Re: Humorous Probability
Might help if we knew what game you were playing. 5 card draw, Pai Gow, Blackjack, Hold 'Em?
Edit: To save time, as I assume it's hold 'em:
[4 * C(47,2)]/C(52,7) = 4324/133784560 = .003% or 30939 to 1.
For 5 card draw:
4/C(52,5) = 4/2598960 = .000154% or 649739 to 1
To have a greater than 50% chance of getting a royal in hold 'em, you'd need to play:
1 - BINOMDIST(21446,21446,1-4324/133784560,FALSE) comes out to just over 50% so, your odds become slightly favorable at 21446 hands to have a royal.
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