A Peculiar Game
You and your best friend decide to play the following game:
Player 1 and Player 2 both start with $100. One round of this games consists of the following:
Both players choose a number randomly and independently from 1 to 5 inclusive. If both players choose the same number, then Player 1 gives $10 to Player 2. Otherwise, Player 2 gives $10 to Player 1.
You decide to be Player 1, and your best friend is Player 2. What is expected amount of money (in dollars) you will be left with after playing 10 rounds of this game?