A probability question about winning the casino

Assume A has \$10 and he goes to casino and play a fair game with 50 percent win. Assume each time he bet \$1 and if he win he will get\$1. He decided to leave the casino once he win \$5.What is the probability that he will win \$5 dollars? I have tried the gambler model but seem not quite reasonable with the answer. When using the Gambler model, if A want to win \$3 with a capital of \$10, then we can assume the casino has \$3 then the probability of winning the \$3 =$\frac{10}{13}$which has a probability higher than the casino, which i think is counterintuitive. Not sure if it is doing right. - See this. – joriki Nov 7 '12 at 7:18 you mean this is a gambler ruin problem? – Mathematics Nov 7 '12 at 7:20 If ever there was one. – Did Nov 7 '12 at 7:21 But i don't quite get, if you consider the casino has capital 5, then it means that we have probability$\frac{1}{2}$to win, but consider now i want to win 3 dollars, then the probability becomes$\frac{7}{10}$which is quite strange that the winning probability is greater than the casino, isn't it? – Mathematics Nov 7 '12 at 7:24 Also, consider if A want to win \$10 this time, the probability is still $\frac{1}{2}$ which has the same probability as winning \\$5, that make me feel strange with Gambler model –  Mathematics Nov 7 '12 at 8:00