A flush is a hand that contains five cards all of the same suit, not all of the sequential rank, such as Q♣ 9♣ 7♣ 2♣ 3♣ (a king-high flush). It ranks below a **full house** and above a straight. Under ace-to-five low rules, flushes are not possible (so K♥ 8♥ 4♥ 3♥ 2♥ is a King-high hand).

Each flush is ranked first by the rank of its highest-ranking card, then by the rank of its second highest-ranking card, then by the rank of its third highest-ranking card, then by the rank of its fourth highest-ranking card, and finally by the rank of its lowest-ranking card.

Example: K♦ J♦ 9♦ 6♦ 4♦ ranks higher than Q♣ J♣ 7♣ 6♣ 5♣, which ranks higher than J♥ 10♥ 9♥ 4♥ 2♥, which ranks higher than J♠ 10♠ 8♠ 6♠ 3♠, which ranks higher than J♥ 10♥ 8♥ 4♥ 3♥, which ranks higher than J♣ 10♣ 8♣ 4♣ 2♣. Flush hands never differ by suit alone. Here 10♦ 8♦ 7♦ 6♦ 5♦ and 10♠ 8♠ 7♠ 6♠ 5♠, are considered as an equal rank.

A flush beats a straight. A flush is any five cards all of the same suit (i.e., all diamonds or all spades, etc.). If two or more players share a flush then the player with the highest card (all the way to the fifth card if necessary) in the flush wins.

A flush consists of five cards which are all of the same suit. We must remember that there are 4 suits each with a total of 13 cards. Thus a flush is a combination of five cards from a total of 13 of the same suit. This is done in C(13, 5) = 1287 ways. Since there are four different suits, there are a total of 4 x 1287 = 5148 flushes possible.

Some of these flushes have already been counted as higher ranked hands. We must subtract the number of **straight flushes** and **Royal Flushes** from 5148 in order to obtain flushes that are not of a higher rank. There are 36 straight flushes and 4 royal flushes. We must make sure not to double count these hands. This means that there are 5148 – 40 = 5108 flushes that are not of a higher rank.

We can now calculate the probability of a flush as 5108/2,598,960 = 0.1965%. This probability is approximately 1/509. So in the long run, one out of every 509 hands is a flush.

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