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Noam Brown

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2022-12-06
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2022-12-06
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  1. Yeah, ultimately, what you're trying to maximize is your expected winnings. So, like your expected value, the amount of money that you're going to walk away from, assuming that your opponent was playing optimally in response. So you're going to assume that your opponent is also playing as well as possible in Ash equilibrium approach. Because if they're not, then you're just going to make more money, right? Like anything that deviates, like by definition, the Nash equilibrium is the strategy that does the best in expectation. And so if you're deviating from that, then you're just, they're going to lose money. And since it's a two-player zero sum game, that means you're going to make money.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  2. Basically, what you want to do is put your opponent into a tough spot. So you want them to always have some doubt. Like, should I call here? Should I fold here? And if you are raising in the appropriate balance between bluffs and good hands, then you're putting them into that tough spot. And so that's what we're trying to do. We're always trying to search for a strategy that would put the opponent into a difficult position.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  3. And that's kind of like a hard to wrap your head around. Like, why are you searching over these other hands that you might have and like trying to figure out what you would do with those hands? And the idea is, again, you want to always be balanced and unpredictable. And so if you're a search algorithm that's saying like, oh, I want to raise with this hand, well, in order to know whether that's a good action, like let's say it's a bluff. Let's say you have a bad hand and you're saying like, oh, I think I should be betting here with this really bad hand and bluffing. Well, that's only a good action if you're also betting with a strong hand. Otherwise, it's an obvious bluff.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  4. So, in a game like chess, the search is like okay, I'm in this chess position and I can like, you know, move these different pieces and see where things end up. In poker, what you're searching over is the actions that you can take for your hand, the probabilities that you take those actions, and then also the probabilities that you take other actions with other hands that you might have.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  5. It was really an algorithmic approach. That was the difference. So 2015, it was much more focused on trying to come up with a strategy up front, like trying to solve the entire game of poker and then just have a lookup table where you're saying like, oh, I'm in this situation. What's the strategy? The approach that we took in 2017 was much more search-based. It was trying to say, okay, well, let me in real time try to compute a much better strategy than what I had pre-computed by playing against myself during self-play.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  6. So we did a competition actually in 2015 where we also played against professional poker players and the bot lost by a pretty sizable margin actually. Now there were some big improvements from 2015 to 2017.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  7. And we had $200,000 in prize money at stake, where it would basically be divided among them depending on how well they did relative to each other. So we wanted to have some incentive for them to play their best

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  8. Yeah, okay, so when I was in grad school, there was this thing called the annual computer poker competition where every year all the different research labs that were working on AI for poker would get together, they would make a bot, they would play them against each other. And we made a bot that actually won the 2014 competition, the 2016 competition. And so we decided we're going to take this bot, build on it, and play against real top professional heads up no limit, Texas hold and poker players. We invited four of the world's best players in this specialty, and we challenged them to 120,000 hands of poker over the course of 20 days.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  9. And trying to do these mind games, it was just trying to approximate the Nash equilibrium, and it crushed them. I think, you know, if we're playing for $50, $100 blinds, and over the course of about 120,000 hands, it made close to $2 million.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  10. This gets down to a big argument in the poker community and the academic community for a long time there was this debate of like what's called GTO game theory optimal poker or exploitative play and up until about like 2017 when we did the liberatus match I think actually exploitative play had the advantage a lot of people were saying like oh this whole idea of game theory it's just nonsense and if you really want to make money you got to like look into the other person's eyes and read their soul and figure out what cards they have But what happened was people started adopting the Game 3 optimal strategy and they were making good money and they weren't trying to adapt so much to the other player. They were just trying to play the Nash equilibrium. And then what really solidified it, I think, was the broadest match where we played our bot against four top heads up no limit hold-em, poker players. And the bot wasn't trying to adapt to them. It wasn't trying to exploit them.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  11. So the thing that I should explain first of all with Nash equilibrium, it doesn't mean that it's predictable. The whole point of it is that you're trying to be unpredictable. Now, I think when somebody like Phil Helmuth might be really successful. Not in being unpredictable, but in being able to take advantage of the other player and figure out where they're being predictable, or guiding the other player into thinking that you have certain weaknesses and then understanding how they're going to change their behavior. They're going to deviate from a Nash equilibrium style of play to try to take advantage of those perceived weaknesses and then counter exploit them. So you kind of get into the mind games there.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  12. I'm going to try to pick a strategy where even if I were to play it for 10,000 hands and you could figure out exactly what it was, you still wouldn't be able to beat it. Basically, what that means is I'm trying to approximate the Nash equilibrium. I'm trying to be perfectly balanced because if I'm playing the Nash equilibrium, even if you know what my strategy is, like I said, I'm still unbeatable in expectation. So that's what the bot aims for. And that's actually what a lot of expert poker players aim for as well, to start by playing the Nash equilibrium and then maybe if they spot weaknesses in the way you're playing, then they can deviate a little bit to take advantage of that.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  13. A good question. So you could approach the game that way. The way that the bots do it, they don't, and the way that humans approach it also, expert human players. The way they approach it is to basically assume that you know my strategy.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  14. The way that the bots handle it that are really successful, they have an explicit theory of mine, so they're explicitly reasoning about what's the common knowledge belief? What do you think I have? What do I think you have? What do you think I think you have? It's explicitly reasoning about that.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  15. Good simplification. I think that's like the main tension, but it's not just how often to bluff or not to bluff. It's like how often should you bet in general? How often should you, what kind of bet should you make? Should you bet big or should you bet small and with which hands? And so this is where the idea of a range comes from. Because when you are bluffing with a particular hand in a particular spot, you don't want there to be a pattern for the other person to pick up on. You don't want them to figure out, oh, whenever this person is in this spot, they're always bluffing. And so you have to reason about, okay, would I also bet with a good hand in this spot? You want to be unpredictable. So you have to think about what would I do if I had this different set of cards?

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  16. Doesn't matter if you're opening with the Queen's Gambit 10 of the time or 100% of the time. The value, the expected value is the same. So that's why we need these algorithms that understand not just we have to figure out what actions are good, but the probabilities. We need to get the exact probabilities correct. And that's actually when we created the bot libratus, libratus means balanced because the algorithm that we designed was designed to find that right balance of how often it should play each action.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  17. You take that to poker. What that means is the value of bluffing, for example. If you're the kind of person that never bluffs and you have this reputation as somebody that never bluffs and suddenly you bluff, there's a really good chance that that bluff is going to work and you're going to make a lot of money. On the other hand, if you got a reputation, like if they've seen you play for a long time and they see, oh, you're the kind of person that's bluffing all the time, when you bluff, they're not going to buy it and they're going to call you down. You're going to lose a lot of money. That finding that balance of how often you should be bluffing is the key challenge of a game of poker. And you contrast that with a game like chess.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  18. And so you can't just say, like, oh, I'm just going to throw a rock every single time because the other person's going to figure that out and notice a pattern. And then suddenly you're going to start losing. And so you don't just have to figure out which action to play. You have to figure out the probability that you play it. And really importantly, the value of an action depends on the probability that you're going to play it. So if you're playing rock every single time, that value is really low. But if you're never playing rock, you play rock like 1% of the time, then suddenly the other person is probably going to be throwing scissors. And when you throw rock, the value of that action is going to be really high.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  19. So, the key thing to understand about why imperfect information makes things difficult is that you have to worry not just about which actions to play, but the probability that you're going to play those actions. So you think about Rock, paper, scissors, for example. Rock, paper, scissors is an imporf information game. Because you don't know what I'm about to throw.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  20. So, Texas Hold on, you get two cards face down that only you see, and so that's the hidden information of the game. The other players also all get two cards face down that only they see. And so you have to kind of, as you're playing, reason about like, okay, what do they think I have? What do they have? What do they think I think they have that kind of stuff? That's kind of where bluffing comes into play, right? Because the fact that you can bluff, the fact that you can bet with a bad hand and still win is because they don't know what your cards are. That's the key difference between a perfect information game like Chess and Go and imprint information games like Poker.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  21. So, first of all, you have the imperfect information aspect. And so we can go into that, but once you introduce imperfect information, things get much more complicated.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  22. A chess, there's a poker. I'm sure David Silver is going to get really angry at me. I'll say, I'm going to say poker actually

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  23. And so the way neural nets help out here is You don't have to run into the same exact situation because that's never going to happen again. The odds of you running into the same exact situation are pretty slim. But if you run into a similar situation, then you can generalize from other states that you've been in that kind of look like that one. And you can say like, well, these other situations I had high regret for this action. And so maybe I should play that action here as well.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  24. Oh no, no, no. I'm saying we played the full game. You can bet whatever amount you want. Another bot maybe was constrained in What it considered for bed sizes, but the person on the other side could bet whatever they wanted

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  25. I mean, it depends on the number of chips that you have, the stacks, and everything, but like the version that we were playing was 10 to the 161.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  26. Now, where the neural nets come in, I said, okay, if it's in that situation again, then it will choose the action that has high regret. Now, the problem is that poker is such a huge game. I think no limit texes hold them. The version that we were playing has 10 to the 161 different decision points, which is more than the number of atoms in the universe squared.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  27. Exactly. Yeah. Self play is not tied specifically to neural nets. It's a kind of reinforcement learning, basically. And I would also say this process of trying to reason oh, what would the value have been if I had taken this other action instead? This is very similar to how humans learn to play a game like poker, right? Like you probably played poker before and with your friends, you probably ask like, oh, what do you have called me if I raised there? And that's a person trying to do the same kind of like learning from a counterfactual that the AI is doing.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  28. So, this counterfactual regret minimization is a kind of self play. It's a principled kind of self play that's proven to converge to Nash equilibria, even in imprivitation games. Now you can have other forms of self-play and people use other forms of self-play for perfit information games where you have more flexibility. The algorithm doesn't have to be as theoretically sound in order to converge to that class of games because it's a simpler setting.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  29. So it updates the regret value for that action. Regret is basically like, how much does it regret having not played that action in the past? And when it encounters that same situation again, it's going to pick actions that have higher regret with higher probability. Just keep simulating the games this way. It'll keep accumulating regrets for different situations. And in the long run, if you pick actions that have high regret with higher probability in the correct way, it's proven to converge to a nash equilibrium.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  30. All right, so there's different ways to find an actual equilibrium. The way that we do it is with this process called self play. Basically, we have this algorithm that starts by playing totally randomly, and it learns how to play the game by playing against itself. So it will start playing the game totally randomly, and then if it's playing poker, it'll eventually get to the end of the game and make $50. And then it will review all of the decisions that it made along the way and say, what would have happened if I had chosen this other action instead? You know, if I had raised here instead of called, what would the other player have done? And because it's playing against a copy of itself, it's able to do that counterfactual reasoning so I can say, okay, well, if I took this action and the other person takes this action and then I take this action and eventually I make $150 instead of $50.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  31. I was listening to this talk by a gaming executive when I was in grad school. And one of the questions that a person in the audience asked is, why are all these games so focused on fighting and killing? And the person responded that it's just so much harder to make an AI that can talk with you and cooperate with you than it is to make an AI that can fight you. I think once this technology develops further and you can reach a point where like not every single line of dialogue has to be scripted, it unlocks a lot of potential for new kinds of games, like much more positive interactions that are not so focused on fighting. And I'm really looking forward to that.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  32. Yeah, honestly, I think this is like one of the first applications where we're going to see real consumer interaction with large language models. I guess Elder Scroll 6 is in development now. They're probably pretty close to finishing it. But I would not be surprised at all if Elder Scroll 7 was using large language models for their NPC.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  33. So those are all different things Yeah, and I think I've heard talks from game designers and they say people that work on AI for actual recreational games that people play. And they say, yeah, there's a big difference between trying to make an AI that actually wins. And, you know, you look at a game like Civilization. The way that the AIs play is not optimal for trying to win. They're playing a different game. They're trying to have personalities. They're trying to be fun and engaging. That makes for a better game

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  34. Fascinating. I think what you're getting at here is that there's a difference between making an AI that wins a game and an AI that's fun to play with.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  35. Think you bring up a couple good points there. So I think a lot of professional poker players, I mean, they get a huge amount of money, not from actually playing poker, but from the sponsorships and having a personality that people want to tune in and watch, that's a big way to make a name for yourself in poker.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  36. Zero sum aspect, so there exists a dash equilibrium in non two player zero sum games as well. And by the way, just to clarify what I mean by two player zero sum, I mean there's two players and whatever one player wins, the other player loses. So if we're playing poker and I win $50, that means that you're losing $50. Now outside of two player zero sum games, there still exists dash equilibria, but they're not as meaningful. Because, you know, you can think of a game like Risk. If everybody else on the board decides to team up against you and take you out, there's no perfect strategy you can play that's going to guarantee that you win there. There's just nothing you can do. So outside of two player zero sum games, there's no guarantee that you're going to win by playing a national equilibrium.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  37. Finite's not a huge constraint. So, I mean, most games that you play are finite in size. It's also true, actually, that there exists this perfect strategy in many infinite games as well. Technically, the game has to be compact. There are some edge cases where you don't have a Nash equilibrium in a two-player zero-sum game. So you can think of a game where if we're playing a game where whoever names the bigger number is the winner, there's no Nash equilibrium to that game. 18. I thought you beat.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  38. A very high variance game, so you're going to have hands where you win, you're going to have hands with you lose, even if you're playing the perfect strategy. You can't guarantee they're going to win every single hand. But if you play for long enough, then you are guaranteed to at least break even in practice probably one.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  39. Now, the same is true for poker. There exists some strategy, some really complicated strategy, that if you play that, you are guaranteed to not lose money in the long run. And I should say this is for two player poker. Six player poker is a different story.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  40. In any finite two player zero sum game, there is an optimal strategy that if you play it, you are guaranteed to not lose an expectation no matter what your opponent does. This is kind of a radical concept to a lot of people, but it's true in chess, it's true in poker, it's true in any finite two-player zero-sum game. And to give some intuition for this, you can think of rock, paper, scissors. In rock paper scissors, if you randomly choose between throwing rock, paper and scissors with equal probability, then no matter what your opponent does, you are not going to lose an expectation. You're not going to lose an expectation in the long run.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  41. I'm drawn in by the beauty of the game. When I started playing poker when I was in high school. And the idea to me that there is a correct, an objectively correct way of playing poker, and if you could figure out what that is, then you're making unlimited money, basically. That's like a really fascinating concept to me. And so I was fascinated by the strategy of poker, even when I was like 16 years old. It wasn't until much later that I actually worked on poker AIs.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  42. I think that's right. I think one of the key strategies in poker is to put the other person into an uncomfortable position. And if you're doing that, then you're playing poker well. And there's a lot of opportunities to do that in no limit hold them. You can have like $50 in there. You throw in a thousand dollar bet. And that's sometimes if you do it right, it puts the other person in a really tough spot. Now it's also possible that you make huge mistakes that way. And so it's really easy to lose a lot of money and no limit hold them if you don't know what you're doing. But there's a lot of upside potential too.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  43. You're playing poker, you always want to choose the action that's going to maximize your expected value. It's kind of like with investing, right? Like if you're ever in a situation where you're the amount of money that's at stake is going to have a material impact on your life, then you're going to play in a more risk-averse style. If somebody makes a huge bet, if you're playing no limit, hold them and somebody makes a huge bet, there might come a point where you're like, this is too much money for me to handle. I can't risk this amount. And that's what throws a lot of people off. So that's the big difference, I think, between no limit and limit.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  44. I think both variants reward strategy, but I think what's different about no limit holdem is it's much easier to get jumpy. You go in there thinking you're going to play for like $100 or something and suddenly there's like $1,000 in the pot. A lot of people can't handle it.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  45. The no limit aspect is there's no limit to how much you can bet and limit hold them, there's like two dollars in the pot, you can only bet like two dollars. But if you've got $10,000 in front of you, you're always welcome to put $10,000 into the pot.

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source

  46. No limit Texas hold and poker is the most popular variant of poker in the world. So you go to a casino, you play, sit down at the poker table, the game that you're playing is no limitex hold'em. If you watch movies about poker like casino royale or rounders, the game that they're playing is no limitex hold in poker. Now it's very different from limit hold em in that you can bet any amount of chips that you want. And so the stakes escalate really quickly. You start out with like one or two dollars in the pot. and then by the end of the hand you've got like thousand dollars in there maybe

    2022-12-06 · Lex Fridman Podcast · #344 – Noam Brown: AI vs Humans in Poker and Games of Strategic Negotiation · IDENTIFIED FROM THE TRANSCRIPT · source