alt Hacker NewsQuite the assumption here: "cards are randomly interleaved from the left or right pile one by one. (Each card gets dropped from either the left or the right pile with a probability that’s proportional to the number of cards remaining in that pile."
... Why would it be proportional to the number of cards in each pile? (Edit: I suppose the person doing the shuffling might adjust the rate of cards coming from each hand ... But not perfectly and continuously)
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tobr • today at 12:35 PM
> But not perfectly and continuously
Isn’t that where the randomness comes in?
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If there is one card in this pile and no cards in the other, the probability of dropping the card from this pile is one. If instead there are some cards still in the other, a) the probability is less than one, and b) we move one step closer to the first state. So by construction it must be proportional - perhaps a poorly behaved proportionality, but that is still enough for the math to work.