There are 38 numbers on the roulette wheel 18 red 18 black a

There are 38 numbers on the roulette wheel, 18 red, 18 black, and 2 green. Let us assume that each time you play, you place a $1 bet. Your expected winnings are calculated using the expected value formula

E = Payoff * P(win) – Bet * P(lose)

a. Suppose you place your bet on 1 number only. The payoff is 35-to-1. What is E?

b. Suppose you place your bet on red. The payoff is 1-to-1. What is E?

c.Suppose you place your bet on the first two columns (#1 though 24). The payoff is 2-to-1. What is E?

d. Suppose you place your bet on the 2 green (0 and 00) spaces. The payoff is 17-to-1. (Note: 0 and 00 do not count as Even numbers when a bet is place on all even numbers.) What is E?

e. Suppose you place your bet on 3 numbers (a row of spaces). The payoff is 11-to-1. What is E?

f. What is the most advantageous way to bet when playing roulette? (Choose from among “a” to “e”).

Solution

a) E = 35 * 1/38 - 1 * 37/38

=> 35/38 - 37/38

=> -1/19 = -0.05263$

b) E = 18/38 * 1 - 20/38 * 1

=> -1/19 = -0.05263$

c) E = 24/38 * 0.5 - 12/38 * 1

=> 0

d) E = 2/38 * 17 - 36/38 * 1

=> -1/19 = -0.05263$

e) E = 3/38 * 11 - 1 * 35/38

=> -0.05263$