Editing Hypergeometric distribution (section)

=== Application to Texas hold'em poker ===
In [[hold'em]] poker players make the best hand they can combining the two cards in their hand with the 5 cards (community cards) eventually turned up on the table. The deck has 52 and there are 13 of each suit.
For this example assume a player has 2 clubs in the hand and there are 3 cards showing on the table, 2 of which are also clubs. The player would like to know the probability of one of the next 2 cards to be shown being a club to complete the [[Flush (poker)|flush]].<br />
(Note that the probability calculated in this example assumes no information is known about the cards in the other players' hands; however, experienced poker players may consider how the other players place their bets (check, call, raise, or fold) in considering the probability for each scenario. Strictly speaking, the approach to calculating success probabilities outlined here is accurate in a scenario where there is just one player at the table; in a multiplayer game this probability might be adjusted somewhat based on the betting play of the opponents.)

There are 4 clubs showing so there are 9 clubs still unseen. There are 5 cards showing (2 in the hand and 3 on the table) so there are <math>52-5=47</math> still unseen.

The probability that one of the next two cards turned is a club can be calculated using hypergeometric with <math>k=1, n=2, K=9</math> and <math>N=47</math>. (about 31.64%)

The probability that both of the next two cards turned are clubs can be calculated using hypergeometric with <math>k=2, n=2, K=9</math> and <math>N=47</math>. (about 3.33%)

The probability that neither of the next two cards turned are clubs can be calculated using hypergeometric with <math>k=0, n=2, K=9</math> and <math>N=47</math>. (about 65.03%)