore, unstable equilibriums-- 534 00:23:44,760 --> 00:23:46,380 it pretty much always is. 535 00:23:46,380 --> 00:23:48,400 Find a reasonable range and figure out 536 00:23:48,400 --> 00:23:50,170 what kind of assumptions we need to make 537 00:23:50,170 --> 00:23:54,980 to make our push/fold decisions correct. 538 00:23:54,980 --> 00:23:56,610 So let's do this first thing. 539 00:23:56,610 --> 00:23:59,590 So if we just-- for each-- say that we 540 00:23:59,590 --> 00:24:01,330 use a hero's range of 50%. 541 00:24:01,330 --> 00:24:04,340 So in PokerTracker, we put top 50% of hands. 542 00:24:04,340 --> 00:24:07,010 And then for each range of hands for the villain, 543 00:24:07,010 --> 00:24:09,530 we calculate the equity for that. 544 00:24:09,530 --> 00:24:13,590 And we do that for whatever I did, like 15 different ranges. 545 00:24:13,590 --> 00:24:18,740 So if we push 50% of the time and he calls 50% of the time, 546 00:24:18,740 --> 00:24:19,560 what's our equity? 547 00:24:19,560 --> 00:24:22,520 What's our chance of winning? 548 00:24:22,520 --> 00:24:23,400 50, right. 549 00:24:23,400 --> 00:24:25,160 So we have an even equity because we 550 00:24:25,160 --> 00:24:28,160 are pushing and calling the same types of hands on average. 551 00:24:28,160 --> 00:24:30,260 Whereas if he calls 100% of the time, 552 00:24:30,260 --> 00:24:32,480 our equity's actually closer to 60. 553 00:24:32,480 --> 00:24:36,020 We are the favorite-- we are a 60/40 favorite on that hand. 554 00:24:36,020 --> 00:24:39,960 Whereas if he calls with just Aces, then we are like 17% 555 00:24:39,960 --> 00:24:40,820 to win the hand. 556 00:24:40,820 --> 00:24:41,810 That's the idea. 557 00:24:41,810 --> 00:24:46,240 So our goal here is to come up with some sort of equation 558 00:24:46,240 --> 00:24:50,255 that we can just plug-in to-- we can do math on. 559 00:24:50,255 --> 00:24:52,130 Like we want to be able to do calculus on it, 560 00:24:52,130 --> 00:24:54,250 so we need an equation. 561 00:24:54,250 --> 00:24:55,960 So what type of function does this look 562 00:24:55,960 --> 00:25:01,500 like because we want to try to fit a curve to it. 563 00:25:01,500 --> 00:25:02,090 Exactly. 564 00:25:02,090 --> 00:25:03,720 It seems like a logarithmic function 565 00:25:03,720 --> 00:25:06,470 and within r squared of 99, it says 566 00:25:06,470 --> 00:25:08,670 that that's the logarithmic equation for it. 567 00:25:08,670 --> 00:25:10,930 So that works when the range is 50%, 568 00:25:10,930 --> 00:25:13,540 but let's take a look at when we change the range to 30%. 569 00:25:13,540 --> 00:25:17,280 So what this is saying is we are pushing 30% of the time 570 00:25:17,280 --> 00:25:19,900 and he is calling x percent of the time. 571 00:25:19,900 --> 00:25:24,710 And what this line is our chance of winning when he does that, 572 00:25:24,710 --> 00:25:26,450 and this is also logarithmic. 573 00:25:26,450 --> 00:25:28,200 So we're seeing a little bit of a pattern, 574 00:25:28,200 --> 00:25:31,150 and then it also has a really good r squared. 575 00:25:31,150 --> 00:25:33,350 And then if we push 10% of the time, 576 00:25:33,350 --> 00:25:37,200 it still like, OK, it's 98 and change 577 00:25:37,200 --> 00:25:39,900 when we look at our equities versus his calling range. 578 00:25:39,900 --> 00:25:42,060 But then it starts to get bad. 579 00:25:42,060 --> 00:25:44,170 If he calls 5% of the time, our r 580 00:25:44,170 --> 00:25:48,110 squared when we fit a log normal function, 581 00:25:48,110 --> 00:25:51,140 or a logarithmic function, is only 95. 582 00:25:51,140 --> 00:25:55,100 And if he only calls 3% of the time, our r squared is 89. 583 00:25:55,100 --> 00:25:58,280 Like this is not really lot logarithmic 584 00:25:58,280 --> 00:26:00,420 when we start getting in very tight ranges. 585 00:26:00,420 --> 00:26:01,930 And in 1%, it sucks. 586 00:26:01,930 --> 00:26:03,710 It's not even close. 587 00:26:03,710 --> 00:26:06,480 So what we're trying to do is develop an equation 588 00:26:06,480 --> 00:26:08,180 for figuring out range versus ranges, 589 00:26:08,180 --> 00:26:11,450 and we see that logarithmic works some of the time. 590 00:26:11,450 --> 00:26:14,140 So the reason it doesn't work, just 591 00:26:14,140 --> 00:26:17,320 to give you kind of an idea why it doesn't work, 592 00:26:17,320 --> 00:26:20,940 is because the top 1% of hands is three hands. 593 00:26:20,940 --> 00:26:23,260 It's Aces, Ace-King, and Kings. 594 00:26:23,260 --> 00:26:28,190 So it's materially changing based on whether he's-- if we 595 00:26:28,190 --> 00:26:33,790 push Ace-King, whether he calls with only Aces or Kings or also 596 00:26:33,790 --> 00:26:36,780 Ace-King jumps us between here and here. 597 00:26:36,780 --> 00:26:39,180 So we have huge gaps when it comes 598 00:26:39,180 --> 00:26:41,280 to very tight percentages, so that's why 599 00:26:41,280 --> 00:26:44,410 we break a little bit up here. 600 00:26:44,410 --> 00:26:47,540 And when we turn it around, we have the same type of thing. 601 00:26:47,540 --> 00:26:49,780 This is looking at OK, say that we know he's 602 00:26:49,780 --> 00:26:52,460 going to call 50% of the time. 603 00:26:52,460 --> 00:26:54,430 If we push x percent of the time, 604 00:26:54,430 --> 00:26:55,890 what is our chance of winning? 605 00:26:55,890 --> 00:27:01,200 So if we 100% of the time and he calls 40% of the time, 606 00:27:01,200 --> 00:27:04,420 then we are 40% to win. 607 00:27:04,420 --> 00:27:07,539 So that's what this chart is telling us, 608 00:27:07,539 --> 00:27:09,080 and you see the same type of pattern. 609 00:27:09,080 --> 00:27:13,260 Where 50% range versus this kind of range is good. 610 00:27:13,260 --> 00:27:16,130 If we push whatever and he calls 30% of the time, 611 00:27:16,130 --> 00:27:17,300 it's still good. 612 00:27:17,300 --> 00:27:20,059 But then if he calls 2% of the time, it starts becoming bad. 613 00:27:20,059 --> 00:27:21,600 So what are we taking away from this? 614 00:27:21,600 --> 00:27:23,580 And the whole plan is we want to come up with an equation that 615 00:27:23,580 --> 00:27:24,950 just gives us these numbers. 616 00:27:24,950 --> 00:27:27,440 I only got these from pushing them into PokerTracker 617 00:27:27,440 --> 00:27:31,080 and were trying to fit a certain equation onto it. 618 00:27:31,080 --> 00:27:34,840 So our takeaways here is that like range 619 00:27:34,840 --> 00:27:37,800 versus range relationship is probably logarithmic. 620 00:27:37,800 --> 00:27:39,380 That seems to be a good estimate, 621 00:27:39,380 --> 00:27:43,490 but it's definitely not good in the top 5%. 622 00:27:43,490 --> 00:27:45,250 So with regard to our model, we're 623 00:27:45,250 --> 00:27:48,480 just going to say this is probably not 624 00:27:48,480 --> 00:27:51,310 that good when you're talking about ranges in 5%. 625 00:27:51,310 --> 00:27:54,300 But realistically, when m is less than 10, 626 00:27:54,300 --> 00:27:56,400 no one is do anything in the 5% range, 627 00:27:56,400 --> 00:27:59,620 so it's not that big of a deal just to ignore it. 628 00:27:59,620 --> 00:28:04,090 So what we did is we populated this table just now. 629 00:28:04,090 --> 00:28:06,435 So we took a look at what's the villain's range up here 630 00:28:06,435 --> 00:28:07,310 and what's our range? 631 00:28:07,310 --> 00:28:11,790 So when we push 100% of the time and he calls 30% of the time, 632 00:28:11,790 --> 00:28:13,940 we win 39% of the time. 633 00:28:13,940 --> 00:28:17,450 Where red means that we are not likely to win and green 634 00:28:17,450 --> 00:28:19,150 means that we are likely to win. 635 00:28:19,150 --> 00:28:22,140 Like when we push 5% and he calls with anything, 636 00:28:22,140 --> 00:28:24,870 we're 73% to win. 637 00:28:24,870 --> 00:28:27,860 So that's what this table is telling us, 638 00:28:27,860 --> 00:28:31,380 and we want to do is we want to come up with an equation that 639 00:28:31,380 --> 00:28:34,360 lets us populate this table without actually having 640 00:28:34,360 --> 00:28:38,700 to do the range versus range calculations by hand. 641 00:28:38,700 --> 00:28:40,950 So what I did was I just ran a regression 642 00:28:40,950 --> 00:28:44,000 based on logarithmic variables, and I found something 643 00:28:44,000 --> 00:28:47,460 that I found to be really, really cool. 644 00:28:47,460 --> 00:28:50,890 So these seem to be the coefficients 645 00:28:50,890 --> 00:28:53,930 with an r squared of 98. 646 00:28:53,930 --> 00:28:56,430 So this equation seems to basically nail 647 00:28:56,430 --> 00:29:00,780 these range versus range equities, which is, I think, 648 00:29:00,780 --> 00:29:01,880 really cool. 649 00:29:01,880 --> 00:29:06,330 So our guess is probably a reason that it starts at 50%, 650 00:29:06,330 --> 00:29:08,670 and it seems to be symmetrical. 651 00:29:08,670 --> 00:29:11,490 Which is-- I don't know if there's 652 00:29:11,490 --> 00:29:14,110 a statistical reason for that, but that's 653 00:29:14,110 --> 00:29:15,660 extremely fascinating. 654 00:29:15,660 --> 00:29:18,150 And it could make sense intuitively 655 00:29:18,150 --> 00:29:21,060 that-- so this is your chance of winning. 656 00:29:21,060 --> 00:29:24,680 So would it make sense that the wider he calls-- 657 00:29:24,680 --> 00:29:28,760 when we take the natural log of the percentage of him calling, 658 00:29:28,760 --> 00:29:30,542 our percent win goes up. 659 00:29:30,542 --> 00:29:32,000 So I think it does because it means 660 00:29:32,000 --> 00:29:34,210 he's calling with a worse hand. 661 00:29:34,210 --> 00:29:36,764 That's why it goes up when he calls greater, 662 00:29:36,764 --> 00:29:39,180 but then goes down when we push greater because this means 663 00:29:39,180 --> 00:29:40,920 that we're pushing worse hands. 664 00:29:40,920 --> 00:29:42,670 So that's the equation there, and that's 665 00:29:42,670 --> 00:29:44,550 giving us something that we can actually differentiate when 666 00:29:44,550 --> 00:29:45,990 we're trying to solve this. 667 00:29:45,990 --> 00:29:49,400 And just in terms of errors, it's not that bad. 668 00:29:49,400 --> 00:29:51,260 We have an r squared of 98. 669 00:29:51,260 --> 00:29:52,920 So I think this is good enough to use. 670 00:29:52,920 --> 00:29:55,220 We can actually use this to try to optimize 671 00:29:55,220 --> 00:29:57,420 our decision making preflop. 672 00:29:57,420 --> 00:29:59,710 So we solved-- we came up with an equation 673 00:29:59,710 --> 00:30:02,540 that we can use for determining our chance of winning 674 00:30:02,540 --> 00:30:06,281 a hand compared to our pushing range and his calling range. 675 00:30:06,281 --> 00:30:08,280 So let's go back to our EV model for semi-bluff. 676 00:30:11,020 --> 00:30:14,825 So we already did that in the fold equity portion, 677 00:30:14,825 --> 00:30:16,200 but we're going to build this out 678 00:30:16,200 --> 00:30:20,450 to be relevant to our situation in particular. 679 00:30:20,450 --> 00:30:23,070 So we're assuming we're talking about in terms of M, 680 00:30:23,070 --> 00:30:26,040 so what's our-- so our blinds are going to be equal to 1. 681 00:30:26,040 --> 00:30:30,440 Like this means this is 1 M and our EV is going to be in terms 682 00:30:30,440 --> 00:30:31,150 of M's. 683 00:30:31,150 --> 00:30:34,690 We're going to-- if our EV ends up being 0.35, 684 00:30:34,690 --> 00:30:37,630 it means 0.35 times all the blinds combined just 685 00:30:37,630 --> 00:30:38,950 to get rid of blinds here. 686 00:30:38,950 --> 00:30:41,450 So all the blinds combined equals 687 00:30:41,450 --> 00:30:43,770 M. Our showdown value is just going 688 00:30:43,770 --> 00:30:45,570 to be-- so our fold equity is going 689 00:30:45,570 --> 00:30:48,820 to be the pot times the chance of him folding, i.e. 690 00:30:48,820 --> 00:30:50,100 1 minus calling. 691 00:30:50,100 --> 00:30:52,280 The chance of him-- our showdown value 692 00:30:52,280 --> 00:30:56,650 is chance of calling times win amount times win percentage 693 00:30:56,650 --> 00:30:59,770 minus lose amount times lose percentage. 694 00:30:59,770 --> 00:31:02,700 The win amount is going to be stacked plus 2/3 695 00:31:02,700 --> 00:31:05,850 because if the blinds are 1-2 or something where 696 00:31:05,850 --> 00:31:07,890 the big blind is double the small blind, 697 00:31:07,890 --> 00:31:11,710 it means that you win his big blind 698 00:31:11,710 --> 00:31:14,840 and then you lose your whole stack. 699 00:31:14,840 --> 00:31:16,900 Depending on when we mark our stack, 700 00:31:16,900 --> 00:31:19,120 it changes it a little bit with regard 701 00:31:19,120 --> 00:31:21,880 to whether we count it as before we pay the blind or after. 702 00:31:21,880 --> 00:31:23,750 But it ends up not making a huge difference. 703 00:31:23,750 --> 00:31:27,190 It just impacts whether this is plus 2/3 or plus 704 00:31:27,190 --> 00:31:29,060 1/3 or just your stack. 705 00:31:29,060 --> 00:31:31,880 But anyway, we also have this equation, 706 00:31:31,880 --> 00:31:33,700 which we just solve for. 707 00:31:33,700 --> 00:31:35,210 Where the chance of us winning is 708 00:31:35,210 --> 00:31:38,530 related to the chance to him calling 709 00:31:38,530 --> 00:31:41,970 and the range that we're pushing. 710 00:31:41,970 --> 00:31:44,130 So what you might see here is all 711 00:31:44,130 --> 00:31:47,970 of these are related to the same three variables, where it's 712 00:31:47,970 --> 00:31:49,810 either the call percentage, the push 713 00:31:49,810 --> 00:31:51,545 percentage, or a stack size. 714 00:31:51,545 --> 00:31:54,170 So we combine this to one giant equation, which obviously we're 715 00:31:54,170 --> 00:31:57,510 not going to remember but we can use to start solving this 716 00:31:57,510 --> 00:31:58,530 mathematically. 717 00:31:58,530 --> 00:32:01,280 So this is what we would end up with. 718 00:32:01,280 --> 00:32:06,560 So when M is 1, we end up with this sort of graph. 719 00:32:06,560 --> 00:32:09,450 When the hero's push range goes up to 100% 720 00:32:09,450 --> 00:32:14,530 here and the villain's call range goes up to 100% here. 721 00:32:14,530 --> 00:32:17,214 This is our equity, which I just color-coded 722 00:32:17,214 --> 00:32:18,880 so we don't need to look at the numbers. 723 00:32:18,880 --> 00:32:21,950 Where green means it's in the hero's favor and yellow 724 00:32:21,950 --> 00:32:23,960 means it's close to zero and red means 725 00:32:23,960 --> 00:32:26,270 it's in the villain's favor. 726 00:32:26,270 --> 00:32:30,720 So what we see here is it's really green over here 727 00:32:30,720 --> 00:32:32,220 and really yellow over there. 728 00:32:32,220 --> 00:32:34,010 And this is telling us this is already 729 00:32:34,010 --> 00:32:37,410 factoring in fold equity and our chance of winning if he calls. 730 00:32:37,410 --> 00:32:41,750 This is saying that if we call 100% of the time, 731 00:32:41,750 --> 00:32:44,500 he should call 100% of the time because he 732 00:32:44,500 --> 00:32:48,340 wants the yellowest area and we want the greenest area. 733 00:32:48,340 --> 00:32:51,220 So that's with 1 M, so it shouldn't be surprising 734 00:32:51,220 --> 00:32:53,900 that our equilibrium at 1 M is going 735 00:32:53,900 --> 00:32:57,580 to be everyone like getting all in 100% of the time. 736 00:32:57,580 --> 00:33:00,720 We see when we switch to 10 M, it's pretty different. 737 00:33:00,720 --> 00:33:04,290 In fact, this 100 is one of the yellowest areas, 738 00:33:04,290 --> 00:33:09,305 whereas our green area is either up here or down here. 739 00:33:09,305 --> 00:33:10,680 So we're going to use this to get 740 00:33:10,680 --> 00:33:14,200 an idea of how our value changes based 741 00:33:14,200 --> 00:33:15,930 on these variables changing to figure out 742 00:33:15,930 --> 00:33:21,030 if we can isolate it to a corner and make that our kind of rule. 743 00:33:21,030 --> 00:33:24,010 So first, let's find out when we can get a Nash equilibrium. 744 00:33:24,010 --> 00:33:27,730 So the villain gets to pick this. 745 00:33:27,730 --> 00:33:29,980 The villain gets to pick his call range 746 00:33:29,980 --> 00:33:32,390 and we get to pick our push range. 747 00:33:32,390 --> 00:33:37,440 That's the flexibility each person has. 748 00:33:37,440 --> 00:33:41,490 So if we push 100% of the time and he calls 100% of the time, 749 00:33:41,490 --> 00:33:43,760 this is a Nash equilibrium for 1 M 750 00:33:43,760 --> 00:33:46,430 because he can't do any better by going up 751 00:33:46,430 --> 00:33:49,400 here because a higher number is worse for him 752 00:33:49,400 --> 00:33:52,040 because this is our equity in the hand. 753 00:33:52,040 --> 00:33:54,370 And the equity comes directly from him 754 00:33:54,370 --> 00:33:56,990 because it's a heads-up situation whereas we can't 755 00:33:56,990 --> 00:33:58,590 do better by pushing left. 756 00:33:58,590 --> 00:34:00,440 Like when we go down here, the next number 757 00:34:00,440 --> 00:34:03,580 is 0.32, meaning that if we push any less, 758 00:34:03,580 --> 00:34:05,360 we're actually losing value because we 759 00:34:05,360 --> 00:34:06,700 want the number to be higher. 760 00:34:06,700 --> 00:34:09,620 And when it comes to 2 M, 100% isn't that much off. 761 00:34:09,620 --> 00:34:12,320 We're talking about 0.01 M of a difference in EV, 762 00:34:12,320 --> 00:34:15,275 but we do actually reach a Nash equilibrium here-- 2 M-- 763 00:34:15,275 --> 00:34:17,790 where we can't do anything any better by moving 764 00:34:17,790 --> 00:34:19,830 and he can't do any better by moving. 765 00:34:19,830 --> 00:34:22,130 So when M is 3, we have an unstable Nash, 766 00:34:22,130 --> 00:34:25,260 and this is when stuff is getting interesting. 767 00:34:25,260 --> 00:34:27,469 If we push 80, he should call 100. 768 00:34:27,469 --> 00:34:30,860 If he calls 100, we should push 65, and so on. 769 00:34:30,860 --> 00:34:32,310 So we end up in a bit of a circle. 770 00:34:32,310 --> 00:34:35,280 It's a rock, paper, scissors situation. 771 00:34:35,280 --> 00:34:36,340 What do we have? 772 00:34:36,340 --> 00:34:37,431 M equals 3. 773 00:34:37,431 --> 00:34:39,639 So this lets us know that this whole Nash equilibrium 774 00:34:39,639 --> 00:34:41,170 thing is not going to work out. 775 00:34:41,170 --> 00:34:43,080 Like it only really works for M of 2, 776 00:34:43,080 --> 00:34:46,675 and that's not the most important situation 777 00:34:46,675 --> 00:34:48,050 to figure out because you're know 778 00:34:48,050 --> 00:34:50,750 that you should be pushing a very, very wide range when 779 00:34:50,750 --> 00:34:53,340 M is 2. 780 00:34:53,340 --> 00:34:55,370 So we need to figure out some sort of pattern. 781 00:34:55,370 --> 00:35:00,340 How do these colors move when your M is more than 2? 782 00:35:00,340 --> 00:35:02,999 So let's make-- let's go to M equals 5 783 00:35:02,999 --> 00:35:04,790 and make the gradient a little bit steeper. 784 00:35:04,790 --> 00:35:07,610 So these are the same numbers except I just made it-- 785 00:35:07,610 --> 00:35:11,290 we're talking about very slight changes in EV, where 786 00:35:11,290 --> 00:35:16,350 the difference between yellow here and green here is 0.1 M, 787 00:35:16,350 --> 00:35:19,330 and this will help us understand where this value is 788 00:35:19,330 --> 00:35:20,610 going to come from. 789 00:35:20,610 --> 00:35:22,870 So let's see how this changes over time, 790 00:35:22,870 --> 00:35:25,110 because our goal here is-- the villain's goal 791 00:35:25,110 --> 00:35:27,550 is to cause this to be in a yellow area, 792 00:35:27,550 --> 00:35:31,950 and the hero's goal is to cause this to be in a green area. 793 00:35:31,950 --> 00:35:33,880 And you can see why we inherently 794 00:35:33,880 --> 00:35:37,670 have this need to figure out what they're going to do. 795 00:35:37,670 --> 00:35:40,890 Because say that we're the villain. 796 00:35:40,890 --> 00:35:43,730 If we know the hero pushes 100, we call 100. 797 00:35:43,730 --> 00:35:48,280 Whereas if we think the hero pushes 30%, we should call 5%. 798 00:35:48,280 --> 00:35:50,650 So let's see how this changes over time. 799 00:35:50,650 --> 00:35:52,840 So this is when M is 2, and then this 800 00:35:52,840 --> 00:35:57,290 is us increasing as M is 3, 4, 5, 6, 7, 8, 9. 801 00:35:57,290 --> 00:35:58,680 We're trying to pick the box that 802 00:35:58,680 --> 00:36:01,090 is kind of the yellowest area. 803 00:36:01,090 --> 00:36:03,490 Where can we realistically come up 804 00:36:03,490 --> 00:36:06,740 with a rule for ending up there? 805 00:36:06,740 --> 00:36:09,210 Based on what this x-coordinate is, what 806 00:36:09,210 --> 00:36:11,100 should be our y-coordinate? 807 00:36:11,100 --> 00:36:13,200 What should be our call? 808 00:36:13,200 --> 00:36:17,450 Do we see any way to figure this thing out? 809 00:36:17,450 --> 00:36:20,460 So what I think we should do is just draw a line right here 810 00:36:20,460 --> 00:36:23,380 and say let's just figure out what the equation of that line 811 00:36:23,380 --> 00:36:26,280 is, and then come up with an estimate of what 812 00:36:26,280 --> 00:36:32,330 his pushing range is, and then throw it into whatever function 813 00:36:32,330 --> 00:36:33,560 we used to get that line. 814 00:36:33,560 --> 00:36:36,750 Which can't be very complicated in order to make sure, 815 00:36:36,750 --> 00:36:39,630 no matter what his pushing range is that we read him for, 816 00:36:39,630 --> 00:36:41,860 we end up in this yellow area. 817 00:36:41,860 --> 00:36:45,540 So what I did was for each M, I highlighted what the lowest EV 818 00:36:45,540 --> 00:36:48,670 decision is for the hero, meaning the best decision 819 00:36:48,670 --> 00:36:49,880 for the villain. 820 00:36:49,880 --> 00:36:52,120 And for 10 M, it's this diagonal. 821 00:36:52,120 --> 00:36:54,320 But for 1 M, it's all the way down here. 822 00:36:54,320 --> 00:36:56,910 Like best you can do is over here. 823 00:36:56,910 --> 00:37:02,670 So are our function is we call 10 times his pushing range. 824 00:37:02,670 --> 00:37:06,380 So if we have 1 M and he pushes 5% of the time, 825 00:37:06,380 --> 00:37:08,560 we call about 50% of the time. 826 00:37:08,560 --> 00:37:11,160 If he pushes 20% of the time, we're calling always, 827 00:37:11,160 --> 00:37:13,870 and anything more than 20%, we're always calling. 828 00:37:13,870 --> 00:37:15,230 That's where M equals 1. 829 00:37:15,230 --> 00:37:18,720 In general, the rule is going to be if M is 1, always call, 830 00:37:18,720 --> 00:37:21,520 and if M is 2, you call twice his pushing range. 831 00:37:21,520 --> 00:37:25,880 So if we think he's pushing 50% or more, we're always calling. 832 00:37:25,880 --> 00:37:30,550 If we think he's pushing 20%, we call 40% of the time. 833 00:37:30,550 --> 00:37:32,740 Like that's the optimal calling range 834 00:37:32,740 --> 00:37:34,800 in this heads-up situation. 835 00:37:34,800 --> 00:37:37,930 So when M is 4-- so I skipped one, but when M is 4 836 00:37:37,930 --> 00:37:40,040 we have basically this straight diagonal. 837 00:37:40,040 --> 00:37:42,250 We try to match his pushing range. 838 00:37:42,250 --> 00:37:44,180 So when he pushes 60, we call 60. 839 00:37:44,180 --> 00:37:46,470 When he pushes 100, we call 100. 840 00:37:46,470 --> 00:37:50,770 That's the best we can do to dominate his range there. 841 00:37:50,770 --> 00:37:53,710 When M is 6, we call 2/3 his range. 842 00:37:53,710 --> 00:37:56,307 And when M is 9, we call half is range. 843 00:37:56,307 --> 00:37:57,890 So those are the rules that we're just 844 00:37:57,890 --> 00:37:58,973 going to have to remember. 845 00:37:58,973 --> 00:38:00,920 When you're in a heads-up situation, 846 00:38:00,920 --> 00:38:04,960 if the stack is basically 1 or 2, you're always calling him. 847 00:38:04,960 --> 00:38:07,530 At 4, you're calling him an even amount. 848 00:38:07,530 --> 00:38:11,880 At 6 and 9, you're calling him like half of what he pushes. 849 00:38:11,880 --> 00:38:13,830 And that's the optimal move. 850 00:38:13,830 --> 00:38:17,670 That is how you will-- if you're in a heads-up situation, which 851 00:38:17,670 --> 00:38:20,100 you will be at the end of every tournament to the extent 852 00:38:20,100 --> 00:38:25,380 that you get there, you will dominate his playing style 853 00:38:25,380 --> 00:38:28,540 based on what you read as his pushing amount. 854 00:38:28,540 --> 00:38:31,930 And you can just count how many hands 855 00:38:31,930 --> 00:38:33,840 did he push versus how many hands 856 00:38:33,840 --> 00:38:36,490 does he fold to get an idea of what his range is here. 857 00:38:36,490 --> 00:38:38,150 And this also works when it's folded 858 00:38:38,150 --> 00:38:39,810 to you in the small blind. 859 00:38:39,810 --> 00:38:41,969 Like even if you're 10 handed, by the time 860 00:38:41,969 --> 00:38:44,010 you get to the small blind, you're heads up again 861 00:38:44,010 --> 00:38:47,100 and these rules apply. 862 00:38:47,100 --> 00:38:49,040 So to the extent you can memorize 863 00:38:49,040 --> 00:38:52,420 this thing will give you the right move in that scenario 864 00:38:52,420 --> 00:38:55,110 for Ms up to 10. 865 00:38:55,110 --> 00:38:59,040 So when you're the hero-- when you're the small but, rather, 866 00:38:59,040 --> 00:39:01,780 and you're pushing, it requires you to estimate 867 00:39:01,780 --> 00:39:03,180 what his calling range is. 868 00:39:03,180 --> 00:39:09,430 Because you end up all over the plAce based 869 00:39:09,430 --> 00:39:12,120 on making different estimates of what you can call with, 870 00:39:12,120 --> 00:39:14,530 and you really don't have any information. 871 00:39:14,530 --> 00:39:17,210 But I'm going to graph it out here 872 00:39:17,210 --> 00:39:19,780 and then we can see what's going to be a good estimate 873 00:39:19,780 --> 00:39:21,460 in basically any scenario. 874 00:39:21,460 --> 00:39:24,260 So there are a couple different ways I can think about this. 875 00:39:24,260 --> 00:39:26,690 So we're going to come up with a bunch of numbers 876 00:39:26,690 --> 00:39:30,050 based on the villains' call range here. 877 00:39:30,050 --> 00:39:33,830 And we can either-- so we're targeting a column 878 00:39:33,830 --> 00:39:36,860 and then like the row is going to be 879 00:39:36,860 --> 00:39:38,550 information we don't have. 880 00:39:38,550 --> 00:39:41,870 So the question is do we pick the column that 881 00:39:41,870 --> 00:39:46,520 has the highest average EV, the highest minimum EV, 882 00:39:46,520 --> 00:39:49,880 or the highest EV versus like a particular bad player 883 00:39:49,880 --> 00:39:51,390 that we're going to be targeting? 884 00:39:51,390 --> 00:39:57,080 And the blue here is what column maximizes your EV 885 00:39:57,080 --> 00:39:58,510 for that scenario? 886 00:39:58,510 --> 00:40:00,220 And your guess is as good as mine 887 00:40:00,220 --> 00:40:03,090 when it comes to what's the best way to strategize it. 888 00:40:03,090 --> 00:40:09,400 Are we looking for-- maximizing the min will help us make sure 889 00:40:09,400 --> 00:40:11,410 that we're not dominated by someone who's really 890 00:40:11,410 --> 00:40:13,860 got our number, whereas maximizing the average 891 00:40:13,860 --> 00:40:15,960 might be better when we're trying to figure out 892 00:40:15,960 --> 00:40:19,650 against a player we know nothing about what would be better. 893 00:40:19,650 --> 00:40:22,400 And maximizing versus tight-- or loose-- 894 00:40:22,400 --> 00:40:25,740 will help us figure out some sort of-- how to capitalize 895 00:40:25,740 --> 00:40:27,340 on the reads that we're making. 896 00:40:27,340 --> 00:40:30,760 So when M is 1, he's over there. 897 00:40:30,760 --> 00:40:32,780 No matter what the scenario, you should 898 00:40:32,780 --> 00:40:34,469 be pushing 100% of the time. 899 00:40:34,469 --> 00:40:35,760 That's what this is telling us. 900 00:40:35,760 --> 00:40:38,790 It shouldn't be a surprise based on all the stuff I told you 901 00:40:38,790 --> 00:40:40,482 about 1 M situations. 902 00:40:40,482 --> 00:40:42,440 No matter what kind of assumption we're making, 903 00:40:42,440 --> 00:40:43,990 push 100%. 904 00:40:43,990 --> 00:40:45,700 So let me pick up to M is 10. 905 00:40:48,630 --> 00:40:49,630 So what's going on here? 906 00:40:49,630 --> 00:40:53,430 So as M increases, they all kind of move at the same time, 907 00:40:53,430 --> 00:40:54,970 except what? 908 00:40:54,970 --> 00:40:58,240 If we're talking loose or we're targeting best/worst case 909 00:40:58,240 --> 00:41:00,890 scenario or best average, it starts 910 00:41:00,890 --> 00:41:03,670 to trickle down to like 50%. 911 00:41:03,670 --> 00:41:06,780 But it's certainly-- they're relatively near each other, 912 00:41:06,780 --> 00:41:08,620 and what's good about this is that means 913 00:41:08,620 --> 00:41:12,490 that if we target any of these, we're basically in the ballpark 914 00:41:12,490 --> 00:41:16,030 where the difference between this column and this column 915 00:41:16,030 --> 00:41:19,450 for any of M is going to be not that material. 916 00:41:19,450 --> 00:41:20,990 If you were just in that ballpark, 917 00:41:20,990 --> 00:41:25,810 you're fine, but which one of them is completely different. 918 00:41:25,810 --> 00:41:27,350 Yeah, against a tight player. 919 00:41:27,350 --> 00:41:29,030 And it should make sense intuitively 920 00:41:29,030 --> 00:41:32,410 why if you read him as tight, as someone who only calls 921 00:41:32,410 --> 00:41:36,220 15% of the time, even with 9 and 10 M, 922 00:41:36,220 --> 00:41:38,040 you should push 100% of the time. 923 00:41:38,040 --> 00:41:39,470 Why? 924 00:41:39,470 --> 00:41:42,840 It's because 85% of the time, he's just going to fold, 925 00:41:42,840 --> 00:41:45,240 and even when you're called, the amount 926 00:41:45,240 --> 00:41:48,730 of value you get from him folding most of the time 927 00:41:48,730 --> 00:41:50,230 just crushes him. 928 00:41:50,230 --> 00:41:54,360 So you should-- to the extent that you can encourage 929 00:41:54,360 --> 00:41:56,280 him to be tight, do it. 930 00:41:56,280 --> 00:41:59,710 But absolutely, if he's tight, push every single hand. 931 00:41:59,710 --> 00:42:03,190 You're never in the scenario where pushing less than top 50% 932 00:42:03,190 --> 00:42:05,950 is good. 933 00:42:05,950 --> 00:42:07,310 So that's it for heads up. 934 00:42:07,310 --> 00:42:09,410 So now let's talk about other positions, 935 00:42:09,410 --> 00:42:15,300 and we end up in a lot of complicated situations, which 936 00:42:15,300 --> 00:42:17,899 we have to just assume away here. 937 00:42:17,899 --> 00:42:19,440 So we can lose in two different ways. 938 00:42:19,440 --> 00:42:21,490 We can lose if we call and he beats us, 939 00:42:21,490 --> 00:42:24,260 or we could also lose if we call and then someone behind us 940 00:42:24,260 --> 00:42:24,770 calls. 941 00:42:24,770 --> 00:42:26,520 So we're estimating that someone behind us 942 00:42:26,520 --> 00:42:29,351 is only going to call if he has a premium hand because if we're 943 00:42:29,351 --> 00:42:31,225 in a short stack situation and someone pushes 944 00:42:31,225 --> 00:42:33,930 and then we call, someone is only calling behind us when 945 00:42:33,930 --> 00:42:35,162 they have a really good hand. 946 00:42:35,162 --> 00:42:36,870 And let's just assume we're going to lose 947 00:42:36,870 --> 00:42:37,960 if we get another caller. 948 00:42:37,960 --> 00:42:40,376 Like we are almost certainly going to be dominated-- let's 949 00:42:40,376 --> 00:42:41,710 say we have 0 EV there. 950 00:42:41,710 --> 00:42:44,020 And because of our equation here, we 951 00:42:44,020 --> 00:42:45,370 can actually solve that. 952 00:42:45,370 --> 00:42:47,790 We can actually figure out what range is going 953 00:42:47,790 --> 00:42:49,780 to be 60% versus another range. 954 00:42:49,780 --> 00:42:52,750 So this is resulting in a really cool rule of thumb here, which 955 00:42:52,750 --> 00:42:54,924 is when you're in a 10 M or less situation 956 00:42:54,924 --> 00:42:57,340 and you're trying to decide whether to call an all-in, you 957 00:42:57,340 --> 00:42:59,930 just ask yourself, are you calling such 958 00:42:59,930 --> 00:43:04,660 that his range is three times more than your range? 959 00:43:04,660 --> 00:43:06,760 And some questions you might ask yourself is 960 00:43:06,760 --> 00:43:10,490 say that you have Ace-10, like you have a 10% range here. 961 00:43:10,490 --> 00:43:13,790 Would he push all in into you with King-Jack-- something 962 00:43:13,790 --> 00:43:15,520 in a 30%? 963 00:43:15,520 --> 00:43:17,820 If you have King-Queen, which is like 30%, 964 00:43:17,820 --> 00:43:22,800 would he push all in with 8-5, which is 50% range, and so on. 965 00:43:22,800 --> 00:43:24,825 So when you're in a [? full ring ?] situation 966 00:43:24,825 --> 00:43:26,990 and you're trying to decide whether to call, 967 00:43:26,990 --> 00:43:29,010 figure out in general what do you think 968 00:43:29,010 --> 00:43:30,540 his pushing range is there. 969 00:43:30,540 --> 00:43:32,920 And it's a good call if your calling range 970 00:43:32,920 --> 00:43:35,787 is 1/3 of his pushing range. 971 00:43:35,787 --> 00:43:36,620 Let's call it a day. 972 00:43:36,620 --> 00:43:38,340 Thanks, guys.