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Documentation Index

Fetch the complete documentation index at: https://docs.trepa.io/llms.txt

Use this file to discover all available pages before exploring further.

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The problem

Imagine five people. The is 97,000. Three guess 96,800 (error 200 each); one guesses 97,500 (error 500); one guesses 98,000 (error 1,000). So are 200, 200, 200, 500, 1,000. The is the 3rd smallest: 200. Under the normal rule you win only if your error is strictly less than 200, so nobody wins (the three with 200 are not strictly below the median). That would punish the three best guesses. The best-coalition exception fixes this: those three form a coalition and all win; the other two lose and fund the prizes.

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The rule

If half or more of all participants share the same best (minimum) error, they form a best coalition and all of them win, even if the normal median rule would say otherwise.

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When does it happen?

Rarely. You need a big cluster of identical or symmetric guesses and an outcome that lines up with them.
Last modified on April 28, 2026