An Examination of Game Theory and Poker
Paterson, Beth P.
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Most card players know that· the object of a good poker game is to amass the maximum amount of winnings you can, or, if you look at the game a little more pessimistically, to make sure you can still go home with your shirt on, i.e., to get.by with a minimal amount of losses, But what can the poker player do to achieve these goals, other than sit there and hope for good cards, deal from the bottom of the deck, or mark the cards, none of which is strongly recommended if he wants to be invited to play with the same people again? The method most used, other than cheating or patiently waiting for the cards to fall your way, is inverted signalling, or bluffing. This involves first of all keeping a straight face as the cards are dealt to you. A larger than normal opening bet accompanied by a big smile from you will generally not lead you to fame and fortune as a poker player. Once the art of facial self-control has been mastered, you can go. on to consider the art· of bluffing. What this involves is giving a misleading idea to your opponents of what your hand is like. Since after the cards are dealt the only information that each player has is what his hand is, and the size of his opponent's bets which he assumes somehow reflect the size of their hands, your job is to somehow mislead them about your part of the information - that the size of your bet necessarily reflects the size of your hand. This, then, is what bluffing is all about. By sometimes bidding high when you hold a weak hand, and sometimes bidding low or dropping out when a strong hand is yours, your opponents will not always be able to outguess you by the size of your bet. Since dropping out of the betting and being the only player still willing to continue betting on a particular hand mean that you do not have to show your cards to the other players, bluffing adds quite a bit of mystery as to what kinds of cards you actually hold. The only real problem, then, is to decide when and how often to bluff. Some hands at either end of the scale are impossible to bluff with - either too high to bet low on or too weak to even open - but between these two extremes how does one know what to do? What I hope to accomplish in what· follows is to find some sort of formula to follow in bluffing. Hopefully I will be able to result in finding some formula which not only maximizes the amount of winnings possible to the one who uses it but is also such that it can be used continuously and still be an efficient mechanism for bluffing - i.e. a. player can use this formula continuously and still have the other players in the dark as to what his hand is, when he is bluffing and when he is not. What I am really asking then is whether a mathematical description of how to bluff is possible.