A millionaire plays European roulette every evening for pleasure. He begins every time with A = 100 chips of the same value and plays on until he has gambled away all 100 chips. When he has lost his 100 chips for that evening's entertainment, he quits. Use computer simulation to find the average number of times the millionaire will play per round, for the Big-Martingale betting system and for the D'Alembert betting system. Also determine the probability that on a given evening the millionaire will acquire B = 150 chips before he is finished playing. Do the same for A = 50 and B = 75. Can you give an intuitive explanation for why the average value of the total number of chips the millionaire stakes per evening is equal to 37A over the long-term, regardless of the betting system he uses?