Question

Consider the following scenario when answering the following questions:
Ivett and Desiree are considering playing a game called Matching Fifties. In this game, Ivett and Desiree will each place a $50 bill on the table. Both players will then toss a fair coin. If both Ivett and Desiree toss heads or if they both toss tails, Ivett wins the $100 on the table. If one woman tosses heads and the other tosses tails, Desiree wins the $100 on the table.

What is the expected value of this game?

Answer 1

The above game - matching fifties - can be denoted in a payoff matrix as follows:

		IVETT
		HEADS	TAILS
DESIREE	HEADS	-100, +100	+100, -100
	TAILS	+100, -100	-100, +100

Given, If both Ivett and Desiree toss heads or if they both toss tails, Ivett wins the $100 on the table. If one woman tosses heads and the other tosses tails, Desiree wins the $100 on the table.

Probability of obtaining two heads in one toss of coin (each) = 1/4 and probability of obtaining two tails = 1/4

Similarly, probability of obtaining head on first and tail on second = 1/4 and probbility of obtaining tail on first and head on second = 1/4.

Thus, expected value of the game = 1/4(100) + 1/4(100) + 1/4(-100) + 1/4(-100) = 0.