  Flip a coin repeatedly, and stop whenever you want. Your payoff is the
proportion of heads, and you wish to maximize this payoff in expectation. This
so-called Chow-Robbins game is amenable to computer analysis, but while
simple-minded number crunching can show that it is best to continue in a given
position, establishing rigorously that stopping is optimal seems at first sight
to require "backward induction from infinity". We establish a simple upper
bound on the expected payoff in a given position, allowing efficient and
rigorous computer analysis of positions early in the game. In particular we
confirm that with 5 heads and 3 tails, stopping is optimal.
