Exact model
Texas Hold’em: high card
- Probability:
- 17.4%
- Odds:
- 1 to 4.7
- dBan
- −6.8 dBan
Sometimes all seven cards miss each other: no pair, straight, flush, or stronger hand. High card is the best result in about one deal in six.
Calculation
p = 23,294,460 exact high-card hands / C(52, 7) = 23,294,460 / 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.