In a game of roulette, there are 37 squares, 18 of which are red and 18 black, 1 square is neither. Suppose you bet on a colour with $1 each bet. You start with $50. Find the probability of doubling your money before ruin, and the probability of ruin before doubling your money. Formulate the model for your fortune as a Random Walk, apply the Optional Stopping Theorem, specifying the appropriate martingale and the stopping time.