How scoring works

1. 01

   We examine every integer from 0 through 1,000,000, written without leading zeros. For each pattern, its probability is its exact match count divided by 1,000,001.

2. 02

   Information is −log₂(probability). Rarer patterns carry more information. Digit sum and distinct-digit count are also scored from their exact distributions; lengths of one to four digits form a separate group.

3. 03

   Within each family, contributions are sorted and weighted 1, 0.35, 0.15, 0.07 and 0.03. Further overlapping signals add no points. The total information is multiplied by 20 and rounded once to an integer.

4. 04

   The percentile counts all numbers whose score is at least this high. Ties are included. Short numbers often rank highly because they are scarce within this fixed range; the highest and lowest boards therefore start at 1,000.

Engine version: art-1.0.0. All counts are generated from this project’s independently implemented rules. Individual rounded contributions may not sum to the final score.