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Well, mean is infinite (easy enough to see): Median is finite though. In code I slightly simplified the problem - function [n,m,k] = so_coins(n) % n=number of coins left in the urn. m=0; % number of coins taken so far k=1; % steps performed - end condition. while (n > 0 && k < 1000000) % stop after 1m steps of taking coins out. r=rand(n,1)...

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This answer draws freely from other answers, in particular, @Gareth's and @Steve's. As pointed out by others our strategy Let's assume that the billionaire gets cold feet once there are a total of M (M>100) coins in the pot. We can give a closed form solution for the expected time $E_{100,M}$ until either this happens or the game ends regularly. This ...

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What a nice coincidence when I found StackExchange's featured hot topic to be almost the same question that I asked some days ago at CrossValidate SE: Intended selection bias. Here I describe the following procedure: Consider a bag of balls of two equally distributed colors. If I pick a ball uniformly at random it is a red or a blue ball with equal ...

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