Question

a modified roulette wheel has 28 slots. one slot is 0,another is00, and the others are numbered 1 through 26. you are placing a bet that the outcome is an odd number. (in roulette, 0 and 00 are neither odd nor even) a. what is your probability of winning? b. what are the actual odds against winning? c. when you bet that the outcome is an odd number, the payoff odds are 1:1. how much profit do you make if you bet $10 and win? d. how much profit should you make on the $10 bet if you could somehow convince the casino to change its paoff odds so that they are the same as the actual odds against winning?

Answer 1

a.

There are total 28 slots and 13 odd slots.

probability of winning = 13/28

b.

The actual odds against winning is number of slots for lose to number of slots for win

which is 15 to 13

= 15:13

c.

The payoff odds are 1:1, so you will get $10 on winning or lose $10.

Expected profit = 10 * (13/28) - 10 * (15/28) = -$0.71

d.

payoff odds = 15:13

For $10 bet you will win (15/28) * 10

and lose (13/28) * 10

Expected profit = (15/28) * 10  * (13/28) - (13/28) * 10 * (15/28) = $0