Re: odds question
- From: "Aardvark" <tom_hummel@xxxxxxxxxxx>
- Date: 16 Nov 2005 12:36:07 -0800
Some card rooms distinguish payouts for royals by the suit (i.e. a
spade royal flush pays more than a diamond royal flush). For this
reason the suit might matter. The odds of hitting a spade royal flush
on any given hand, assuming that you need to use both hole cards can be
calculated as follows:
# possible hands and boards = 52C2 * 50C5 = ((52 * 51) / 2) * ((50 * 49
* 48 * 47 * 46) / (5 * 4 * 3 * 2)) = 2,809,475,760.
# hands that make a royal of one specific suit using two hole cards =
5C2 * 3C3 * 47C2 = ((5 * 4)/2) * 1 * ((47 * 46)/2) = 10810.
Odds of making the royal in spades = (2,809,475,760 - 10,810)/10,810 =
259,895:1 against.
The 650K number is if you are given only 5 cards to work with total, so
that would be the odds of the board coming out with a royal flush.
-Tom.
.
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