Poker Probability
January 22, 2008
There are literally 2,598,960 possible combinations of 5 cards randomly drawn from a full deck of 52, without wild cards. This chart gives a breakdown of each possible poker hand being drawn.
Hand | Frequency | Probability | Odds against |
40 | .00154% | 64,973 : 1 | |
624 | .0240 % | 4,164 : 1 | |
3,744 | .144 % | 693 : 1 | |
5,108 | .197 % | 508 : 1 | |
10,200 | .392 % | 254 : 1 | |
54,912 | 2.11 % | 46.3 : 1 | |
123,552 | 4.75 % | 20.0 : 1 | |
1,098,240 | 42.3 % | 1.37 : 1 | |
2,598,960 | 50.1 % | 0.995 : 1 | |
TOTAL | 2,598,960 | 100% |
Note: The royal flush is included as a straight flush above. By itself, the royal flush can be formed 4 ways (one for each suit), giving it a probability of .000001539077169 and odds of 649,740 : 1.