Texas Holdem Flush Statistics

A flush is any 5 cards of the same suit. Below shows the probabilities of obtaining a flush for both suited and non-suited hole cards. The calculations include straight flushes and excludes flushes of different suits than your hole cards.

You can see that suited hole cards have almost a 3.5x better chance of getting a flush than non-suited hole cards. (C(n,r) choose function)

Suited hole cards:
(C(11,3)*C(39,2) + C(11,4)*39 + C(11,5)) / C(50,5) = 6.399%

Off-suit hole cards:
2*[C(12,4)*38 + C(12,5)] / C(50,5) = 1.85%

Probabilities for completing a flush draw with suited hole cards after flop
Complete on Turn or RiverComplete on TurnComplete on River
Need 1 card34.967%19.15%19.165%
Need 2 cardsn/an/a3.33%