Greedy

https://www.desmos.com/calculator/2zfvwpf64i

To start with you choose any number x between 0 and 1. We’ll call x your “risk tolerance.” There is a reason this should be large—the higher is x, the higher will be the pay-off each time you play the game. But there is also a reason your risk tolerance should be small—the higher it is, the more likely you are to be kicked out of the game after each round. Somewhere in the middle there ought to be an optimal risk tolerance.

This is a wonderful grade 12 calculus max-min problem. But we are excited to see what a grade 10 or 11 class can do with it. It’s about finding the right level of risk.