The question is this:
Say you're playing a coin flip game, where you start with 30 dollars. If you flip heads, you win 1. If you get tails, you lose 1. You keep playing until you either run out of money or reach 100. What is the probability that you will reach 100. The coin is fair.
I have seen many questions about expected number steps, expected earnings and so on. However I am having trouble with this question because the game need not even end for certain (I think). In such situation, how would we either get a probability, or explain why it can’t be arrived at, if that is the case?