I'm curious whether anyone picked a number higher than twenty-five - and what would you call that, a zero-leveler?
Actually, a sizable fraction of clever pranksters may get a kick out of thwarting the "rational" choice, since there is no punishment for guessing wrong, and pick 100.
(No, I am not telling you what I picked.)
Every time I've played this in real life there's been someone who's done that.
NPR's Planet Money is running an experiment which could be an interesting way to test your other-people-modeling skills.
This is a guessing game. To play, pick a number between 0 and 100. The goal is to pick the number that's closest to half the average of all guesses.
http://www.npr.org/blogs/money/2011/10/03/133654225/please-help-us-pick-a-number?sc=fb&cc=fp
The other people guessing are self-selected, I would assume primarily NPR listeners.