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Three divisions of an army defend a town, which has two roads approaching it. The town is attacked by two divisions of army I, either one along each road or two along the same road. The defenders, army II, can either put all three divisions to guard one road or two to guard one road and one the other. Whichever army has more divisions on a given road will command the road. If there are equal numbers of defenders and attackers on the same road then half the time the defenders will hold the road and half the time the attackers will enter the city. Calculate the payoff matrix of the attackers’ chances of entering the town. Hence, find the value of the game and the optimal strategies.

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