What's the probability of a gambler losing \$10 in this dice game? What about making \$5? Is there a third possibility? Can you please help me with this question:

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!

The game is fair as $P(2 \text{ or } 7)=P(3 \text{ or } 8)=\frac 7{36}$, 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 $10$.
