Question

A roulette wheel has 38 slots and a ball that rolls until it falls into one of the slots, all of which are equally likely. Eighteen slots are black numbers, eighteen are red numbers, and two are green zeros. If you bet on “red”, and the ball lands in a red slot, the casino pays you your bet, otherwise the casino wins your bet.

1. What is the expected value of a $1 bet on red?
2. Suppose you bet $1 on red, and if you win you “let it ride” and bet $2 on red. What is the expected value of this plan?

Answer 1

a) probability of winning =18/38

expected value of a $1 bet on red =E(X)=xP(x)=1*(18/38)-1*(20/38)=$ -0.05

b)

for this plan:

P(X=3) =P(win consecutive twice) =(18/38)*(18/38)

P(X=-1)=1-(18/38)*(18/38)

therefore expected value of this plan =xP(x)=3*(18/38)*(18/38)-1*(1-(18/38)*(18/38))=$ -0.10