Re: What are the odds of a royal flush in Hold\'em?
With your two cards and the 5 board cards consider C(52,7)=133784560 combinations of poker hands. Of those, C(4,1)*C(47,2)=4324 are royal flushes. [the first term is for 4 suits and the second term is for the combination of the other 2 cards from the remaining 47 cards in the deck after you assume 5 of the 7 cards make the royal flush]. So dividing the two numbers gives a 1 in 30490 chance. If your interested in only royals with at least one of your cards participating, just subtract the chance of a royal on the board which is 4/C(52,5) or 1 in 649740. This would give you a probability of 1 in 32487. I just did this on the back of an envelope so buyer beware.
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