KöMaL 2012 B4419

Jack Potter is an addicted gambler. Yesterday, he threw 20 000 forints (HUF, Hungarian currency) in a one-armed bandit machine without his family knowing about it. To make things worse, he took that money from the amount that the family reserved for food. To avoid the affair being revealed, today he is taking the remaining 40 000 forints of the family, too, and goes back to the casino to play roulette. Since he does not want to risk too much, he is betting 1000 forints on red or on black in each game. If he wins, which has a probability of 18/37, then he gets another 1000 forints. Otherwise he loses his bet. He stops playing either when he has gathered a total of 60 000 forints -- in that case he can put all the money back in its place -- or when he has lost all the money. What is the probability that Jack Potter will manage to gather the 60 000 forints?