I'm a tourist to this forum; I used to be an astronomer with math oozing from my pores, but I'm a bit rusty at it lately, I am sad to admit.
Anyway, I am trying to recall the solution to a classic mathematics problem, which in grad school was called the "beauty contest problem." Here is the set up.
You are the sole judge of a beauty contest, which has 100 contestants. The contestants will come out, one at a time, in a randomized order. You are allowed to select the winner at any time, but you can select a winner only when that person first comes out. Therefore, once a contestant leaves the stage, you are no longer allowed to select that person.
What is the strategy you should use in order to have the highest probability of selecting "the most beautiful contestant."
I recall that the winning strategy was to allow N contestants to come out onto the stage, one at a time, effectively setting a baseline population. After N contestants have come and gone, you would select the FIRST contestant that comes onto the stage that was more beautiful than any of the preceding contestants.
But what was N?
I'm VERY interested in the solution to this question because it currently has direct bearing on a significant practical decision I am making!