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math.PR2022
Exact Solution to the Chow-Robbins Game for almost all n, using the Catalan Triangle
John H. Elton
The payoff in the Chow-Robbins coin-tossing game is the proportion of heads when you stop. Knowing when to stop to maximize expectation was addressed by Chow and Robbins(1965), who…
math.PR2009
Notes on Feige's gumball machines problem
John H. Elton
We give a detailed proof, in the identically distributed case, of a conjecture of Feige about the maximum probability that the sum of n independent non-negative integer valued rand…