Poker Probabilities
(Five Card Poker Hands)



Name of Poker Hand Number of Ways
to form this hand
Prob. of Hand Prob. of Hand
(Decimal)
Royal Flush
(Ace, King, Queen, Jack, and Ten of the same suit)
4 4 / 2,598,960 0.00000153
Straight Flush
(five cards in sequence and of the same suit)
40 40 / 2,598,960 0.0000153
Four of a Kind
(four cards of one face value and one additional card)
624 624 / 2,598,960 0.0002401
Full House
(three cards of one face value and two cards of another)
3,744 3,744 / 2,598,960 0.0014406
Flush
(five cards of the same suit but not in sequence)
5,108 5,108 / 2,598,960 0.0019654
Straight
(five cards in sequence, but not all of the same suit)
10,200 10,200 / 2,598,960 0.0039246
Three of a Kind
(exactly three cards of one face value and two different cards)
54,912 54,912 / 2,598,960 0.0211285
Two Pairs
(one pair of each of two different face values and one other card)
123,552 123,552 / 2,598,960 0.0475390
One Pair
(two cards of one face value and three cards of different face values)
1,098,240 1,098,240 / 2,598,960 0.4225690
No Pair
(five different face values, not in sequence, not the same suit)
1,302,540 1,302,540 / 2,598,960 0.5011774



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