Question

A gambler enters a casino with an initial fortune of $100. Then, on each successive gamble, he will pay $1 to play and either wins $1 or loses $1 with the probabilities 49% and 51%, respectively. 2 The probability of winning or losing a gamble is independent of the past gambles. What is the probability that he has not run out of money in 100, 1000, 10000, 100000 gambles?

Exact answer not required, just the concept will also work.

Answer 1