  In this expository note, we give a simple proof that a gambler repeating a
game with positive expected value never goes broke with a positive probability.
This does not immediately follow from the strong law of large numbers or other
basic facts on random walks. Using this result, we provide an elementary proof
of the strong law of large numbers. The ideas of the proofs come from the
maximal ergodic theorem and Birkhoff's ergodic theorem.
