Players A and B play a betting game. Player A starts with initial money n. In each of k rounds, player A can wager an integer w between 0 and what he has currently. B then decides whether A wins or loses. If A wins, he receives w money, and if A loses, he loses w money. A total of k rounds are played, but A can only lose r times. What strategy should A use to end with the maximum amount of money, D(n, k, r)?

In this paper, we provide a strategy for A to maximize his money and the algorithm to calculate D(n, k, r). We study the periodicity of D(n+1, k, r)−D(n, k, r) relative to n. We will also extend n and w to non-negative real numbers. The maximum amount of money that A can obtain with continuous money is C(n, k, r), and we study the relationship between C and D.