Been given this as practice for my Stochastic Processes course. I'm fairly new to the concept, so I haven't been exposed to a general method. Any hints/tips for the following?
A gambler plays a (fair) game, where at each stage he has probability $\frac{1}{2}$ to win $ \$1 $ and probability $\frac{1}{2}$ to lose $ \$1 $. If he starts with $ \$k $, what is the probability that he will go bankrupt before $n$ games ? What is the probability that he will eventually go bankrupt , if he plays the game indefinitely ?
Intuition tells me the last part is 1.