Keynes's Beauty Contest

The problem
pick a number from 0 to 100target = ⅔ × (group average)closest guess winsall players are perfectly rationalwhat do you pick?

A roomful of perfectly rational people each privately pick a number between 00 and 100100. The winner is whoever picks closest to 23\tfrac{2}{3} of the average of all guesses.

What do you pick?