Probability and 7-card Poker — How do these extraordinary Poker hands compare?
Posted by admin in Poker on 02 22nd, 2010 | one response
What is the probability of these 7-card Poker hands occuring using a 52-card deck without wild cards?
1. Four-of-a-kind and three-of-a-kind
2. Three-of-a-kind & two pair
Six-card combinations
3. Four-of-a-kind, one pair
4. Two threes-of-a-kind
5. Three pair
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1. (3/51 * 2/50 * 1/49) * (3/47 * 2/46) * 7!
2. (3/51 * 2/50) * (3/48) * (3/46) * 45/47 * 7!
3. (3/51 * 2/50 * 1/49) * (3/47) * 44/46 * 7!
4. (3/51 * 2/50) * (3/48 * 2/47) * 45/46 * 7!
5. (3/51) * (48/50 * 3/49) * (44/48 * 3/47) * 40/46 * 7!
Note: As I read it, #2-#4 exclude the possibility of #1. If you think #1 is a special case of the others, then add the value of #1 to the other three. Likewise, as I read it, #5 excludes #2.