I've invented a paradox, or at least I think I have. Here is how it goes:
On an infinite line, a point is placed at random. You start at point 0 on the line, and your job is to find the point, but you can only recognize that you have found it by standing on it. You can only move left or right along the line.
Logically, you would want to go the greatest distance possible in either direction before turning around, as that would prevent backtracking the best. But you do intend to eventually find the point given infinite time, which would be impossible if you only go in one direction for infinity- turning around is a necessity. So you have guaranteed inefficiency, that is, you want to go as far as you possibly can before turning around but you can not go as far as you can, as that would strip you of the assurance of finding the point, cutting the odds down to 50%.
So the question is: have I really invented this paradox. More specifically, is this a paradox and has it been thought of before?