Rarest Number in RNGdle

The highest total in the complete 0–1,000,000 domain is 186,186,584 EP. Exactly 1 number reaches it: 1. This is a result of evaluating every valid integer against the captured badge definitions, not an estimate from a sample of player rolls. The top is unusual partly because a single small number can qualify for several exact-value and mathematical badges at once. It would be misleading to infer the theoretical maximum from a daily leaderboard, which records only the numbers that happened to appear during one UTC day.

Scores below the maximum often have ties. Across 1,000,001 numbers there are only 60,392 reachable EP values, a mean of 16.559 numbers per distinct total. The average is a compact way to describe the amount of sharing, not a claim that every score has sixteen or seventeen owners. Some values recur many times; the maximum occurs once. The full score-frequency dataset used for the tier chart records the exact count for each of the 60,392 reachable totals.

High EP comes from overlapping properties of the drawn integer. A perfect power can also be even, divisible by several smaller values, have a low digit sum, or carry repeated characters in its decimal form. A named mathematical constant can contain shorter recognizable digit runs as well as satisfy unrelated numerical tests. When those conditions meet, many badges match simultaneously. Their scores are fixed, but family grouping decides which related badges actually contribute to the final EP.

To keep examples anchored to an observed source, the numbers below are selected at build time from the frozen 100-entry public leaderboard fixture. The pattern label is calculated from each number; the value is taken from that same frozen record. They illustrate why a number can be rich in structure, but the list is not itself a theoretical ranking and does not make a claim about current player activity.

• 524,288 — 2^19; the frozen record gives 38,338,031 EP.
• 15,625 — 5^6; the frozen record gives 20,216,185 EP.
• 16,807 — 7^5; the frozen record gives 18,754,523 EP.
• 832,040 — a Fibonacci number; the frozen record gives 3,337,669 EP.
• 31,415 — an opening decimal block of π; the frozen record gives 25,011,501 EP.
• 271,828 — an opening decimal block of e; the frozen record gives 25,004,817 EP.

These examples show several routes to a striking total: exponentiation, recursive sequences, and digit strings that coincide with mathematical constants. There is no technique for choosing a future official roll from these examples. The original draw and this site’s sandbox both concern a finite integer range; learning that a number has many patterns changes how we describe it after selection, not the probability that it will be selected next time.

First, the rule engine checks every integer in the inclusive range. It records all badge matches rather than stopping at the first interesting feature. Next, it applies a family rule: among matching badges with the same family ID, only the one with the highest fixed EP adds to the score. Unrelated badges each add their own fixed value. Ties within a family preserve the first definition in captured order. The result is one total EP per number, and the number’s tier follows the all-domain score distribution.

The counts and top 100 table were generated by running this independent rule engine across every one of the 1,000,001 numbers. The reachable-score frequency file lists each EP value and exactly how many numbers produce it. That makes the reported maximum, number of maxima, mean tie count, and seven-tier distribution reproducible from one finite enumeration. We also compared all 233 badge decisions for every number against a local development bitmap, and checked 100 separate public leaderboard EP values against the engine. The public board provides an independent test because its values were returned by the original site rather than calculated from our bitmap.

A mathematical condition can overlap with a digit condition in surprising ways, so isolated examples are not enough to validate a rule set. The full-domain check catches edge cases such as zero, one, powers, and digit strings at the six-digit boundary. The separate public EP comparison checks the aggregation rule as well. These methods have different strengths; reporting both is more informative than presenting a plausible formula without a measured cross-check.

The compressed CSV files below let you sort and filter the finite domain without scraping this page. The all-number and top-10,000 tables use four columns: number,ep,tier,badge_count. A separate top-100,000 file maps each number to the IDs of all matching badges. The files are static outputs of the same captured rule version as the page. They do not contain player profiles or account histories.

• All 1,000,001 numbers · CSV.gz
• Top 10,000 · CSV.gz
• Top 100,000 badge IDs · CSV.gz

Within a shared EP value, the smaller number appears first. That sorting rule also governs the HTML top 100. If you compare a downloaded ranking with a saved public day board, remember that they answer different questions: the CSV enumerates possible outcomes, while the day board records activity visible at a timestamp.