Problem 62 Answer - Probabilities in Poker

Below are the probabilities of drawing the following hands, without discarding:

 
                                           Approximate            
    Hand             Exact Probability     Probability
---------------   ----------------------   ------------
Royal Flush:              4 in 2,598,960   1 in 649,740 
Straight Flush:          36 in 2,598,960   1 in 72,193 
Four of a Kind:         624 in 2,598,960   1 in 4,165
Full House:           3,744 in 2,598,960   1 in 694
Flush:                5,108 in 2,598,960   1 in 509
Straight:            10,200 in 2,598,960   1 in 255
Three of a Kind:     54,912 in 2,598,960   1 in 47
Two Pair:           123,552 in 2,598,960   1 in 21
One Pair:         1,098,240 in 2,598,960   1 in 2.4
Nothing:          1,302,540 in 2,598,960   1 in 2.0