Exact model
Texas Hold’em: exactly one pair
- Probability:
- 43.8%
- Odds:
- 1 to 1.3
- dBan
- −1.1 dBan
A lone pair is the most familiar sight in Hold’em: it is the best five-card hand in about 44% of seven-card deals.
Calculation
p = 58,627,800 exact one-pair hands / C(52, 7) = 58,627,800 / 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.