interesting problem

[limitti]

Not exactly poker problem but I thought someone might find this interesting...

A game where you must choose a number between 0-100. There is 20 people and the winner is the one who chooses the number that is two thirds of the arithmetic mean of all the chosen numbers (or closest to it). What number should you pick to have highest chance to win? Does it depend on the number of participants?

I don't know the answer and I can't figure out how to calculate it but I found the problem interesting.