What is the expected pay-off in a Colonel Blotto game where Blotto has troops in the formation of 3100 and the enemy has troops in the formation of 2100?

 

3. Our Guerrillas vs. Police is a type of game known in the literature as a "Colonel Blotto" game. In the original paper introducing this type of game [McDonald and Tukey, 1949), Colonel Blotto had four units with which to battle for four forts against an enemy with three units. A battle would always be won by the side with the larger force, and the smaller force would be destroyed. Blotto's payoff was +1 for each enemy unit destroyed and each fort he captured, -1 for each of his units destroyed and each fort captured by the enemy. The game matrix is Enemy splits 3000 2100 1110 4000 1 3100 Blotto 2200 splits 2110 1111 1 1 a) Once a player has decided how to split his forces, he should certainly choose forts at random to send them to, so each payoff in this game is an expected value. One of the hardest-to-calculate payoffs is 3100 vs. 2100, where there are seven cases to consider. Do the calculation to verify this payoff. Cind it 11431 4 - -/2 O