Exact model
Texas Hold’em: a flush
- Probability:
- 3.03%
- Odds:
- 1 to 32
- dBan
- −15.1 dBan
Five cards of one suit become the best hand in about 3% of seven-card deals.
Calculation
p = 4,047,644 exact flush hands / C(52, 7) = 4,047,644 / 133,784,560
Assumptions
A standard 52-card deck has no jokers. Two private cards and five community cards are dealt with no cards known in advance. The best five of seven cards sets the exact category, so stronger categories are excluded. Folding, opponents, and the chance of winning are outside this model.