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Poker, solved (Posted on 2008-03-29) Difficulty: 2 of 5

Tables are available giving the probabilities of various poker hands. Such tables can readily be adapted to give the chances that the hand you are holding will be the strongest among N random opponent hands.

Based on such a table, it is a simple matter to develop an algorithm to determine a handís chances even before the "drawing round". The algorithm could also advise on which cards to throw down and can refine the win probability calculation in consideration of the number of cards your opponent has drawn.

Suppose you are playing poker while using such an algorithm. You decide to completely ignore your opponents' bidding behaviour as you regard this information as unreliable. I.e., we can assume that your opponent is a skilled gambler who understand how to undermine the information content of his bids with carefully calibrated bluffs. Rather, you determine your bids based solely on the algorithms probability calculation: Whenever the probability indicates a positive payout for your participation, you bid to the limit, otherwise you fold.

As soon as your opponent comes to understand your approach - for instance, because he is an astute observer, or because the nature of your algorithm is publicly known - he can be expected to abandon bluffing as well. (Why would he bid on a weak hand when you canít be influenced?) Next, he will be pressed to adopt your algorithm himself, since deviations from the optimal participation decision only lead to a lower payout.

Iíve presented the case for 1-vs-1 play, but it works as well for 1-vs-N if a large enough number of players are using the same algorithm.

Consider: Have I shown that there is no point in bluffing? Is there any point in relying on inferences drawn from oneís opponentsí bidding behaviour? Is there ever any reason to bid less than the maximum? and, most fundamentally, why hasnít poker been set aside (like checkers) to the pile of solved games?

  Submitted by FrankM    
Rating: 2.5000 (2 votes)
Solution: (Hide)

The original motivation for neglecting opponents' bidding behaviour is that this information is likely to be unreliable. Indeed, a skilled player will know how to mix the optimal level of misleading signals with the bids' straightforward financial function so as to seriously compromise the value bid information for making inferrences.

The presentation suggests that the bluffing can be suppressed. If this were true, bidding behaviour would suddenly become an important indicator. I.e., a player using a modified algorithm which factored in opponent's bidding behaviour would be at a distinct advantage.

Thus that presumption that the simple algorithm can suppress bluffing is false. You and I may think there are more interesting games, but poker still has a future.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Some ThoughtsImperviousness to aggressive bluffingFrankM2008-04-01 11:54:00
re: Exchange with Dej MarDej Mar2008-04-01 05:43:13
Exchange with Dej MarFrankM2008-04-01 00:09:15
Hints/TipsAnswer to EdFrankM2008-03-31 23:47:21
re: Response to Dej MarDej Mar2008-03-31 23:20:38
No Subjected bottemiller2008-03-31 12:10:55
Hints/TipsResponse to Dej MarFrankM2008-03-31 10:35:34
No SubjectDej Mar2008-03-31 00:19:00
Hints/TipsYou're not there yet - Reply to reviewers remarksFrankM2008-03-30 20:54:51
SolutionAs for you last question ...Steve Herman2008-03-30 08:48:37
SolutionNo SubjectLeming2008-03-29 17:38:03
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