# What's the probability of a gambler losing \$10 in this dice game? What about making \$5? Is there a third possibility?

In a gambling game, each turn a player throws 2 fair dice. If the sum of numbers on the dice is 2 or 7, the player wins a dollar. If the sum is 3 or 8, the player loses a dollar. The player starts to play with 10 dollars and stops the game if he loses all his money or if he earns 5 dollars. What's the probability for the player to lose all the money and what's the probability to finish the game as a winner? If there some 3rd possibility to finish the game? If yes, what's its probability?

Thanks a lot!

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I tried to make the phrasing and grammar a bit better, as well as making the title more descriptive. – Zev Chonoles Dec 20 '12 at 22:45

Therefore, the probability that the player makes \$5 before losing \$10 is the same probability as flipping coins against somebody with $5, or 2/3. And the probability of the opposite event is 1/3. The third outcome, that the game goes on forever, has a probability that vanishes to zero. - Perfect! Thank you – Tina Dec 26 '12 at 11:15 The game is fair as$P(2 or 7)=P(3 or 8)=\frac 7{36}$, so if we ignore the non-paying rolls, it just flipping a coin. As the game is fair,$\frac 23$of the time he will earn$5$and$\frac 13$of the time lose$10\$.