The gambler's ruin is usually presented as a repeated game where the gambler can either win or lose one unit. We examine cases where the profits from winning gambles are multiple times the stake at risk, with the expected profit per gamble being either zero, positive or negative. For positive...

To analyze whether stock-market prices follow a random walk, the algebraic sign of their returns has been compared with a coin toss, which is a prominent example for a Bernoulli trial with equiprobable outcomes. Like coin tosses, signed returns lend themselves for a simple runs test for...