Runner-runner outs in Texas hold ’em
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Some outs for a hand require drawing an out on both the turn and the river—making two consecutive outs is called a runner-runner. Examples would be needing two cards to make a straight, flush, or three or four of a … Read More

Example of drawing outs
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The unseen cards principle states that to calculate the probability (from the point of view of a player about to act) that the next card dealt will be among a certain set, he must divide the number of cards in … Read More

Texas Hold’em – After the flop
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During play—that is, from the flop and onwards—drawing probabilities come down to a question of outs. All situations which have the same number of outs have the same probability of winning. For example, an inside straight draw (e.g. 34 67 … Read More

Flopping overcards when holding a pocket pair
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It is useful to look at the chances different starting hands have of either improving on the flop, or of weakening on the flop. One interesting circumstance concerns pocket pairs. When holding a pocket pair, overcards (cards of higher rank … Read More

The flop
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The value of a starting hand can change dramatically after the flop. Regardless of initial strength, any hand can flop the nuts—for example, if the flop comes with three 2s, any hand holding the fourth 2 has the nuts. Conversely, … Read More

Probability of the dominated hands in Texas Hold’em
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When evaluating a hand before the flop, it’s useful to have some idea of how likely the hand is dominated. A dominated hand is a hand that is beaten by another hand (the dominant hand) and is extremely unlikely to … Read More

Starting hands against multiple opponents in Texas Hold ’em
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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) = 1,381800 hands. For calculating probabilities we can ignore the distinction between the two opponents holding A♠ J♥ … Read More

Probability for starting hands in Texas Hold ’em
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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 … Read More

Poker probability for Texas hold ’em
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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 … Read More