Probabilities of five-card poker hands

Probabilities of five-card poker hands

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PROBABILITIES OF FIVE-CARD POKER HANDS

Hand	Number	Approx Odds (to 1)
Royal Flush Straight flush Four of a kind Full House Flush Straight Three of a kind Two pairs one pair No hand	4 36 624 3,744 5,108 10,200 54,912 123,552 1,098,240 1,302,540	649,740 72,192 4,164 693 508 254 46 20 1.37 1

ODDS AGAINST IMPROVING A HAND

Cards Held	Drawn	Improved hand	Odds against (to 1)
One Pair	3	Two pair Three of a kind Full House Four of a kind Any improvement	5.3 7.8 97 360 2.5
One Pair plus kicker	2	Two Pairs Three of a kind Full house Four of a kind Any improvement	4.8 12 120 1080 2.8
Three of a kind	2	Full house Four of a kind Any improvement	15.3 22.5 8.7
Four straight cards (open both ways)	1	Straight	5
Inside straight	1	Straight	10.8
Four card flush	1	Flush	4.2
Four card flush (open ended)	1	Straight Flush Straight or better	22.5 2
Four card straight flush (inside)	1	Straight Flush Straight or better	46 3

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