simple game theory question

[jogsxyz]

I mean your statement is FALSE.

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I mean your statement is FALSE.

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A nash eq is defined where each player plays with the best response to his opponents strategy. Each player thus plays with an optimal strategy, because no player can gain by deviating.

A bad player is one who deviates, and therefore loses.

Hence, my statements have been correct.

[jogsxyz]

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Game theory is about how you would play against an opponent playing the optimal strategy. ....


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This is the garbage they teach in school.

If opponents were able to play anywhere near optimal strategy, this game is unbeatable. The rake is outrageously high.
Game theory is also about using best exploitive strategy against bad opponents. These bad opponents are oblivious to your strategy and will fail to exploit you.

Chess is a deterministic game. You don't need game theory for chess. In chess a good move against a good player is a good move against a weak player. You can't make this same statement in poker. In exactly the same situation it may be correct to call player A, fold to player B, and randomize against player C.

[_D&L_]

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Game theory is about how you would play against an opponent playing the optimal strategy. ....


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This is the garbage they teach in school.

If opponents were able to play anywhere near optimal strategy, this game is unbeatable. The rake is outrageously high.
Game theory is also about using best exploitive strategy against bad opponents. These bad opponents are oblivious to your strategy and will fail to exploit you.

Chess is a deterministic game. You don't need game theory for chess. In chess a good move against a good player is a good move against a weak player. You can't make this same statement in poker. In exactly the same situation it may be correct to call player A, fold to player B, and randomize against player C.

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Your original argument was that game theory (as I defined it - a Nash Strategy) can't be used profitably against a bad player. I showed that was false.

You come back at with some silly argument about how rake would make it unprofitable to play against a perfect player. Obviously we wouldn't be playing poker if such players existed (in any significant number). A better argument would have been that a Nash strategy is unprofitable to play (given rake) against a bad player. That, i know you can't prove and i'm certain is not the case. A nash poker strategy is quite complex, and gives opponents plenty of room for mistakes.

There are many potential uses for a nash strategy. Besides being profitable in its own right, it can be used as a baseline for creating exploitative strategies, and as a default strategy while collecting data-points - which all exploitative strategies need because they rely on opponent modeling.

But unfortunately, even when begining my statements by saying that an exploitative strategy is better than a nash strategy against a flawed opponent, somone feels compelled to restate what I just said as if they were reinventing the wheel or something. And using that to argue that all discussion of Nash strategies are worthless.

Finally, if you want to call exploitative strategies game theory - go ahead. I try to avoid semantics arguments, as they are ultimately pointless. Its just in any gametheory , p1's strategy is generally a function of p2's strategy. Here, you made p1 exploitable because he doesn't adapt anymore. Because p1 doesn't adapt anymore, maximizing your payouts against him is a simple math problem that was generally understood and solved for before "game theory" as a field ever came about. Hence, when economists speak of game theory, they really aren't referring to these problems. They are referring to games with rationally adaptive opponents.

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[jogsxyz]

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You come back at with some silly argument about how rake would make it unprofitable to play against a perfect player. Obviously we wouldn't be playing poker if such players existed (in any significant number). A better argument would have been that a Nash strategy is unprofitable to play (given rake) against a bad player. That, i know you can't prove and i'm certain is not the case. A nash poker strategy is quite complex, and gives opponents plenty of room for mistakes.



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You haven't a clue what's Nash equilibrium for hold'em. No one knows it. But we do know many of the most successful players deviate from it. You don't really think Ivey, Negreanu, or Hansen are using optimal strategy, do you?

In poker it's about using the best exploitive strategy. This strategy will blow up if opponents' knew what you were doing and exploited you. Still it's the best EV strategy.

[jogsxyz]

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Playing heads up limit hold em - how many bets max can it be optimal to go without the nuts on the river?



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Change this a little. Fixed-limit lowball. A two-way pot, the other players have folded. After the draw. The wheel(5432A) is the best hand in lowball. Assume both players know how to play and both knows the other knows how to play. 3rd raise after the draw. You must have the wheel. With less than the wheel the 2nd raise is it. When a player puts in the 4th raise, the other players get mad at him for slowing the game down.

[jogsxyz]

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Game theory is often described as a branch of applied mathematics and economics that studies situations where players choose different actions in an attempt to maximize their returns. ...

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This is a much better definition of game theory, especially as it applies to hold'em.

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Game theory is a branch of applied mathematics that is often used in the context of economics. It studies strategic interactions between agents. In strategic games, agents choose strategies which will maximize their return, given the strategies the other agents choose.

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http://en.wikipedia.org/wiki/Game_theory

words are just boxes to put ideas. this is the last response i'm making to any arguments over what "is" game theory. As wiki indicates, its where a players strategy is rationally adaptative to that of his opponent.

If u want it to have a broader meaning, i don't mind. I'm not on here to debate definitions. I can see u like to argue for sport, but maybe u can pick something more substantive than definitions. And even if u do stick that field, at least use accepted definitions....


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[DrVanNostrin]

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You haven't a clue what's Nash equilibrium for hold'em. No one knows it.

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That's true. But we still have an idea of what it would look like. In this situation we know that the optimal strategy will have the probability of a player's hand being a bluff asymototically approach 0. Most of us have learned, from experience that players tend to deviate from this equilibrium by actually bringing that probability to 0 after 3 or 4 bets; and by doing this they are only deviating slightly, and the edge one could gain from this deviation is extremely small.

OP's question was about the optimal strategy, not the maximal strategy. The question you keep answering pertains to the maximal strategy.

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That's true. But we still have an idea of what it would look like.

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Van nostrin is right. We can't solve for it, but we have a pretty good idea of what it looks like. This informs us of where opponents can make mistakes, even what the magnitude of those mistakes might be.

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