Probability of getting different card hands.
- From: mike4ty4@xxxxxxxxx
- Date: 13 Oct 2005 16:38:21 -0700
Hi.
Suppose you have a deck of 52 playing cards, and you are going to play
an 8-card (yep, 8 cards!) extended (because we have more than five
cards) poker game. In this type of game, there would be the following
hands:
Royal flush: AKQJ10987 all of the same suit
Straight flush: In numeric order (either A2345678910JQK or
2345678910JQKA), all of the same suit, but not a royal flush
Flush: All of the same suit, but not straight or royal
Straight: Numeric order but not all the same suit
Dual quads: Two quads, like AAAAKKKK
Quads/four of a kind: Four cards of the same number: 22223KJ9
Quads and three of a kind: Ex. 4444KKKA
Quads and a pair: Ex. 10101010AA32
Dual three of a kind and a pair: Ex. 555JJJ1010
Dual three of a kind: Ex. 999AAA3J
Three of a kind & a pair: Ex. 777225KA
Three of a kind: Three of the same number: 555AKJ107
Four pair: Four pairs, ie. 88AA2266
Three pair: Three pairs, ie. KKJJ10106Q
Two pair: Two pairs, ie. JJ9952KA
One pair: Two cards of the same number, ie. AA32910KJ
No pair: No pairs and no other patterns at all, ie. 6JQ8K10A2
What is the probability of each of these, if the game is played w/a
single deck? I figured that for a royal flush you ahve a probability of
1 in 188,134,537.5, for a straight flush it's 1 in 31,355,756.25, and
for dual quads, 1 in 4,823,962.5. Are these right? What abou thte other
hands? What are the probabilities of those? The probabilities are
needed to figure out which hands are worth more. Like, for example,
dues dual three of a kind & a pair beat four pair, or the other way
around? Does four of a kind beat three pair? Thanks for any help.
.
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