Two-Thirds of the Room

The Keynesian beauty contest as a story: pick the number closest to two-thirds of the room's average.

A hundred people each write a number from 0 to 100. The winner is whoever comes closest to two-thirds of the average. Nobody sees anyone else's card and the rule is common knowledge. The story hands you the blank card and asks what you write. You lock in a guess, then step through the answer and breakdown.

Why quant interviews test this

Quant desks ask this because markets are this game: you are pricing what average opinion expects average opinion to be. The written solution at /brain-teasers/beauty-contest/solution covers level-k reasoning.

The Two-Thirds of the Room guide covers how scoring works, the strategy that wins, a worked example and the mistakes most players make.

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