### What The Hare Said To Hector

**Hector:** Alright, explain your game to me, Mr. Hare.

**Hare:** First, I will stand somewhere along the race track, but I won’t tell you where, and this wall hides me from view. Now, do you see this large contraption here?

**Hector:** Indeed. There is a -meter long net suspended from a high cable that extends along the track between two poles. Attached to the pole at this end (behind the wall) is a box with a crank, a lever, an anemometer, and a graphing calculator. I surmise that the crank moves the net along the cable, and that the lever releases it.

**Hare:** Very astute!

**Hector:** And I suppose that my goal is to trap you under the net?

**Hare:** Without any information to guide you? No such nonsense. In fact, the game is much more subtle than that. You will indeed crank the net to a position of your choosing — let’s name the end closest to you — and then release it. I will then reveal my position — call it — to you, and you must wager with me on whether I am under the net.

**Hector:** Too easy! If , then I wager that you are under the net; otherwise, that you aren’t. I can’t lose!

**Hare:** Ah, not so fast. You see, there are random winds along the direction of the race track in these parts, and so the net may be blown considerably off from a straight downward course.

**Hector:** Which, of course, I won’t be able to see, due to the wall.

**Hare:** Precisely.

**Hector:** So, we could say that the net covers not , but , where is a -mean Gaussian process with standard deviation .

**Hare:** If you like.

**Hector:** Hence the anemometer, from which I can estimate . I see. Thus, my task is reduced to the following: given , , , and , compute the probability that . From there, I can decide whether the wager has a positive expected value for me.

**Hare:** Well played, Hector. But there is still one outstanding consideration.

**Hector:** And that is?

**Hare:** Actually computing the probability you speak of quickly enough to make your wager! I have somewhere to be promptly after this game, and as you know, we leporids hate to be late…

*And with that, the Hare races off around the wall and down the track.*