decision that has the largest expected value. (Although sometimes it is correct not to choose this decision for the larger goal of long-term deception.) If you could see all your opponents' cards, you would always be able to calculate the correct decision with mathematical certainty. (This is certainly true heads-up, but is not always true in multi-way pots.) The less you deviate from these correct decisions, the better your long-term results. This is the mathematical expression of the fundamental theorem.
The fundamental theorem of poker applies to all heads-up decisions, but it does not apply to all multi-way decisions. This is because each opponent of a player can make an incorrect decision, but the "collective decision" of all the opponents works against the player. This type of situation occurs mostly in loose-passive games, when a player has a strong hand, but several opponents are chasing with draws. Sometimes such a situation is referred to as implicit collusion. Experts disagree on the prevalence of implicit collusion in particular games, as well as the extent to which implicit collusion might be unethical.
The fundamental theorem of poker is simply expressed and appears axiomatic, yet its proper application to the countless variety of possible circumstances that a poker player may face requires a great deal of knowledge, skill, and experience.
HAND
The word hand in the game of poker is used to mean any of the following:
• The set of cards held by an individual player during play. Joe took another look at his hand when Virginia raised. The term holding can be used for less ambiguity. In Texas hold 'em, these are more commonly known as hole cards or pocket cards.
• The value of a player's hand (1), as determined by the rules of the game being played. Karen's hand was a flush, but lost to Steve's full house. The term hand value can be used for less ambiguity.
• A single instance of poker game play, also called a deal. We played eight hands of draw poker, then eight hands of stud poker.
There are many poker variants, but unless otherwise specified in the rules of the variant being played, hands are evaluated using the traditional set of five-card hands. These are, from worst to best:
No pair (for example, A-Q-10-5-2)
A no pair hand is a poker hand such as K♥ J♣ 8♣ 7♦ 3♠, in which no two cards have the same rank, the five cards are not in sequence, and the five cards are not all the same suit. It is sometimes simply referred to as "high card", as its highest value card determines its rank compared with other no pair hands. It is also known as "nothing" or "garbage", and many other derogatory terms. It ranks below all other poker hands.
Two such hands are ranked by comparing the highest ranking card; if those are equal, then the next highest ranking card; if those are equal, then the third highest ranking card, etc.
No-pair hands are often described by the one or two highest cards in the hand, such as "king high" or "ace-queen high", or by as many cards as are necessary to break a tie.
Examples:
A♦ 10♦ 9♠ 5♣ 4♣ ("ace high") defeats K♣ Q♦ J♣ 8♥ 7♥ ("king high")
A♣ Q♣ 7♦ 5♥ 2♣ ("ace-queen") defeats A♦ 10♦ 9♠ 5♣ 4♣ ("ace-ten")
7♠ 6♣ 5♣ 4♦ 2♥ ("seven-six-five-four") defeats 7♣ 6♦ 5♦ 3♥ 2♣ ("seven-six-five-three")
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