In the paper we derive a closed form formula for a probability of success in a roulette-type game. The player begins the game having j chips and plays one chip at a time. In each game, he either wins w chips with probability p or loses his chip with probability 1 - p. The game terminates when the player loses all his fortune or when his capital reaches, or exceeds level C. The present solution rectifies the incorrect one, presented in Section 3 of Kozek (Stochastic Process. Appl. 55 (1) (1995) 169).