Consider the following two-player game played in a particular office lunch room. Player 1 picks an integer between 1 and 4, and player 2 picks an integer between 3 and 6. If the sum of the two numbers...

Consider the following two-player game played in a particular office lunch room. Player 1 picks an integer between 1 and 4, and player 2 picks an integer between 3 and 6. If the sum of the two numbers equals 7, player 2 wins $8 from player 1. If the sum of the two numbers equals 6, player 1 wins $6 from player 2. If the sum of the two numbers equals 9, player 1 wins $9 from player 2. If the sum of the numbers is anything other than 6, 7, or 9, the game is a tie and neither player wins or loses. Determine the expected strategy for player 1 and the expected value of this game to player 1.