Re: At least two Aces?
but if she keeps dealing out one 13 card hand at a time from a well-shuffled deck until she can tell you honestly that "this hand contains at least one ace" would you then be prepared to bet that the hand contains at least two aces, at even money?[
No, your odds just got even worse.
Odds of 2 or more aces is 4.4%. 4.4%/26% = 17%.
or if, instead, in the latter case, she could say honestly "this hand contains the ace of spades" would you then be prepared to bet that the hand contains at least two aces, at even money?
Yes, now you are a favorite.
P(2+ aces|As) = [P(As|2 aces)P(2 aces) + P(As|3 aces)P(3 aces) + P(As|4 aces)P(4 aces)]/25%
= [.5(.216) + .75(.041) + 1(.0026)]/.25 = 56.5%
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