What is your expected value for a game where your probability of winning is 1/9 and your profit is four times your wager? (Round your answer to one decimal place.) %

Question

What is your expected value for a game where your probability of winning is 1/9 and your profit is four times your wager? (Round your answer to one decimal place.)

 %

Answer 1

Equation for expected value (EV):

EV = ∑P_i*x_i

where P is probability and x is the value of that probability.

Specifically for betting games, you can think of it like this:

EV = (probability of winning)*(profit) - (probability of losing)*(loss)

Since no wager amount is given, and we want the answer as a percent, we will take the wager as being equal to 1, so that our answer comes out as a proportion.

With this in mind,

EV = (1/9)*(4) - (8/9)*(-1) = -4/9

Expressed as a percentage, -4/9 is -44.4%

This means that as continue to play, you will expect to lose 44.4 cents for every dollar you put in.