Poker question from alphatmw

[curious123]

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I have a question. Would an optimal game theory strategy be profitable in poker? My guess is not and especially not if you consider the rake.

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Tom Weideman, one of David's picks for the top 10 smartest poker players, once wrote...


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In fact, I think an optimal opponent would beat a (typical) suboptimal player handily.

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FWIW, I agree w/ him wholeheartedly.

[kdotsky]

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Kdotsky is the one who thinks no player should ever deviate from optimal strategy.

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Quote where I said that. Or quote one incorrect statement I've made in this thread.

Please just let it go, you're detracting form the value of the thread.

[Shandrax]

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Optimal strategy in game theory is unexploitable.
No one is disputing that statement.

Would an expert game theorist blindly always use optimal strategy? No.
Here are the results from a
roshambo tournament. The most successful programs used
data history gathering methods.

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It's quite simple actually. A program using game theory (aka completely randomizing it's moves in Roshambo) would simply finish in the middle of the pack, realizing it's expectation of exactly 50%.

Game Theory prevents someone from exploiting your strategy. The downside is that your opponent cannot make a mistake anymore. Regardless what he does, his EV stays the same.

[stump5727]

Its seems as though that a perfect game theory is unbeatable the psychology but not unbeatable (through perhaps sheer luck, or another optimal game theory), does that mean there’s a more specific game theory is maybe more optimal?

I guess my main question is that one of the arguments is stating that perfect game theory is unbeatable, that mean against a psychologist, correct?

My next question is, is a game theory always constant whether full table, short table, or heads up, then does it take into affect stack size or is this all part of the optimal game strategy?

And lastly is optimal game strategy for efficiency or consistency?

[Brocktoon]

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Game Theory prevents someone from exploiting your strategy. The downside is that your opponent cannot make a mistake anymore. Regardless what he does, his EV stays the same.



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I'm not sure if you're talking about poker here but if you are this is not true. Poker is not rock, paper, scissor. If you're playing a perfect game theory bot the more mistakes you make and the more eggregious they are the more you will lose I believe.

[kdotsky]

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Game Theory prevents someone from exploiting your strategy. The downside is that your opponent cannot make a mistake anymore. Regardless what he does, his EV stays the same.



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I'm not sure if you're talking about poker here but if you are this is not true. Poker is not rock, paper, scissor. If you're playing a perfect game theory bot the more mistakes you make and the more eggregious they are the more you will lose I believe.

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Yep, I mentioned this before -- In poker, against a game theory strategy, the further the opponent strays from the optimal strategy the more -EV he is. This is where the roshambo example fails to illustrate.

In regards to the roshambo tournament and the game theory strategy falling in the middle of the pack. It's not because some players are better than the game theory bot. It's because when two exploitive strategies face each other, one gains a better than 50/50 edge on the other. This gives the better one an overall edge in the tournament. Basically the good exploitive strategies do well because they're better at exploiting the bad exploitive strategies than the game theory strategy.

[kdotsky]

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Its seems as though that a perfect game theory is unbeatable the psychology but not unbeatable (through perhaps sheer luck, or another optimal game theory), does that mean there’s a more specific game theory is maybe more optimal?

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The game theory strategy, by proof, is unbeatable, regardless of the opponent (think of the rock-paper-scissors example). There may be more than one optimal strategy, but by definition if they played against each other neither would loose. And by loose we mean have a negative long run expectation -- meaning that yes one may win by sheer luck as you mentioned.
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I guess my main question is that one of the arguments is stating that perfect game theory is unbeatable, that mean against a psychologist, correct?

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No. It's not an argument for one -- it's mathematically proven. The strategy would be the exact same against any opponent. Keep in mind, though, that though we have an algorithm to calculate this strategy, it would take a computer an impractical amount of time to compute.
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My next question is, is a game theory always constant whether full table, short table, or heads up, then does it take into affect stack size or is this all part of the optimal game strategy?

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The optimal strategy would change if you added more players to the table. It does take into account stack sizes. It calculates the optimal strategy (e.g. raise 30%, fold 30%, call 60% of the time) for every possible scenario you can be in in the game. The opponent have different stack sizes, or there being different numbers of opponents, are different scenarios.

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And lastly is optimal game strategy for efficiency or consistency?

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I have no idea what this means. I would call it for "security". You are guaranteed not to lose (which means you will most likely win), but against worse players you could win a lot more playing an exploitive strategy (though you would loose a lot more doing this with a better opponent).

[JaredL]

A couple comments:

- There is absolutely no chance in hell that the world's greatest mathematician/game theorist could come close to solving heads-up poker in any form played today. It's effectively impossible for limit forms and beyond impossible for no limit. The strategy space for even limit poker is extremely, extremely large. Even heads-up, poker is so many orders of magnitude more complicated than games that theorists solve (by whom I include the top people in the field at the top universities). Admittedly these people are economists, top mathematicians could no doubt do hard-core theory better than economists but the point still would stand if it was top mathematicians doing it.

- Assuming hero played an equilibrium strategy, this strategy would be at worst 0 EV (ok a bit negative considering rake). Assuming no rake, it would be 0 EV only if the opponent was playing a best response (which would then, with hero's strategy an equilibrium make). In equilibrium, the player in position will almost certainly have a positive expectation and the player without position a negative one. It would even out though so assuming that the button moves each would be 0 EV in the game. If the opponent did not play a best response, then hero would be +EV.

- Most of the claims above are only true if the game is heads-up. Playing an equilibrium strategy in a 3 handed game does not guarantee that one is not a loser.

- If there are multiple equilibria, they all must have the same payoff if the game is heads-up (assuming no rake). This also does not hold if there are 3 players.

- If they play a while (long enough for hero to get a read on the psycho's play) then the superhero game theorist acting optimally will at some point stop playing the equilibrium strategy in favor of a strategy that is superior given the strategy that the psychologist is playing. Such a strategy will obviously be more +EV as otherwise it wouldn't be wise to change to it.

[JaredL]

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You are misunderstanding what it means to employ perfect game theory.

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You are misunderstanding the question. It nowhere says that the mathematician uses perfect game theory, instead it describes him only as "the world's greatest mathematician and game theorist." How can you assume that this person, just because he knows more in this discipline than anybody else alive, uses an absolute perfect strategy as you describe?

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The world's greatest mathematician and game theorist is almost certainly not the person who "knows more in this discipline than anyone else alive." As Einstein said "Imagination is more important than knowledge."

[JaredL]

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"the world's greatest mathematician and game theory expert goes heads up against the world's greatest behavioral psychologist / people reader. both have average skills in the other person's expertise, and both have a good understanding of poker. who has the edge, and how much is it?"

If you use perfect game theory and have no physical tells, no one can have an edge on you head up.

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Wrong

This is a game of imperfect information in which the game theory guy does not know the type of his opponent. By type I simply mean the way any 'realisation of' the psychologist plays the game. In any optimal strategy chosen by the game theory wiz there will (almost certainly) be realisations of his opponent's type against which he is an underdog-It is possible that the psychologist can have an edge against Mr. game theory.

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Way Way Wrong. The optimal game theory strategy is the same against any opponent, regardless of how he is playing, and it is already proven to be unbeatable.

The term game theory is thrown around loosely in poker. You don't understand what it really means to play by optimal game theory.

But again, keep in mind the mathematician cannot play this optimal strategy because it takes too long to compute.

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Heres a simple example of what I'm talking about

Opponent type A: Bets 100% of the time he has nothing, Checks 100% of the time he has hit.

Opponent type B: Checks 100% of the time he has nothing,
Bets 100% of the time he has hit.

Do you still contend that there is a unique optimal strategy for Mr. Game Theory against these two types of his opponent, given that Mr Game theory does not know which type he is up against?

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I think that your problem is a semantic one. People for some reason in poker discussion continually throw the terms "optimal strategy" or worse the "optimal game theory strategy" when really what they mean is "an equilibrium strategy."

In your example, if the superhero theorist doesn't know the type of the opponent then she would not know the optimal strategy (using the standard definition of optimal). She would play an optimal strategy given the probability that the opponent is each type (assuming no other types exist). This strategy would be different from the strategy she would use if she knew the opponents type.

The point others have made is that if she played an equilibrium strategy for the game, it wouldn't matter. Either opponent type would lose money to her every single hand. However, her use of the equilibrium strategy would certainly not be optimal.

Jared