Problem: $A, B, C, D$ are playing an archery game. They have equal probability of landing their arrow on any spot the target with radius of $R$. Their score is the distance to the center of the target. They take turn to shoot at the target $A, B, C, D, A, B, C, D...$. If one's score is closer to the center of the target than all previous arrows by all players, he survives, goes to the back of the queue, otherwise he is eliminated. We can assume the arrows always hit the target.
What's the probability that $D$ wins this game?
My thoughts: The distribution of the score is obviously linearly scaling from 0 to $R$. But I'm not sure if the distribution of the score matters here. Since we only care about the orders, any order of $x_1, ... x_n$ has $\frac{1}{n!}$ probability regardless of the distribution.
Other than that, I have little clue...