No 1 in Gambling

When facing two opponents, for any given starting hand the number of possible combinations of hands the opponents can have is

(50/2)(48/2) = 1,381,800

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When comparing two starting hands, the head-to-head probability describes the likelihood of one hand beating the other after all of the cards have come out. Head-to-head probabilities vary slightly for each particular distinct starting hand matchup, but the approximate average probabilities, as given by Dan Harrington in Harrington on Hold'em [p.125], are summarized in the following table.

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For any given starting hand, there are 50 × 49 ÷ 2 = 1,225 hands that an opponent can have before the flop. (After the flop, the number of possible hands an opponent can have is reduced by the three community cards revealed on the flop to 47 × 46 ÷ 2 = 1,081 hands.) Therefore, there are

(52/2)(50/2) / 2 = 812,175

possible head-to-head match ups in Hold 'em. (The number of total number of match ups is divided by the two ways that two hands can be distributed between two players to give the number of unique match ups.) However, since there are only 169 distinct starting hands, there are 169 × 1,225 = 207,025 distinct head-to-head match ups.^[1]

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The probability of being dealt various starting hands can be explicitly calculated. In Texas Hold 'em, a player is dealt two down (or hole) cards. The first card can be any one of 52 playing cards in the deck and the second card can be any one of the 51 remaining cards. This gives 52 × 51 ÷ 2 = 1,326 possible starting hand combinations. (Since the order of the cards is not significant, the 2,652 combinations are divided by the 2 ways of ordering two cards.) Alternately, the number of possible starting hands is represented as the binomial coefficient

(52/2) = 1,326

which is the number of possible combinations of choosing 2 cards from a deck of 52 playing cards.

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In poker, the probability of many events can be determined by direct calculation. This article discusses how to compute the probabilities for many commonly occurring events in the game of Texas hold 'em and provides some probabilities and odds^[1] for specific situations. In most cases, the probabilities and odds are approximations due to rounding.

When calculating probabilities for a card game such as Texas Hold 'em, there are two basic approaches.

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In 1998, the movie Rounders starring Matt Damon and Edward Norton gave moviegoers a romantic view of poker as a way of life. Texas hold 'em was the main game played during the movie and the no-limit variety was described, following Doyle Brunson, as the "Cadillac of Poker". There was also a clip of the classic showdown between Johnny Chan and Erik Seidel from the 1988 World Series of Poker incorporated into the film.

CommanderBond.net reports that the centerpiece card game in the next James Bond film, Casino Royale, will be no-limit Texas hold 'em instead of Baccarat as in the original Ian Fleming novel.^[1]

Spectator sport

Joe Hachem, winner of 2005 World Series of Poker main event

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The World Series of Poker is the most prestigious set of poker tournaments in the world.

The main event

The main event of the WSOP is the $10,000 buy-in no-limit Texas Hold 'Em tournament since 1972. (In 1971, the buy-in was $5,000.) Winners of the event not only get the largest prize of the tournament and a gold bracelet, but additionally their picture is placed into the Gallery of Champions at Binion's.

The Gallery of Champions in 1979

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Doyle Brunson is credited with bringing poker strategy to a wider audience

Most poker authors recommend a tight-aggressive approach to playing Texas hold 'em. This strategy involves playing relatively few hands (tight), but betting and raising often with those that one does play (aggressive). Although this strategy is often recommended, some professional players successfully employ other strategies as well.^[1] While most poker authors focus on playing primarily premium starting hands, some authors claim that the importance of starting hands is overstated.^2]

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There are (52 × 51)/2 = 1,326 distinct possible combinations of two hole cards from a standard 52-card deck. However, since suits are only relevant for flushes, many of these hands are indistinguishable from the point of view of pre-flop strategy. In fact, considering suits to be equivalent unless both cards are the same suit, there are precisely 169 distinct possible starting hands in hold 'em.^[3]

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In Poker, a drawing hand is a hand that is not yet "complete"; that is, one which does not yet rank highly, but which may later, depending on what cards a player receives. This contrasts with a made hand - a hand which is already somewhat strong.

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Sample showdown

Here's a sample showdown:

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The descriptions below assume a familiarity with the general game play of poker, and with poker hands.

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Each player is dealt two private cards in hold 'em. They are dealt first.

http://upload.wikimedia.org/wikipedia/commons/6/6b/Texas_Hold_%27em_Hole...

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