Four equally skilled robots take turns shooting arrows at a target proceeding in order: A, B, C, D. When it is a given robot’s turn, it shoots a single arrow. If it is closer to the center of the target than all previous arrows by all players, that robot remains in the tournament, going to the back of the queue to await its next turn. Otherwise that robot is eliminated immediately. The last robot remaining in the queue is the winner.

What is the probability that D wins?