Poker probability
Frequency of 5-card poker hands

Poker probability

Section Title: Frequency of 5-card poker hands
Table Section Text: None

Hand	Distinct hands	Frequency	Probability	Cumulative probability	Odds	Mathematical expression of absolute frequency

Royal flush 10 of spades Jack of spades Queen of spades King of spades Ace of spades	1	4	0.000154%	0.000154%	649,740 : 1

Straight flush (excluding royal flush) 4 of hearts 5 of hearts 6 of hearts 7 of hearts 8 of hearts	9	36	0.00139%	0.0015%	72,192 : 1

Four of a kind Ace of hearts Ace of diamonds Ace of clubs Ace of spades 4 of diamonds	156	624	0.0240%	0.0256%	4,165 : 1

Full house 8 of hearts 8 of diamonds 8 of clubs King of hearts King of spades	156	3,744	0.1441%	0.17%	693 : 1

Flush (excluding royal flush and straight flush) 10 of clubs 4 of clubs Queen of clubs 7 of clubs 2 of clubs	1,277	5,108	0.1965%	0.367%	508 : 1

Straight (excluding royal flush and straight flush) 7 of clubs 8 of hearts 9 of diamonds 10 of hearts Jack of spades	10	10,200	0.3925%	0.76%	254 : 1

Three of a kind Queen of hearts Queen of clubs Queen of diamonds 5 of spades Ace of diamonds	858	54,912	2.1128%	2.87%	46.3 : 1

Two pair 3 of hearts 3 of diamonds 6 of clubs 6 of hearts King of spades	858	123,552	4.7539%	7.62%	21.0 : 1

One pair 5 of hearts 5 of spades 2 of clubs Jack of clubs Ace of diamonds	2,860	1,098,240	42.2569%	49.9%	1.37 : 1

No pair / High card 2 of diamonds 5 of spades 6 of spades Jack of hearts Ace of clubs	1,277	1,302,540	50.1177%	100%	0.995 : 1

Total	7,462	2,598,960	100%	--	0 : 1

Sentence(s)

There are 4 different ways to draw a royal flush (one for each suit), so the probability is one in 649,740.

final_sentence: There are 4 different ways to draw a royal flush (one for each suit), so the probability is one in 649,740.