Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

The Steely, Headless King of Texas Hold ’Em

nytimes.com

Post reply on HN
Print view View original

51–60 of 99 posts

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

#51

Post by ianstallings »

gonvaled wrote: post #25
cuu508 wrote: post #21

Earlier quoted context omitted.

writing a game that cheats and doesn't raise suspiction might be as hard as writing a game that plays fair :-)

Parafrasing Clarke, "A sufficiently complex system is indistinguishable from magic". You, and nobody, will not notice small probabilistic variations. Whenever you discover it (let us say, 30 years from now), you will be told that there was a difficult to find bug in the random generator. Nobody will be prosecuted. It could be a couple of lines of code in a subsystem somewhere, available only to a handful of engineers…

This is true but the Gaming Control Board audits the software and they are also audited by outside parties. Could they cheat? Of course. So can human dealers, rigged card shufflers, etc. But Las Vegas makes its money from table games, slot machines, and apparently poker machines that play so well you'd have to be a pro to win consistently. It's not in their best interest to cheat you. As always in life: your mileage will vary.

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

#52

Post by ianstallings »

dschatz wrote: post #30
hannibal5 wrote: post #24

Illegal poker bots grind constantly on low level online poker games and take the money from low level players by just value betting them. Computers can easily calculate probabilities and expected values for every hand. So why they are not beating professionals? Poker has no optimal strategy that wins against all other strategies. To play poker in higher level you must model the strategies of others, including them tr…

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 opponent (this does not mean an opponent who can see your cards, but one who always knows your range whenever you take an action and makes the best choice against that range). In the game “rock, paper, scissors,” the equilibrium strategy is to randomly choose between the three options, choosing each one a third of the time in the long run. Finding equilibriums in poker is much more complicated, but the concept can be useful when you’re playing lots of hands against tough opponents. For example, if your opponent bets half the pot on the river after a particular series of actions, the pot is offering him 2-1 on his bluff. If he were a perfect player, the right thing to do would be to call his bet a third of the time, since if you called more he’d exploit you by never bluffing and if you called less he’d exploit you by always bluffing. In reality, of course, our opponents are never perfect, and so the idea of playing an equilibrium strategy at the table is usually pretty academic. *

http://pokerpromagazine.com/proscorner/bryce-paradis/

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

#53

Post by pedrocr »

gonvaled wrote: post #23
pedrocr wrote: post #12

Earlier quoted context omitted.

>You are joking, aren't you? No, I'm not. >You are telling me that nobody would program a secret algorithm, standing to win loads of money, to tilt the chances at the right moment? No I didn't make that generalized statement. What I did say was that in this particular case that hypothesis is of low probability: 1) The people building the machines don't make money on poker playing, but by selling them to casinos 2) Th…

Sorry, not convinced. All that control and regulation applies to more important parts of society, and it does not work (NSA). So, according to you, I, Mr. unbeatable hold'em player, can go to this machine, bet a million dollars and be sure that, in that perfect moment when I know I am going to crush it, it will not play tricks against me? When I lose, how do I know? How can I be sure that it has not dealt itself favo…

>So, according to you, I, Mr. unbeatable hold'em player, can go to this machine, bet a million dollars and be sure that, in that perfect moment when I know I am going to crush it, it will not play tricks against me?

No, I never said you could be sure of that. What I do argue is that no one has much of an incentive to cheat you in this case.

>It is not a matter of whether they are doing it: it is a matter of whether they can do it. If there is no independent dealer, this is not for me.

Don't change the subject. The discussion was around if they were doing it. We all know it could be done, that's why we discussed this in the first place.

>And, by the way, as long as the machine can know what cards I am holding, I am not playing it either. Give me an independent dealer, and then we talk.

That's fine. You require 100% certainty of not cheating and this machine doesn't offer it. That is in no way an argument to say that they are in fact cheating. It's not even an argument to say that the probability that they are indeed cheating is very small (which is what I argued).

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

#54

Post by jib »

Someone wrote: post #42
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…

Is it actually possible to mathematically solve those games? Suppose player Alice bets $100; how does player Bob judge that bet? As a strong hand or as a bluff? Any software program will have to model what's inside the head of its opponent, and we know way too little of that to do that. Moreover, if we could, the opponent may choose a different strategy. It may be like a game with nontransitive dice: if you figure ou…

Yes it is possible to mathematically solve limit poker (as well as no-limit poker, but no-limit poker is orders of magnitude more difficult - they are effectively different games).

The definition of solvable is "Does there exist a strategy that, regardless of opponents play, is not a losing strategy" though (because the game is symmetrical). It is not possible to solve for "Does there exist a strategy that, regardless of opponents play, guarantees maximum profits". You can solve it for not losing money, but you cant solve it for making the max amount of money.

Trivially it's not possible to write software that beats any opponent (because what would it do playing against itself?) . Less trivially, any game that has a finite amount of decisions (and limit hold-em does) has at least one Nash equilibrium, so there exists a strategy that will at least have you break even.

The way to solve the game is to calculate your odds of winning based on previous actions and ensure that you take actions that make any future decision of the opponent have the same outcome (to reach a Nash equilibrium).

That strategy hasnt been calculated yet, but the best limit players are most likely playing very close to it, at least if you compare to the best no-limit players playing no-limit (the variable amounts possible to bid in no-limit multiplies the possible strategies massively).

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

#55

Post by omni »

ianstallings wrote: post #36
pepve wrote: post #32

Earlier quoted context omitted.

Just a note, you don't have to mathematically solve a game in order to win it.

I agree that it can win, but so can pros and they make mistakes everyday. But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Unlike say chess, where clear pathways to a checkmate can be calculated using mathematics, no matter how the opponent plays. It's impossible to do that, right now, using computers, when the opponents are human and unpredictable and don't…

> But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough.

Is this even possible in a game of imperfect information?

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

#56

Post by swang »

1. Is there anything Phil Hellmuth won't shill for?

2. When this machine showed up ~2? years ago, there was a thread on 2+2 about it, and it would sometimes do some weird things like not value bet in obvious situations. They explain it in this article by saying it's, "playing dumb" but that seems like it would be a huge leak against Limit Hold'em HU specialists. I am guessing that they assume that they can make up for it in the weaker players losing consistently against this machine.

3. It is kind of annoying that the guy is proud that he "broke" a 24 year old player.

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

#57

Post by lazyant »

TomGullen wrote: post #17
scotch_drinker wrote: post #2

In his book Super System, Doyle Brunson wrote that a computer would never be able to play elite poker because you played the man, not the cards or the game. He greatly underestimated the power of modern computing it appears. Personally, I'd rather see resources go into a robot that can cook for me but development follows the money I suppose.

"Playing the man" is merely an abstract reference to maths in Poker that a lot of old timers in these (slightly out of date) books couldn't quite put their finger on. Super System was a good book for its time, but I think there's a lot of better books out there now (Harrington on Holdem for example). A simple example, common stats software for poker will record what % of hands an opponent raises on the button if it's…

"Playing the man" means exploiting the particular tendencies (weaknesses) of an adversary

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

#58

Post by lazyant »

Someone wrote: post #42
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…

Is it actually possible to mathematically solve those games? Suppose player Alice bets $100; how does player Bob judge that bet? As a strong hand or as a bluff? Any software program will have to model what's inside the head of its opponent, and we know way too little of that to do that. Moreover, if we could, the opponent may choose a different strategy. It may be like a game with nontransitive dice: if you figure ou…

The example is not very good because solving or beating the game is always defined "in the long run" ie over a large sample of hands, not one particular hand (ex: if Alice bets $100 all the time she is bluffing a lot since good cards are hard to get)

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

#59

Post by jib »

omni wrote: post #55
ianstallings wrote: post #36

Earlier quoted context omitted.

I agree that it can win, but so can pros and they make mistakes everyday. But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Unlike say chess, where clear pathways to a checkmate can be calculated using mathematics, no matter how the opponent plays. It's impossible to do that, right now, using computers, when the opponents are human and unpredictable and don't…

> But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Is this even possible in a game of imperfect information?

Yes, because you know all possible states of the game.

Starting out you have 2 cards and you know your opponent has one of 2450 possible combinations of cards.

You know exactly how your 2 cards stack up in chances of winning against those 2450 combinations, and you know how much money is on the table initially. Each time an opponent has an action he can take one of two or three actions (call, raise or fold) - your job is to calculate a strategy that makes either of those decisions have the same expected value for your opponent. That is doable, but quite complex, because it requires you to consider not only what your opponent has, but also what possible hands you could have based on your previous actions.

The complexity is obviously enormous (hence why it hasnt been computed yet) but it is not impossible to compute by any definition.

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

#60

Post by ianstallings »

omni wrote: post #55
ianstallings wrote: post #36

Earlier quoted context omitted.

I agree that it can win, but so can pros and they make mistakes everyday. But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Unlike say chess, where clear pathways to a checkmate can be calculated using mathematics, no matter how the opponent plays. It's impossible to do that, right now, using computers, when the opponents are human and unpredictable and don't…

> But I'm saying that a mistake-free strategy cannot be found without some kind of mathematical breakthrough. Is this even possible in a game of imperfect information?

Not to my knowledge. Not with current computing power and software. That's why I think it would require a breakthrough in mathematics. It boggles my mind even thinking about how it could be tackled. I did find a few papers that dig into the topic: http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.51.1...

http://www.econ.ohio-state.edu/jpeck/gametheory/gameL8.pdf

http://robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:I...

It's a problem that is incredibly challenging.

Post reply on HN