We consider a two-person multi-stage finite-horizon game related to the ruin problem. At each of the n stages, two players with different initial capitals play one unit of capital. It is assumed that the players are asymmetric and have unequal chances of winning at each stage. A player wins if their opponent runs out of capital, i.e. is ruined. The players’ payoffs are determined at the end of the game taking into account the costs c that the player incurred at each stage of the game. If the opponent goes broke at stage τ , then the player receives a payoff of 1 − cτ. If the game has not ended within the n interval, the players’ payoffs are −cn. Various scenarios are examined: with one player having unlimited capital while the other has limited capital, and with both players having unlimited capital. The player’s strategy is to stop the game so as to maximize their expected payoff. The ruin probability and the players’ optimal stopping strategies are calculated using the properties of an asymmetric random wal describing the process of the game. Optimal stopping strategies and expected payoffs of the players were found using the dynamic programming method. Payoffs were compared in the problem without the option of stopping before the final time n and using the optimal stopping strategy. In the problem with both playershaving unlimited capital, optimal stopping strategies were found using the best response procedure. Numerical simulations of the obtained results are presented for different values of the problem parameters.