3. We have seen that by betting on “red” in American roulette, you have a chance of winning, therefore doubling the money you bet. Suppose that you have $5 and you want to bet until either you reach (and stop with) $10 or you go broke. Is placing individual $1 bets on red more, less, or equally likely to reach this goal than just placing a single $5 bet? First, try to give an answer based on intuition, taking into account the casino’s advantage.

You could also explore the following formula that gives the probability of going from dollars to dollars without going broke by making $1 bets on red in American roulette:

Discuss how the strategy for maximizing the chance of reaching a financial target compares with the strategy for maximizing the length of time that your money lasts (for entertainment value).