Exact model
Texas Hold’em: four of a kind
- Probability:
- 0.168%
- Odds:
- 1 to 594
- dBan
- −27.7 dBan
All four cards of one rank come together in about one seven-card deal out of 595.
Calculation
p = 224,848 exact four-of-a-kind hands / C(52, 7) = 224,848 / 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.