Poker probability (Texas hold 'em)

In poker, the probability of many events can be determined by direct calculation. This article discusses computing probabilities for many commonly occurring events in the game of Texas hold 'em and provides some probabilities and odds 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. The first approach is to determine the number of outcomes that satisfy the condition being evaluated and divide this by the total number of possible outcomes. For example, there are six outcomes (ignoring order) for being dealt a pair of aces in Hold 'em: A♠ A♥, A♠ A♦, A♠ A♣, A♥ A♦, A♥ A♣ and A♦ A♣. There are 52 ways to pick the first card and 51 ways to pick the second card and two ways to order the two cards yielding ${\displaystyle {\tfrac {52\times 51}{2}}=1326}$ possible outcomes when being dealt two cards (also ignoring order). This gives a probability of being dealt two aces of ${\displaystyle {\begin{matrix}{\frac {6}{1326}}={\frac {1}{221}}\end{matrix}}}$.

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