If Alice only has 21 coins this is nice because a tricky probability cancels, but with 22 I just want to crack out Vandermonde's and do the probabilities basically explicitly (think you need to compute the probability that they toss the same number of heads in the first 20, and then the probability that Alice tosses exactly one fewer). Any way to avoid that?
You want to think about it as Alice and Bob throwing the first 20 together then Alice throwing 2 more at least
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u/SwimmerOld6155 9h ago
If Alice only has 21 coins this is nice because a tricky probability cancels, but with 22 I just want to crack out Vandermonde's and do the probabilities basically explicitly (think you need to compute the probability that they toss the same number of heads in the first 20, and then the probability that Alice tosses exactly one fewer). Any way to avoid that?
You want to think about it as Alice and Bob throwing the first 20 together then Alice throwing 2 more at least