Poker Odds
Apr 19th, 2005 by Dave
Hand odds drawing 5 cards from a deck (using Bayes b(n,k) notation - n represents the population, k the selection)
| Hand | Count | Formula | Notes |
|---|---|---|---|
| Royal Flush | 4 | b(4,1) | 1 per suit |
| Straight Flush | 36 | b(9,1)*b(4,1) | 9 chances per suit |
| Four of a kind | 624 | b(13,1)*b(4,1)*b(12,1) | 1 in 13 for a given suit +filler |
| Full house | 3,744 | b(13,1)*b(4,3)*b(12,1)*b(4,2) | 1 in 13 for 3 suits; 1 in 12 for 2 |
| Flush | 5,108 | b(13,5)*b(4,1)-40 | Less the straight and royal flush |
| Straight | 10,200 | b(10,1)*b(4,1)^5-40 | Ditto prev |
| 3 of a kind | 54,912 | b(13,1)*b(4,3) *b(12,2)*b(4,1)^2 |
1 in 13 for 3 of the suits; +filler |
| Two pair | 123,552 | b(13,2)*b(4,2)^2*b(11,1) *b(4,1) |
2 in 13 for 2 of the suits; +filler |
| One pair | 1,098,240 | b(13,1)*b(4,2)*b(12,3)*b(4,1)^3 | 1 in 13 for 2 of the suits |
| Nothing | 1,302,540 | (b(13,5)-10)*(4^5-4) | All the rest |
| Total | 2,598,960 | b(52,5) | Drawing 5 out of 52 |