The only stable guess is 0 — but that assumes everyone reasons all the way there. Where the crowd actually lands measures how many steps ahead it thinks.
Nagel 1995; Keynes' beauty contest (1936).
payoff · Two-Thirds #15110
I played Two-Thirds tonight. Can you out-think the crowd?
▁▁▁█▅▁▁▁▁▁▁▁ 3 players · payoff.games
10 to play · Guess two-thirds of the average. · non-revealers forfeit their stake.