Game Theorists - Never Nash in Poker?
 

Given that poker is an asynchronous, non-cooperative game, isn't it true that the most effective strategy for each player is almost always changing to meet changing conditions so that while they are evolving for each player, they will seldom converge to the point of an absolute Nash Equilibrium?

Re: Game Theorists - Never Nash in Poker?
 

correct

Re: Game Theorists - Never Nash in Poker?
 

It depends on your assumptions on why players are at the table and how you define your strategy space. But I agree that it's hard to come up with a realistic set of assumptions that has an absolute Nash equilibrium. In practice, individual players often can find profitable niches that no individual other player has an incentive to destroy, but I've never seen a table that appeared to be in Nash equilibrium.

Re: Game Theorists - Never Nash in Poker?
 

I can imagine a time in the future - perhaps quite distant future - when a large number of people know a near-optimal strategy for poker, and they all sit down at a table and don't have much to do except follow their strategies and see how the cards fall.

I certainly agree that you are very unlikely to ever see a real table today that settles into anything like that -- simply because so many players do things so wildly far from their optimal strategies, and the rate of turnover is so high.

In a home game where the same people see each other week after week, I imagine that they approach some kind of stable state, and then one or more of the players gets bored and deliberately changes his style of play - not because he things it's better but because he is bored.

Re: Game Theorists - Never Nash in Poker?
 

Isn't any non-equilibrium strategy exploitable by some other non-equilibrium strategy? I've assumed that a very good player can recognize exploitable strategies and adjust their strategies accordingly. A couple of good player might adjust their strategies in the same way to take advantage of a player who does not adjust.

It seems to me that you need some sense of what the equilibrium space looks like in order to recognize strategies off of it. I imagine several good players all adjusting their strategies against each other in some sort of orbit around equilibriums. Could one of the players implement a sort of Lyapunov function in the way they chance strategies to guide the group to a stable equilibrium?

This is probably a bit academic and not of very much practical use. At least I haven't figured out a way to make use of it. And I'm not really sure that it is correct. I know just enough about this stuff to be dangerous.

Re: Game Theorists - Never Nash in Poker?
 

The nash strategy exists.

Finding it is another thing.

Re: Game Theorists - Never Nash in Poker?
 

CallMeIshmael and Alan3 have defined the two extremes. The resolution depends on how you define "strategy." Alan3's orbiting non-equibria could be defined as a strategy, in which case a Nash equilibrium should exist, or the orbits could be defined as constantly changing strategies with no equilibrium. Is the solar system in equilibrium because the orbits are stable (maybe, anyway) or in constant nonequilibrium as gravity battles momentum?

As a practical matter, the important thing is how to do calculations. If you want to know where the Earth will be in a month, you just trace its orbit (that is, you treat the solar system as in equilibrium). If you want to know where the Earth will be in a second or a million years, you have to simulate all the bodies in the solar system (that is, you treat it as something constantly changing).

Re: Game Theorists - Never Nash in Poker?
 

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The nash strategy exists.

Finding it is another thing.

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Huh? There's a trivial Nash strategy -- don't play.

Re: Game Theorists - Never Nash in Poker?
 

Actually, the changing dynamics just show that there isn't a PURE strategy to solve the game. If you employ the correct mixed strategy, in theory, you could have an optimal solution. For example, if your opponent is playing very tightly, it's profitable to play aggressively and bluff a lot. But then it's profitable for him to loosen up and snap your bluffs. Then it's profitable for you to tighten up, at which point he may also tighten up, which makes you loosen up again, etc etc. So your solution would be to play aggressivly and passively and tight and loose (etc etc) with a mix of percentages such that he cannot exploit you one way or the other.


However, it is very likely impossible to be able to define and understand poker well enough to develop such a strategy. There are too many decision points and too large of a state space for it to be reasonably solveable. We just have to operate on intuition and experience to approximate it as best we can.


Everett

Re: Game Theorists - Never Nash in Poker?
 

[ QUOTE ]

However, it is very likely impossible to be able to define and understand poker well enough to develop such a strategy. There are too many decision points and too large of a state space for it to be reasonably solveable. We just have to operate on intuition and experience to approximate it as best we can.

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Actually, I'm pretty sure that structured 5-card draw (especially heads-up) is well within the computable realm while 10 man NLHE is not.