Players $A$ and $B$ play a game where whoever loses gives $USD 1$ to the winner. They repeat the game until one player is bankrupt. Suppose Player A has more skill, and wins each game with probability $2/3$. If Player A starts with $USD 1$, and Player B begins with $USD 2$, whats the probability that Player B wins?
Really don't know how to solve this... any links, hints or suggestions?