How to play Two Thirds — the daily ⅔-of-the-average game

Two Thirds is a one-number game you play against everyone else who plays today. Here is how it works, and how to think about it.

What is this?

Two Thirds is a free browser edition of a classic experiment from game theory, often called the beauty contest or the guess two-thirds of the average game. Economists have run it in classrooms, magazines and newspapers for decades because it measures something nothing else does: how many steps ahead people think about what everyone else is thinking. Here it runs every day, with one public crowd, and the whole crowd’s picks are published at midnight UTC.

How to play

1. Pick a whole number from 0 to 100 with the number pad (or just type it).
2. Tap Lock in. You get one pick per day and it cannot be changed.
3. You immediately see your thinking level — a label for the reasoning your number suggests — and a countdown to midnight UTC.
4. At midnight UTC the day closes. The game takes the average of every pick and multiplies it by two-thirds. That is the target. Whoever picked the whole number closest to it wins; if several numbers are equally close, they all win.
5. Come back to see the reveal: a histogram of every pick, the target line, your own pick, and how many players you beat. The reveal card can be shared or saved as an image.

How to think about it

If everybody picked at random, the average would be about 50 and the target about 33. But if everybody expects that, they all pick 33, and the target becomes 22. If they expect that, it becomes 15, then 10, and so on. Follow the chain forever and you reach 0, the game’s only Nash equilibrium. The catch is that real crowds never follow it forever. In the famous newspaper editions the winning number has usually landed somewhere between about 13 and 22 — when the Danish newspaper Politiken ran it in 2005 with 19,196 readers, the winning number was 21.6.

Where the game comes from

The idea is older than the internet. In 1936 the economist John Maynard Keynes compared the stock market to a newspaper competition in which readers had to pick the faces that other readers would find prettiest: to win, you do not choose what you like, you choose what you expect the average opinion to expect. That is why economists still call this family of games the beauty contest.

The number version appeared in 1981, when the French magazine Jeu & Stratégie asked its readers to play it and roughly 4,000 did. In the 1990s the economist Rosemarie Nagel turned it into a laboratory experiment, and her results became the standard reference: most people reason one or two steps ahead, very few go all the way to zero, and groups that play repeatedly drift lower each round. Newspapers in several countries have run large public editions since then. Two Thirds asks the same question every day, in public, so you can watch whether an internet crowd learns the same way a classroom does.

Tips

• Numbers above 67 can never win: even if everyone picked 100, the target would be 66.7.
• Zero is perfectly logical and almost never wins against real people. You are playing the crowd, not the textbook.
• Think about who is playing today. A crowd that arrived from an economics forum reasons further than one that arrived from a group chat.
• Watch the past-days strip. If returning players learn, the target should fall from day to day; if new players keep arriving, it may not.
• Expect protest picks. A handful of 100s pulls the average up more than you would think.
• Sharing before the reveal is spoiler-free: the locked-in message names your thinking level, never your number.

FAQ

Is it free? Do I need an account? Yes, it is free, and there is no account, sign-up or email.

Is there a prize? No. Winning is for bragging rights only, and it will stay that way.

When does a day start and end? At midnight UTC, the same moment for everyone in the world.

Why can’t I see today’s picks? Seeing them would change them. Only closed days are published; today you only see how many people have played.

Can people cheat by voting many times? Each device gets one pick a day and each network a small number, which stops casual ballot-stuffing. The card always prints the player count, so a tiny crowd is never dressed up as a big one.

What does the thinking level mean? It is a light-hearted label based on the classic reasoning chain: Level 1 expects random players and picks about 33, Level 2 expects Level 1 and picks about 22, and so on.