Is a "perfect strategy" possible?

[DarkMagus]

Does anyone think it is possible to come up with a "perfect strategy" that is guaranteed to be at least breakeven (ignoring rake) against all opponents? Could there, theoretically, be a Call%/Raise%/Fold% for every situation that is unexploitable over the long term?

Let me illustrate.

Suppose you're playing heads up NLHE. You're on the Big Blind with KK and your opponent makes a standard raise to 3xBB. Stack sizes don't really matter here.

Against a good, aggressive opponent (opponent A), you'd probably decide to randomize your actions by calling X% and 3betting (100-X)% of the time.

Against a very bad, very loose opponent (opponent B) it might be better to just always raise since he'll put his money in with all sorts of crap.

And against a ridiculously weak-tight opponent (opponent C) who you somehow know will only raise with AA, you should always either fold or call, depending on whether you have set mining odds.

But now let's suppose you are against an unknown opponent, and furthermore suppose that you will only play 1 hand against him so that image is not something to worry about. Would there be an appropriate Raise%/Call%/Fold% to guarantee that you always at least break even no matter what your opponent chooses to do?

If you're playing against opponent C, 3-betting him is obviously very -EV. But the fact that he loses value on other hands by almost never raising should make up for this lost EV, right? And against opponent B, calling is going to be a much worse strategy than raising, but we still probably profit by calling.

Now suppose you are to play a series of these hands against completely random opponents. Each hand might be against different opponents, so you have no ability to track any sort of read, although your opponents have the ability to watch previous hands and get a read on you.

In this situation, it seems reasonable to me that you should, in theory, be able to develop a strategy that should break even against top-notch opponents and profit slightly against opponents who make mistakes. It would be much less profitable than a strategy that exploits our opponents' specific mistakes, but this isn't possible since we never have a read.

Does this make any sense? Comments?

[JavaNut]

There is a perfect strategy and that is to adapt perfectly to all opponents at all times.

But that is not something that can be put down in a simple formula and most surely not in percentages.

[rufus]

It's very easy to mathematically prove such a strategy exists. Finding such a strategy is, of course, practically intractable.

[75s]

I think there is a difference between an unexploitable strategy and a perfect strategy.

[El_Hombre_Grande]

[ QUOTE ]
There is a perfect strategy and that is to adapt perfectly to all opponents at all times.


[/ QUOTE ]

That's the problem. This is certainly the correct answer. But insofar as someone who is looking for a chartable strategy or decision tree, this obviously isn't the answer, because you need 1) perfect information and 2) a new box on the chart for every opponent in every situation.

This is what playing poker is. Everything that is written is based on correct reactions, or moves with respect to particular player tendencies that your actual opponents may or may not have to greater or lesser extents, all set in the context of what has already occurred at the table and the respective position, stack sizes, and emotional condition of the players at the table.

So the perfect strategy is a hypothetical concept that is necessary to think about but will never result in a chart that you can pull out of your pocket.

[DarkMagus]

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It's very easy to mathematically prove such a strategy exists. Finding such a strategy is, of course, practically intractable.

[/ QUOTE ]

Could you expand on this? What kind of mathematics would be involved?

[ QUOTE ]
I think there is a difference between an unexploitable strategy and a perfect strategy.

[/ QUOTE ]

Yeah, this is what I was getting at. I guess I was asking about an unexploitable strategy. It's clear that a perfect strategy tailored to our specific opponent would at least break even. But an unexploitable strategy would be one that isn't tailored to any specific opponent. I just wonder if it's possible to come up with such a strategy and at least break even regardless of what our opponent does.

[Flip-Flop]

What you are asking for is what the bot owners try to do, with moderate success so far.

[jukofyork]

[ QUOTE ]
[ QUOTE ]
It's very easy to mathematically prove such a strategy exists. Finding such a strategy is, of course, practically intractable.

[/ QUOTE ]

Could you expand on this? What kind of mathematics would be involved?

[/ QUOTE ]
http://en.wikipedia.org/wiki/Nash_equilibrium

For simple games at least, software packages such as Gambit can do the maths for you so long as you understand some basic game theory terminology.

[ QUOTE ]
[ QUOTE ]
I think there is a difference between an unexploitable strategy and a perfect strategy.

[/ QUOTE ]

Yeah, this is what I was getting at. I guess I was asking about an unexploitable strategy. It's clear that a perfect strategy tailored to our specific opponent would at least break even. But an unexploitable strategy would be one that isn't tailored to any specific opponent. I just wonder if it's possible to come up with such a strategy and at least break even regardless of what our opponent does.

[/ QUOTE ]
It's not always possible to "at least break even" in multi-player poker, as it may turn out that 2 or more opponents are using a strategy which concidentally work together to make it so that the you lose even when playing optimally against them (see this thread's discussion).

Juk [img]/images/graemlins/smile.gif[/img]

[JavaNut]

I guess for this to become a good discussion we have to define what we mean when we say perfect strategy or unexploitable strategy.

To me a perfect strategy is a strategy that will win, but not nescesarily win big, no matter what the opposition do.
This is to me a mirage. The reason I think it is wrong to think there is such a strategy is the following:

If you play at a table which is generally LAG style players you can beat this by playing a TAG style game yourself. The TAG style will be winning because you get paid off due to the heavy action when you have a good hand.

If you play at a table which is generally TAG style you can beat this by playing a LAG style, getting paid off because you can steal a lot of pots.

To me this 'proves' that no single strategy can be said to be perfect.

An unexploitable strategy to me is a strategy where noone can take advantage of it by their strategy or style or by changing their strategy.

I think it is important to get the last part included, as it is needed for the strategy to be unexploitable by any players current strategy and any strategy that player may choose in the future.

To get back to the fundamental theorem on poker, everything is about taking advantage of the 'mistakes' your opponent does because he is not able to see your cards. To me that says, that you need to be able to identify the 'mistakes' inherent in your opponents style and make sure he makes a lot of them. To me that requires adaption of strategy to opponent style of play.

[JocK]

[ QUOTE ]
It's very easy to mathematically prove such a strategy exists. Finding such a strategy is, of course, practically intractable.

[/ QUOTE ]
We have to be careful here: the Nash-equilibrium strategy is unexploitable only against players who don't collude (explicitely or implicitely).

So, placing N-1 'Nash-bots' at an N-handed table leaves the Nth player helpless, in the long run there is no way he can extract any money from the game.

One can't claim the same when placing fewer 'Nash-bots' at the table...

(And yes, constructing a 'Nash-bot' for a full poker game seems practically pretty impossible...)