Hand Distinct hands Frequency Probability Cumulative probability Odds Mathematical expression of absolute frequency Royal flush 0.000154 % 0.000154 % 649,739: 1 (4 1) (\ displaystyle (4 \ choose 1)) Straight flush (excluding royal flush) 9 36 0.00139 % 0.0015 % 72,192: 1 (10 1) (4 1) − (4 1) (\ displaystyle (10 \ choose 1) (4 \ choose 1) - (4 \ choose 1)) Four of a kind 156 624 0.0240 % 0.0256 % 4,164: 1 (13 1) (12 1) (4 1) (\ displaystyle (13 \ choose 1) (12 \ choose 1) (4 \ choose 1)) Full house 156 3,744 0.1441 % 0.17 % 693: 1 (13 1) (4 3) (12 1) (4 2) (\ displaystyle (13 \ choose 1) (4 \ choose 3) (12 \ choose 1) (4 \ choose 2)) Flush (excluding royal flush and straight flush) 1,277 5,108 0.1965 % 0.367 % 508: 1 (13 5) (4 1) − (10 1) (4 1) (\ displaystyle (13 \ choose 5) (4 \ choose 1) - (10 \ choose 1) (4 \ choose 1)) Straight (excluding royal flush and straight flush) 10 10,200 0.3925 % 0.76 % 254: 1 (10 1) (4 1) 5 − (10 1) (4 1) (\ displaystyle (10 \ choose 1) (4 \ choose 1) ^ (5) - (10 \ choose 1) (4 \ choose 1)) Three of a kind 858 54,912 2.1128 % 2.87 % 46.3: 1 (13 1) (4 3) (12 2) (4 1) 2 (\ displaystyle (13 \ choose 1) (4 \ choose 3) (12 \ choose 2) (4 \ choose 1) ^ (2)) Two pair 858 123,552 4.7539 % 7.62 % 20.0: 1 (13 2) (4 2) 2 (11 1) (4 1) (\ displaystyle (13 \ choose 2) (4 \ choose 2) ^ (2) (11 \ choose 1) (4 \ choose 1)) One pair 2,860 1,098,240 42.2569 % 49.9 % 1.37: 1 (13 1) (4 2) (12 3) (4 1) 3 (\ displaystyle (13 \ choose 1) (4 \ choose 2) (12 \ choose 3) (4 \ choose 1) ^ (3)) No pair / High card 1,277 1,302,540 50.1177 % 100 % 0.995: 1 ((13 5) − 10) ((4 1) 5 − 4) (\ displaystyle \ left ((13 \ choose 5) - 10 \ right) \ left ((4 \ choose 1) ^ (5) - 4 \ right)) Total 7,462 2,598,960 100 % -- - 0: 1 (52 5) (\ displaystyle (52 \ choose 5))
what are the odds of getting a royal flush in poker
649,739: 1