Expected Value of a Game

A game offers a player a 20% chance to win $100 and an 80% chance to win nothing. To determine whether this game is favorable in the long run, we can calculate the expected value of the game.

The expected value (EV) can be calculated using the formula:

$$EV = (P_1 imes V_1) + (P_2 imes V_2)$$

where:

• $P_1$ = Probability of winning ($0.20$)
• $V_1$ = Value of winning ($100$)
• $P_2$ = Probability of losing ($0.80$)
• $V_2$ = Value of losing ($0$)

What is the expected value of playing this game?