Minggu, 31 Januari 2010

Poker Probabilities

There are 311,875,200 ways (permutations) of being dealt five cards from a 52 card deck,but since the order of cards does not matter there are only possible distinct hands.

ROYAL FLUSH and STRAIGHT FLUSH
There are 40 possible straight flushes, including the four royal flushes. The probability of being dealt one in a five-card deal is

QUADS/FOUR OF KIND
There are 624 possible hands including four of a kind; the probability of being dealt one in a five-card deal is .

FULL HOUSE
There are 3,744 possible full houses; the probability of being dealt one in a five-card hand is

FLUSH
There are 5,148 possible flushes, of which 40 are also straight flushes; the probability of being dealt a flush in a five-card hand is

STRAIGHT
There are 10,240 possible straights, of which 40 are also straight flushes; the probability of being dealt a straight in a five-card deal is

THREE OF KINDS
here are 54,912 possible three of a kind hands in a five-card deal which are not also full houses; the probability of being dealt one in a five-card hand is .

TWO PAIR
There are 123,552 possible two pair hands that are not also full houses; the probability of being dealt one in a five-card deal is

ONE PAIR
There are 1,098,240 possible one pair hands; the probability of being dealt one in a five-card deal is .

HIGH CARD
Of the 2,598,960 possible hands, 1,302,540 do not contain any pairs and are neither straights nor flushes. As such, the probability of being dealt "no pair" in a five-card deal is

LIST OF PROBABILITIES FROM HIGH
1. 50% = High Card
2. 42% = One Pair
3. 4,8% = Two Pair
4. 2,1% = Three of Kinds
5. 0,39% = Straight
6. 0,20% = Flush
7. 0,14% = Full House
8. 0,024% = Quads/Four of Kinds
9. 0,0015% = Straight Flush /Royal Flush

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