=+7.8. Here is a common martingale. Just before the nth spin of the wheel, the gambler has before him a pattern x1, ..., x, of positive numbers (k varies with n). He bets x1 + x2, or x, in case k = 1. If he loses, at the next stage he uses the pattern x 1, . .., * *, x , + x , (x 1, x , in case k = 1). If he wins, at the next stage he uses the pattern x2, ..., X4 - 1, unless k is 1 or 2, in which case he quits. Show that play is certain to terminate if p > ; and that the ultimate gain is the sum of the numbers in the initial pattern. Infinite capital is again required.