Exact model
Texas Hold’em: three of a kind
- Probability:
- 4.83%
- Odds:
- 1 to 20
- dBan
- −12.9 dBan
Three cards meet on one rank as the best five-card hand in about one seven-card deal out of 21.
Calculation
p = 6,461,620 exact three-of-a-kind hands / C(52, 7) = 6,461,620 / 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.