Guess 2/3 of the Average

You and four CPUs each pick a number from 0 to 100. The player whose number is closest to two thirds of the average of all five numbers wins. It is a game of guessing what everyone else will choose.

How to play

1. Pick a difficulty and press Start. There are 10 rounds.
2. Set a number from 0 to 100 with the slider and press "Lock it in".
3. The average of all the numbers is computed, and two thirds of it becomes the target.
4. Whoever picked the number closest to the target wins. If there is a tie, everyone tied wins.

Three difficulties

• Easy: the CPUs mostly pick by gut feeling.
• Normal: the CPUs adjust their numbers using the last round's result.
• Demon: the CPUs think deeper and head toward smaller numbers every round. You need to pick even lower than last round's target.

Scoring and ranks

A win earns 100 points. Even if you lose, you earn up to 60 points when you are close to the target. The maximum is 1,000 points over 10 rounds, with ranks from "Swallowed by the average" to "Ruler of 2/3".

Thinking hints

• If everyone picks 50, the target is about 33. If everyone then picks 33, it becomes 22, and so on, one level deeper each time.
• The theoretical answer is 0. But 0 does not win unless the others pick 0 too.
• Use the last round. The CPUs react to the previous target.

FAQ

What problem is this in game theory?

It is a famous problem based on Keynes's beauty contest. If everyone keeps reasoning deeper to the end, the answer is 0.

Do the CPUs always behave the same way?

No. Their choices vary a little at random each time.

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