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.

Sources

  1. Brian Alspach: seven-card poker frequencies
  2. PokerStars: Texas Hold’em rules