Another well-known gambling system is the martingale doubling system. Suppose that you are betting on red to turn up in roulette. Every time you win, bet 1 dollar next time. Every time you lose, double your previous bet. Suppose that you use this system until you have won at least 5 dollars or you have lost more than 100 dollars. Write a program to simulate this and play it a number of times and see how you do. In his book The Newcomes, W. M. Thackeray remarks “You have not played as yet? Do not do so; above all avoid a martingale if you do.” Was this good advice?

Notes