Question

You and a rival are engaged in a game in which there are three possible outcomes: you win, your rival wins (you lose), or the two of you tie. You get a payoff of 50 if you win, a payoff of 20 if you tie, and a payoff of 0 if you lose. What is your expected payoff in each of the following situations where nature decides if you win or not:
A) There is a 50% chance the game ends in a tie, 10% chance you win (and therefore a 40%
chance you lose).
B) There is a 50-50 chance of winning and there are no ties.
C) There is an 80% chance you lose and a 10% chance you win or tie.

Answer 1

Answer:

A) There is a 50% chance the game ends in a tie, 10% chance you win (and therefore a 40%  chance you lose).

expected value = (50% x 20) + (10% x 50) + (40% x 0) = 10 + 5 + 0 = 15

B) There is a 50-50 chance of winning and there are no ties.

expected value = (50% x 50) + (50% x 0) + = 25 + 0 = 25

C) There is an 80% chance you lose and a 10% chance you win or tie.

expected value = (10% x 20) + (10% x 50) + (80% x 0) = 2 + 5 + 0 = 7

The expected value of an event is determined by adding up all the possible outcomes multiplied by their respective value.