The Gambler’s Ruin with Asymmetric Payoffs

Karl Whelan

No 202503, Working Papers from School of Economics, University College Dublin

Abstract: 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 value games with an equal expected return per gamble, we show that higher winning payoffs imply higher probabilities of ruin and lower average final wealth. The opposite results apply for negative value games. For fair games with zero expected profit, probabilities of ruin are generally (but not always) close to the ratio of starting wealth to target wealth (the ruin rate in the symmetric game) but ruin rates converge faster for games with higher winning payoffs.

Keywords: Gambler's ruin; Random walks; Stopping problems (search for similar items in EconPapers)
JEL-codes: D81 G11 (search for similar items in EconPapers)
Pages: 32 pages
Date: 2025-03
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