Question

DQ 4: Counting & Probability A bet on "black 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 leaned 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? Explain using information you learned in this module's material, such as expected value.

Answer 1

In case of winning on a $1 bet (18/38) you gain a net of $ 1 In case losing on a $1 bet (20/30) you 10% your original bet for a net of - $1 Therefore E(x) = 18/38 times + 20/38 times (-1) E(x) = -2/38 = -1/19 Therefore E(x) = -1/19 Tildeequalto -0.053 this bet obviously favors the house and you are losing an average of about 5.3 cents per $1 bet the best strategy would be leave the table with your $ 10 starting bet and not to play But if you must play and ypu want to extend the play time as much as possible you should always bet $1 and no more