Exact model
Texas Hold’em: a full house
- Probability:
- 2.6%
- Odds:
- 1 to 38
- dBan
- −15.7 dBan
A trio joined by a pair makes the best five-card hand a full house in about one seven-card deal out of 39.
Calculation
p = 3,473,184 exact full-house hands / C(52, 7) = 3,473,184 / 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.