Page:CIAdeceptionMaximsFactFolklore 1980.pdf/58

C00036554 7. Further, a value of "1" is attached to the outcome associated with the attack of an undefended position and "0" otherwise. The resulting two-by-two, zero sum game has the payoff structure,

and the optimal solution is a mixed strategy of (1/2, 1/2) for both the attacker and defender, resulting in a value of 1/2 — numerically equal to the probability that the attack will occur against an undefended position. Suppose now, that the attacker can broaden the options and convince the defender that there are three threatened locations. The resulting three-by-three, zero sum game,

has optimal mixed strategies (1/3, 1/3, 1/3) for attacker and defender, and a value of both the 2/3 — a quantity larger than that of the first game. Multiplication of options thus increases the likelihood of success. It is evident that the value of this game is (N-1)/N, as the number of options is increased and approaches unity (complete success) as the number grows large.