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him a Kaleidoscope to play with and he used it as a looking glass."
A simple example of an attack/defense game will show the active principle. Suppose the attacker has a choice between two locations. Likewise, the defender can choose to defend either location (for illustrative purposes, the option of allocating some of his forces to each location is omitted). Success is defined as an attack against an undefended location. It is apparent from this construct that, ceteris paribus, the attacker has a 50/50 chance of choosing an undefended location. But, what if the attacker could convince the defender that there were three possible locations for the attack? Here it follows that the success probability climbs to 2/3, and so forth, reaching unity as a mathematical limit when the number of threatened sites grows arbitrarily large.7 It is, of course, necessary that the options introduced be both individually and collectively credible to the victim. As a practical matter the number of threats cannot grow arbitrarily large. Cruickshank (39), for example, recounts how this was appreciated by deception planners in connection with the invasion of Sicily:
