AbstractThe general problem of a marksman versus a mobile target, with a time lag in the gunner's information as to the target's position, appears in many guises in many situations. It is a classic military problem. Formulated in terms of game theory, the desiderata are: How should the target best maneuver to confound prediction of his positions How and when should the marksman make this prediction? What hit probability is to be expected when both participants behave optimally?This paper discusses this general class of problems and then settles on one which seems to be the simplest possible example that is not trivial. Nevertheless it is difficult. In two previous papers devoted to it, the evader's best strategy and value of the game were given. Here the emphasis is on the marksman. He has no optimal strategy, but does have an ideal strategy with the property that every near optimal strategy is close to it. He also has a class of passive ε‐strategies such that if and only if he obeys their dictates will he either come within ε of the best hit probability or else always remain in a position where it is possible to do