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#11
12-24-2006, 02:15 AM
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Re: Imagine two perfect players playing heads up.
[ QUOTE ]
[ QUOTE ] It would come down to a situation where the sb pushes a hand like a small pp, and the bb calls with suited overcards. [/ QUOTE ] Forgot about that - that's a good point. I guess JTs vs. 88 or so could even do this even on the very first hand. 88 would be correct to push here, knowing JTs would have to call. [/ QUOTE ] The people don't know each other's cards. The optimal strategy would be a very complex mixed strategy. And there would be flops. 
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#12
12-24-2006, 12:08 PM
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Re: Imagine two perfect players playing heads up.
[ QUOTE ]
[ QUOTE ] [ QUOTE ] It would come down to a situation where the sb pushes a hand like a small pp, and the bb calls with suited overcards. [/ QUOTE ] Forgot about that - that's a good point. I guess JTs vs. 88 or so could even do this even on the very first hand. 88 would be correct to push here, knowing JTs would have to call. [/ QUOTE ] The people don't know each other's cards. The optimal strategy would be a very complex mixed strategy. And there would be flops. [/ QUOTE ] If they were both playing a perfect system which are identical they would never deviate from this system because that would make there play imperfect- in poker we at times knowingly dont play (what we feel is) optimal ABC poker because the villain may have some leaks- if they were leakproof then its correct not to adjust your play if you are identically optimal Is it not possible though that they may be playing 2 different systems which are both optimal vs the other players system; Working in a game theory sense For example player A could raise more often preflop because player B's optimal system is tighter than his own giving complete =EV and equal standard dev. over the long term Sorry about the rambling nature of this post, hope my point is put across though
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#13
12-24-2006, 05:56 PM
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Re: Imagine two perfect players playing heads up.
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.
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#14
12-24-2006, 08:48 PM
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Re: Imagine two perfect players playing heads up.
[ 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.
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#15
12-25-2006, 01:28 AM
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Re: Imagine two perfect players playing heads up.
[ QUOTE ]
[ QUOTE ] [ QUOTE ] [ QUOTE ] It would come down to a situation where the sb pushes a hand like a small pp, and the bb calls with suited overcards. [/ QUOTE ] Forgot about that - that's a good point. I guess JTs vs. 88 or so could even do this even on the very first hand. 88 would be correct to push here, knowing JTs would have to call. [/ QUOTE ] The people don't know each other's cards. The optimal strategy would be a very complex mixed strategy. And there would be flops. [/ QUOTE ] If they were both playing a perfect system which are identical they would never deviate from this system because that would make there play imperfect- in poker we at times knowingly dont play (what we feel is) optimal ABC poker because the villain may have some leaks- if they were leakproof then its correct not to adjust your play if you are identically optimal Is it not possible though that they may be playing 2 different systems which are both optimal vs the other players system; Working in a game theory sense For example player A could raise more often preflop because player B's optimal system is tighter than his own giving complete =EV and equal standard dev. over the long term Sorry about the rambling nature of this post, hope my point is put across though [/ QUOTE ] The thing is, this optimal strategy would be a mixed one, i.e. a player folds, calls, raises (and different amounts) with cards XX at varying %s.
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#17
12-27-2006, 05:34 PM
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Re: Imagine two perfect players playing heads up.
[ QUOTE ]
Finally, is it plausible that a perfect chess like strategy could exist for poker? [/ QUOTE ] John Nash proved that for any multi-player game there exists at least one equilibrium such that no player may improve his/her return by deviating from his/her equilibrium strategy. In a two-player game this could be considered the "perfect" strategy.
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#19
12-27-2006, 09:17 PM
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Re: Imagine two perfect players playing heads up.
[ QUOTE ]
[ QUOTE ] Finally, is it plausible that a perfect chess like strategy could exist for poker? [/ QUOTE ] John Nash proved that for any multi-player game there exists at least one equilibrium such that no player may improve his/her return by deviating from his/her equilibrium strategy. In a two-player game this could be considered the "perfect" strategy. [/ QUOTE ] I really think the NE has been found for a 2 player HU game. It's workable in a Short stack situation, such as a tournament. But the game would last too long in a deep stack game where the blinds never change.
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#20
12-27-2006, 09:34 PM
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Re: Imagine two perfect players playing heads up.
[ QUOTE ]
[ QUOTE ] [ QUOTE ] Finally, is it plausible that a perfect chess like strategy could exist for poker? [/ QUOTE ] John Nash proved that for any multi-player game there exists at least one equilibrium such that no player may improve his/her return by deviating from his/her equilibrium strategy. In a two-player game this could be considered the "perfect" strategy. [/ QUOTE ] I really think the NE has been found for a 2 player HU game. It's workable in a Short stack situation, such as a tournament. But the game would last too long in a deep stack game where the blinds never change. [/ QUOTE ] What evidence/references do you have for this claim?
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