Imagine two perfect players playing heads up.

[tsearcher]

Eastbay has charts for it in his SNG Power Tools. And it is also explained in "The Mathematics of Poker" by Bill Chen and Jerrod Ankenman. It's entirely possible I'm misunderstanding all this.

[JaredL]

I think it has been solved for the all-in or fold situation.

To extend this to the general case takes another big step. You would have to describe what the other player will do if you made a raise that wasn't all-in with every possible hand, for every possible raise amount (also limping/completing). This response function would have to make it so that you never would want to limp/complete or make a raise that's not all-in. So you would have to show that the all-in or folding strategy is better than every strategy that involves limping or raising short against whatever strategy the opponent would use against your all-in raises as well as when you bet less than your stack. This would all be extremely difficult and probably not worth doing, especially if you have an equilibrium assuming plyaers may only go all in or fold.

BTW I haven't yet read Chen and Ankerman but will as soon as I manage to secure it, so I'm not sure what they do.

[tsearcher]

Their solution is also just an all in or fold one.

[Jerrod Ankenman]

[ QUOTE ]
Their solution is also just an all in or fold one.

[/ QUOTE ]

If we solved HU NL, we sure as hell wouldn't publish it in a book. [img]/images/graemlins/smile.gif[/img]

jerrod

[thylacine]

[ QUOTE ]
[ QUOTE ]
Their solution is also just an all in or fold one.

[/ QUOTE ]

If we solved HU NL, we sure as hell wouldn't publish it in a book. [img]/images/graemlins/smile.gif[/img]

jerrod

[/ QUOTE ]

If you did, how much would the book weigh? Ballpark figure is fine, within a few orders of magnitude or so.....

[Jerrod Ankenman]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Their solution is also just an all in or fold one.

[/ QUOTE ]

If we solved HU NL, we sure as hell wouldn't publish it in a book. [img]/images/graemlins/smile.gif[/img]

jerrod

[/ QUOTE ]

If you did, how much would the book weigh? Ballpark figure is fine, within a few orders of magnitude or so.....

[/ QUOTE ]

Um. A lot. :P

jerrod

[thylacine]

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Their solution is also just an all in or fold one.

[/ QUOTE ]

If we solved HU NL, we sure as hell wouldn't publish it in a book. [img]/images/graemlins/smile.gif[/img]

jerrod

[/ QUOTE ]

If you did, how much would the book weigh? Ballpark figure is fine, within a few orders of magnitude or so.....

[/ QUOTE ]

Um. A lot. :P

jerrod

[/ QUOTE ]

Aw, C'mon, you guys quantify everything! Gimme some concrete numbers, lol! [img]/images/graemlins/grin.gif[/img]

[AKQJ10]

[ QUOTE ]
[ QUOTE ]
In NL this game would never see the flop until there was a preflop coinflip.

[/ QUOTE ]

This makes no sesnse whatsoever. These are hypothetically "perfect" players, but they still can't see each other's cards. There would be plenty of calls due to pot odds and for other reasons both preflop and beyond.

[/ QUOTE ]

I haven't read from here on down, but it seems the confusion is between "perfect" decisions in the FToP sense and in the game theory sense. Of course perfect decisions in the FToP make the OP thoroughly uninteresting, and it's correct that the only action would be on hands where the favorite's edge is less than the blind money in the pot.

[JocK]

[ QUOTE ]
is it plausible that a perfect chess like strategy could exist for poker?

[/ QUOTE ]
It is not plausible, it is certain. John Nash got a Nobel Prize for proving this (not just for poker, but for any finite multi-player game).

Unfortunately (?), John Nash's proof of existence is not constructive, and for all practical purposes it is equally certain that no human being will ever unlock the perfect strategy for multi-player poker.

[ QUOTE ]
Interesting ideas here in this thread, but you guys are simlifying things too much. And ABC mathematical poker is far from an optimal strategy heads up. I think you have forgotten about hand reading skills, traps, bluffs, etc.

[/ QUOTE ]
The mathematically optimum strategy (Nash equilibrium) for poker will certainly be a mixed strategy (i.e. contain stochastic elements) and thereby addresses issues like (preventing) hand reading, bluffs, traps etc.

[Dire]

Nash equilibrium explicitly requires finite possible strategies. This invalidates its application to just about anything. I'll start sweating when roshambo is 'solved'. [img]/images/graemlins/wink.gif[/img]