Inevitable mathematical solving of chess, and Limit / NL hold'em

[DarkMagus]

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I think I may be missing something here, but surely with any game where by you can see all of your opponents moves and pieces, there is an exact strategie and counter strategie to every move.

In something like Hold 'em whereby cards are hidden, then there is never an exact strategie that a computer can completely solve with the type of examples you have given for Chess and Checkers.

It can work out the likely hood of cards appearing, odds, probabilities, position etc. This just makes it a good micro limit player. If it plays the perfect strategie against even a slightly good player it will get wiped out. Why, cos we will know when it has a good hand or a bad hand.

So therefore it needs to learn how to mix up things up, adjust to peoples play etc. This is nothing like the complete mathmatical solving of Chess.

This requires artificial intelligence, which can be programed with the outcomes of millions of hands and draws its conclusion using weighted decisions. At the moment AI has been very impressive in certain tasks (Travelling Sales man), and absolutely aweful in other seemingly simple tasks for a human.

I have no doubt tho, that it will get to a level withing the near future where it can trade blows with a good player and not get white washed. But do not assume this has anything to do with it ever having solved Poker in a mathmatical sense, it is just playing really good, probabilty sound, variable poker, whilst learning everyone else's habits and tells.

It does not give it cart blanche way to win

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A perfect strategy, requiring no adjustments to opponents, can guarantee an EV >= 0 game, for heads up matches. This is of course neglecting rake.

[TheGam]

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A perfect strategy, requiring no adjustments to opponents, can guarantee an EV >= 0 game, for heads up matches. This is of course neglecting rake.

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That depends what a perfect strategie is defined as. A perfect mathmatical strategie will see you get annilated in Heads Up versus a good player. Particually in No limit. It almost tells the you what cards they are holding.

You need to need to play much more than odds to win heads up, even with no rake.

[jesse8888]

Solving the entire game tree for chess is impossible, or rather cannot be done in less time than the currently accepted age of the universe. This was explained to me in college by a pretty smart professor, and I'll try and see if I can simulate his numbers...or better yet, look it up on Wikipedia:

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

Basically, there are 10^80 or so atoms in the universe, and the game tree for chess has around 10^120 possibilities. If you converted every atom in the universe to a supercomputer, each would have to solve 10^40 combinations. If it could perform 10^15 combinations per second, you would still need 10^25 seconds to solve chess. 10^25 seconds is 3.17 * 10^17 years. The universe is only about 10,000,000,000 (10^9) years old, so we're still off by a factor of a billion or so.

[DarkMagus]

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A perfect strategy, requiring no adjustments to opponents, can guarantee an EV >= 0 game, for heads up matches. This is of course neglecting rake.

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That depends what a perfect strategie is defined as. A perfect mathmatical strategie will see you get annilated in Heads Up versus a good player. Particually in No limit. It almost tells the you what cards they are holding.

You need to need to play much more than odds to win heads up, even with no rake.

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

[Alan McIntire]

Years ago I read a relatively simple book on strategy, "The Compleat Strategyst", by John Davis Williams. I was disappointed to find that in most 2*2 games, and in a lot of other relatively simple games, your "best" strategy not only guarantees a minimum expected win rate, but this result is also guaranteed that same result to your opponent regardless of how poorly he played. In contrast, games like chess allow plenty of sub-optimum strategies for your opponent to pick and go wrong.

I don't know if there is a perfect strategy for a multiple player game. Such a strategy assumes that your opponents don't make bad plays, but several could act together, in effect colluding in their stupidity, to make a good play bad. Dan Harrington gave such an example in one of his books, where the top 4 finishers win an equal prize. 4 are tied at $4000 and 2 are tied at $1000.00.

A perfect mixed strategy for heads up Hold'Em poker must exist. I wonder if it would do better than break even against an expert, or your perfect strategy would make the game a coin flip. Are there any plays you should NEVER make which are sometimes employed by experts? This would be the only way you could have a positive expectancy.- A. McIntire

[EmmaDillema]

chess wont be solved neither will nl