# 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.

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– 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
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