Preliminary Calculation
These are the same hand. Order is not important.
The Poker Hands
Poker Hand | Definition | |
---|---|---|
1 | Royal Flush | A, K, Q, J, 10, all in the same suit |
2 | Straight Flush | Five consecutive cards, |
all in the same suit | ||
3 | Four of a Kind | Four cards of the same rank, |
one card of another rank | ||
4 | Full House | Three of a kind with a pair |
5 | Flush | Five cards of the same suit, |
not in consecutive order | ||
6 | Straight | Five consecutive cards, |
not of the same suit | ||
7 | Three of a Kind | Three cards of the same rank, |
2 cards of two other ranks | ||
8 | Two Pair | Two cards of the same rank, |
two cards of another rank, | ||
one card of a third rank | ||
9 | One Pair | Three cards of the same rank, |
3 cards of three other ranks | ||
10 | High Card | If no one has any of the above hands, |
the player with the highest card wins |
Counting Poker Hands
Poker Hand | Count | Probability | |
---|---|---|---|
2 | Straight Flush | 40 | 0.0000154 |
3 | Four of a Kind | 624 | 0.0002401 |
4 | Full House | 3,744 | 0.0014406 |
5 | Flush | 5,108 | 0.0019654 |
6 | Straight | 10,200 | 0.0039246 |
7 | Three of a Kind | 54,912 | 0.0211285 |
8 | Two Pair | 123,552 | 0.0475390 |
9 | One Pair | 1,098,240 | 0.4225690 |
10 | High Card | 1,302,540 | 0.5011774 |
Total | 2,598,960 | 1.0000000 |