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What are the chances you got that hand!?!
This section on poker odds borrows a chart from the rec.gambling.poker
FAQ. The information is simply mathematical, and shows why we rank poker
hands in the way that we do. The hands are ranked according to the odds
of that hand being built when 5 cards are pulled from a 52-card deck.
Poker hand ranks are based on the odds of that hand coming up, relative
to the other hands.
Hand 3 cards 5 cards 7 cards
==== ======= ======= =======
Straight Flush 48 40 41,584
Four of a Kind 0 624 224,848
Full House 0 3,744 3,473,184
Flush 1,096 5,108 4,047,644
Straight 720 10,200 6,180,020
Three of a Kind 52 54,912 6,461,620
Two Pair 0 123,552 31,433,400
One Pair 3,744 1,098,240 58,627,800
High Card 16,440 1,302,540 23,294,460
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TOTALS 22,100 2,598,960 133,784,560
Notes:
1. The standard rankings are incorrect for 3-card hands, since
it is easier to get a flush than a straight, and easier to get a straight
than three of a kind.
2. For 7-card hands, the numbers reflect the best possible 5-card
hand out of the 7 cards. For instance, a hand that contains both a straight
and three of a kind is counted as a straight.
3. For 7-card hands, only five cards need be in sequence to make
a straight, or of the same suit to make a flush. In a 3-card hand a sequence
of three is considered a straight, and three of the same suit a flush.
These rules reflect standard poker practice.
4. In a 7-card hand, it is easier for one's *best* 5 cards to have
one or two pair than no pair. (Good bar bet opportunity!) However, if
we changed the ranking to value no pairs above two pairs, all of the one
pair hands and most of the two pair hands would be able to qualify for
"no pair" by choosing a different set of five cards.
5. Within each type of hand (e.g., among all flushes) the hands
are ranked according to an arbitrary scheme, unrelated to probability.
Poker odds are fairly straightforward. Much like craps or blackjack, the
possibilities are finite, and to some degree predictable. Poker odds change
as cards are dealt from the deck. One of the most important aspects of
developing a sense for evolving poker odds over the course of a hand is
to study as much up-card information as possible in relation to your own
hand.
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