Exact model
Texas Hold’em: a royal flush
- Probability:
- 3.23 × 10⁻³%
- Odds:
- 1 to 30,900
- dBan
- −44.9 dBan
Ten through ace arrive in one suit in roughly one seven-card deal out of 31,000.
Calculation
p = 4,324 royal-flush seven-card hands / C(52, 7) = 4,324 / 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.