Guess 2/3 of the Average

• Your level shows how many steps ahead you thought. A guess near 50 is level 0: no thought about the others. Near 33 is level 1: "people will guess about 50". Near 22 is level 2: "people will think one step ahead". Each step is 2/3 of the one before [1].
• Game theory's answer is 0. If everyone reasoned all the way, every guess would shrink to 0. Real players never do this, so 0 has never won a public contest [1][2].
• Can never win: a guess above 66.7 can't win, because even if everyone guessed 100, the target would be 66.7.
• This week's winner appears when the round ends (each round is a week, Monday to Sunday, UTC). We never show the live average before that: it would spoil the game. A round needs at least 30 players to have a result.

1. Pick a whole number from 0 to 100 and lock it in.
2. Everyone's guesses this week are averaged when the round closes, and the target is 2/3 of that average.
3. The closest guess wins. Ties share the win. On Monday, the page shows last week's players, average, target, winning guess and how every number was guessed.

One guess per person counts in each round. We count one guess per browser and one per internet connection, so people sharing a network (a school, an office, a family) count once a week. A second guess is saved but doesn't count. Right after you guess, the page shows where your number sits on the reasoning ladder and how it would have done in the famous contests above.

Economists call this game the p-beauty contest, with p = 2/3 here. Rosemarie Nagel made it a famous lab experiment in 1995 [1]. Her finding: people don't reason all the way to 0, and they don't guess at random either. Most stop after one or two steps of "they think that I think".

That idea, that people reason a limited number of steps about others, became the level-k and cognitive hierarchy models of strategic thinking [4][7]. The newspaper contests that followed, with thousands of readers each, showed the same steps at 33 and 22, plus a group who chose 0 or 1 [2].

Your level describes one guess in one game. It isn't a measure of intelligence, and a deeper level isn't better: the winner is whoever predicts the crowd best, and the crowd usually stops at one or two steps. A level-4 guess is clever reasoning that usually ends up below the target.

The players here are whoever visits that week, not a fixed sample, so the target moves from week to week. The famous contests used slightly different rules: the Financial Times allowed whole numbers only, and Politiken and Spektrum allowed decimals [2][3].