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The Steely, Headless King of Texas Hold ’Em

nytimes.com

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Re: The Steely, Headless King of Texas Hold ’Em

#71

Post by hannibal5 »

tedsanders wrote: post #65
hannibal5 wrote: post #46

Earlier quoted context omitted.

Nash Equilibrium assumes that each player knows equilibrium strategies of the other players. It does not apply to No Limit Hold Em. You can solve equilibrium for simplified poker games like just Heads Up with only shove or call an all-in options though.

Nash equilibrium certainly applies to No limit hold 'em. It's a zero-sum game with finite choices over finite time. Could you explain why you think otherwise? Are you just saying it's practically impossible to calculate?

You can calculate Nash equilibrium only when you know the strategies of your opponents. There is no single winning strategy in complete No limit Holdem, so you don't know how your opponent is going to play.

It's theoretically possible to find Nash equilibrium over all possible strategies but that's not winning strategy. You just lose as little as possible. You lose against most/all strategies.

Take for example Kuhn poker (https://en.wikipedia.org/wiki/Kuhn_poker). It's very simple but first player has several optimal strategies.

Re: The Steely, Headless King of Texas Hold ’Em

#72

Post by hannibal5 »

ianstallings wrote: post #52
dschatz wrote: post #30

Earlier quoted context omitted.

Head's Up Hold'em has a nash equilibrium. Therefore there is at least one mixed strategy (I do X with probability P in Y situation) which cannot be negative expected value to any other strategy. In this sense, there is an optimal strategy. It doesn't mean that it is the maximum expected value against a particular opponent, but no opponent can win by playing (which is largely the goal of a casino). Opponent modeling i…

I found this artile by Bryce Paradis that elaborates on using a Nash equilibrium for optimal play. He is known for bringing advanced mathematics to the game of limit poker and winning a small fortune because of it. Here is his take: * Q: What’s a Nash Equilibrium or “game theory optimal” strategy? – Failed Math, Port Perry, Ontario A: An equilibrium strategy is one that wins the most money possible against a perfect…

I can see the possibility for confusion here.

You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up.

But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equilibrium that would be optimal in actual game against specific strategies.

Re: The Steely, Headless King of Texas Hold ’Em

#73

Post by ianstallings »

thisisnotatest wrote: post #67
ianstallings wrote: post #31

Earlier quoted context omitted.

(Putting this as its own thread because it's so large and slightly off-topic). I've thought long and hard on this, it's one of my life goals to create a piece of software that could mimic good players in texas hold-em, and I think I might have found a way to do just that using big data, hand histories, neural-networking, and a ton of input by actual players. Or at least a good start. How would I accomplish this? Well…

I don't see what you get from asking people what they think they'd do in certain situations, when you could instead use the actual outcome of the hand as your training labels.

Validation mainly. Because I worry that the hand histories might not be enough and they may be tainted with more examples of bad play than good. I would like to qualify good play with some human validation.

But I think it's worth looking at to only use hand histories and if possible only validate when something unexpected results. Maybe then I could use the human input to validate the computer's decision. I'm still hashing that out.

Re: The Steely, Headless King of Texas Hold ’Em

#74

Post by psutor »

ianstallings wrote: post #10

The article says the machine can't be beaten. And then points out that a pro has consistently won against it. This article is filled with bold claims by people that want to sell the idea IMHO. I'm not buying it because even limit texas Hold'Em has never been solved mathematically by super computers, let alone a single machine. Limit Hold'Em is close to being solved but if you check out the last match of pros against…

IIRC, the article only mentioned the "dumbed down" version now in casinos being beaten by pros.

The earlier part of the article (when it was full strength and in testing) has no mention of it being beaten.

Re: The Steely, Headless King of Texas Hold ’Em

#75

Post by ianstallings »

hannibal5 wrote: post #72
ianstallings wrote: post #52

Earlier quoted context omitted.

I found this artile by Bryce Paradis that elaborates on using a Nash equilibrium for optimal play. He is known for bringing advanced mathematics to the game of limit poker and winning a small fortune because of it. Here is his take: * Q: What’s a Nash Equilibrium or “game theory optimal” strategy? – Failed Math, Port Perry, Ontario A: An equilibrium strategy is one that wins the most money possible against a perfect…

I can see the possibility for confusion here. You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up. But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equil…

Yeah in heads up play using a Nash equilibrium to "balance your range" and play a more unbeatable strategy while also using it to calculate probable hands your opponent holds might be helpful, but it's far from a solution to the problem of devising a winning strategy that always works. I think that's why he calls it academic. Because it won't work in the real world.

Re: The Steely, Headless King of Texas Hold ’Em

#76

Post by iopq »

hannibal5 wrote: post #72
ianstallings wrote: post #52

Earlier quoted context omitted.

I found this artile by Bryce Paradis that elaborates on using a Nash equilibrium for optimal play. He is known for bringing advanced mathematics to the game of limit poker and winning a small fortune because of it. Here is his take: * Q: What’s a Nash Equilibrium or “game theory optimal” strategy? – Failed Math, Port Perry, Ontario A: An equilibrium strategy is one that wins the most money possible against a perfect…

I can see the possibility for confusion here. You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up. But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equil…

Yes, you can.

Your opponent has 1352 different hand combinations. Assume he is playing the Nash equilibrium strategy. Make the perfect plays based on this. If he plays worse than the Nash equilibrium strategy, you beat him. If he plays perfectly, you tie.

Assuming your opponent plays perfectly works in chess. Chess programs are stronger than the best humans now.

Re: The Steely, Headless King of Texas Hold ’Em

#77

Post by iopq »

hannibal5 wrote: post #71
tedsanders wrote: post #65

Earlier quoted context omitted.

Nash equilibrium certainly applies to No limit hold 'em. It's a zero-sum game with finite choices over finite time. Could you explain why you think otherwise? Are you just saying it's practically impossible to calculate?

You can calculate Nash equilibrium only when you know the strategies of your opponents. There is no single winning strategy in complete No limit Holdem, so you don't know how your opponent is going to play. It's theoretically possible to find Nash equilibrium over all possible strategies but that's not winning strategy. You just lose as little as possible. You lose against most/all strategies. Take for example Kuhn p…

No, you will tie or beat all strategies because your opponents will make huge mistakes like calling when you are almost never bluffing and folding when you are frequently bluffing.

Re: The Steely, Headless King of Texas Hold ’Em

#78

Post by iopq »

b0b0b0b wrote: post #28

Assuming the machine is stateless, why can't the space of hole cards be mapped out and and strategies/responses enumerated? But ultimately, the whole enterprise just seems distasteful: "Look, there was a 24-year-old who had beaten it for a while. Now he’s broke. And I think this machine had something to do with his demise."

There's 1352 card combinations, many more flops, many more turns, many more rivers and also 1352 combinations for your opponent too and 3 actions per round of betting

There's more poker situations than amount of atoms in the universe

Re: The Steely, Headless King of Texas Hold ’Em

#79

Post by hannibal5 »

iopq wrote: post #76
hannibal5 wrote: post #72

Earlier quoted context omitted.

I can see the possibility for confusion here. You can certainly use Nash equilibrium when you have figured out the strategies your opponents are using. This is what Bryce Paradis is talking about. It can have practical value when playing Heads Up. But If we are talking game theory and "solving poker", there is no single winning strategy that works against all other strategies and you can't calculate single Nash equil…

Yes, you can. Your opponent has 1352 different hand combinations. Assume he is playing the Nash equilibrium strategy. Make the perfect plays based on this. If he plays worse than the Nash equilibrium strategy, you beat him. If he plays perfectly, you tie. Assuming your opponent plays perfectly works in chess. Chess programs are stronger than the best humans now.

>Assume he is playing the Nash equilibrium strategy.

You you can't do that assumption because you don't know what the strategy is. You can calculate Nash equilibrium only if you know the strategy your opponent is using. In full no limit hold em there is no single strategy winning strategy, so you don't know the strategy your opponents are using.

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