The Absent-Minded Driver

An absent-minded driver starts driving at START in Figure 1. At X he can either EXIT and get to A (for a payoff of 0), or CONTINUE to Y. At Y he can either EXIT and get to B (payoff 4), or CONTINUE to C (payoff 1). The essential assumption is that he cannot distinguish between intersections X and Y, and cannot remember whether he has already gone through one of them.