Question

A bet in roulette has a probability of 18/38 of winning. If you win, you double your money. You can bet anywhere from $1 to $100 on each spin. A. Suppose you have $10, and are going to play until you go broke or have $20. What is your best strategy for playing? Explain using information you learned in this module's material, such as expected value. B. Suppose you have $10, and are going to play until you go broke or have $30. What is your best strategy for playing?

Answer 1

The best strategy for playing in both scenarios is to bet the minimum amount ($1) on each spin until you reach your target amount ($20 or $30). Betting more than $1 per spin would increase your losses over the long run.

Step-by-step explanation:

In this scenario, your best strategy for playing is to bet the minimum amount ($1) on each spin until you reach $20. This is because the expected value of this bet is positive, meaning that over the long run, you are expected to make a profit. The expected value is calculated by multiplying the probability of winning (18/38) by the amount you win ($1), and subtracting the probability of losing (20/38) multiplied by the amount you lose ($1). In this case, the expected value is (18/38 * $1) - (20/38 * $1) = -$0.0526, which is negative. This means that on average, you would lose money if you were to bet more than $1 per spin.

In the second scenario, your best strategy for playing is still to bet the minimum amount ($1) on each spin until you reach $30. This is because the expected value is still negative when betting more than $1 per spin. The expected value in this case is (18/38 * $1) - (20/38 * $1) = -$0.0526, which is still negative. This means that even though you have a higher target amount, betting more than $1 per spin would increase your losses over the long run.