Re: Odds of hitting Broadway...
I believe you're double counting:
[C(4,1) * C(4,1) * C(4,1) * C(47,2)]/C(50,5) = 3.265%
If your opponent held A-K, I think it should be:
[C(4,1) * C(3,1) * C(3,1) * C(45,2)]/C(48,5) = 2.08%
Although that would include the times you lose to a boat/quads.
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