matrix game
Aggie and Baggie are fighting a duel each with one lemon meringue pie starting at 20 paces. They can each choose to throw the pie at either 20 paces, 10 paces, or 0 paces. The probability either player hits the other at 20 paces is 1 3 ; at 10 paces it is 3 4 and at 0 paces it is 1. If they both hit or both miss at the same number of paces, the game is a draw. If a player gets a pie in the face, the score is −1, the player throwing the pie gets +1. Set this up as a matrix game and solve it.
matrix game