Poker hand odds calculator.

Answer

In a 5-card deal, a flush (excluding straight flushes) is 5,108 of 2,598,960 hands, 0.197%, about 1 in 509. Using the best five of seven cards, a flush is 3.025% and a royal flush is 0.0032% (1 in 30,940).

Worked example

A full house in a 5-card deal: pick the rank of the three-of-a-kind (13), choose 3 of its 4 suits (4), pick the rank of the pair (12), choose 2 of its 4 suits (6): 13 x 4 x 12 x 6 = 3,744 hands. Out of 2,598,960 total, that is 0.1441%, or 1 in 694. Over 100 deals the chance of at least one is 1 - (1 - 0.00144)^100 = 13.43%.

How it works

Method. A hand is ranked by the best category it satisfies, so each category excludes the stronger ones: the flush row excludes straight flushes and royal flushes, the straight row excludes straight flushes, and so on. The 5-card counts come from combination formulas for each category and sum to C(52, 5) = 2,598,960.

Seven cards. For the best five of seven cards, the counts total C(52, 7) = 133,784,560 possible seven-card hands and match the published figures in the Poker probability article. In Texas hold'em each player has two hole cards and the best five-card hand from those and the five community cards wins; this table is the chance to hold each hand once all seven cards are known, before any betting.

In N hands. The chance of a hand at least once in N independent deals is 1 - (1 - p)^N. The royal flush row is counted separately from straight flushes; "At least" in the last column adds that row and every stronger one.

Sources and basis (opened 2026-10-08): Poker probability (Wikipedia) for the 5-card and 7-card frequency tables and the C(52,5) and C(52,7) totals; Texas hold 'em (Wikipedia) for the seven-card setup.

FAQ

What are the odds of being dealt a royal flush?

In a 5-card deal 4 of 2,598,960 hands are royal flushes, 0.000154%. The odds against are 649,739 to 1.

What are the odds of a flush in Texas hold'em?

Using the best five of seven cards, a flush (not a straight flush) occurs in 3.03% of hands, about 1 in 33.

Why are the 7-card odds different from the 5-card odds?

With seven cards you choose the best five, so strong hands are much more likely. A pair or better is far more common and high card is much rarer.

Are these the odds of making a hand from a particular starting hand?

No. These are the chances before any cards are known. Once you hold specific cards, use the outs calculator for the chance of improving.

How is "chance in N hands" calculated?

As 1 - (1 - p)^N, treating each deal as independent from a freshly shuffled deck.