Two players simultaneously put up one or two fingers, and each player calls out a guess as to what the total sum of all the outstretched fingers will...

Two players simultaneously put up one or two fingers, and each player calls out a guess as to what the total sum of all the outstretched fingers will be. If you guess

right, but your opponent does not, you receive a payment (from your opponent) equal to your guess. In all other cases, it is a draw and no one earns anything.

Formulate and solve a linear program to identify the maximin/minimax strategies for the players. What is the value of the game? What is the optimal randomized strategy for each player? Does either player have an advantage?