Methodology and sources
This page exists so you can check the arithmetic rather than trust it. Every rarity figure is derived below or verified by enumeration; every print-run figure comes from a named government document; and where the data runs out, it says so instead of guessing.
Two companion pages carry the rest: sources names every dataset behind these figures — including the two that have none — and coverage sets out exactly which notes the data does and does not contain, denomination by denomination.
How the odds are computed
A print run of US notes carries serial numbers 00000001 through 99999999. Serial 00000000 is never issued — a press reaching all zeros produces an error note, which is destroyed and replaced with a star note. That leaves exactly 99,999,999 serials, which makes rarity a counting problem with an exact answer, not an estimate.
No figure on this site is copied from a competitor. Several of the numbers circulating in this niche do not survive being added up: the commonly published counts for the three binary radar sub-patterns sum to more binary radars than the 630 that can exist.
| Pattern | Reasoning | Count | Odds |
|---|---|---|---|
| Solid | Eight identical digits, one choice of digit, minus 00000000 which is never issued. 10 − 1 = 9 | 9 | 1 in 11,111,111 |
| Perfect ascending ladder | Eight consecutive digits with no wrap. The first digit must leave room for seven more, so it is 0, 1 or 2. 3 | 3 | 1 in 33,333,333 |
| Radar | A palindrome is fully determined by its first four digits. 10⁴ − 1 = 9,999 | 9,999 | 1 in 10,001 |
| Binary radar | A palindrome using exactly two distinct digits: choose the pair, then choose a first half that uses both. C(10,2) × (2⁴ − 2) = 45 × 14 = 630 | 630 | 1 in 158,730 |
| Repeater | The last four digits are fixed by the first four. 10⁴ − 1 = 9,999 | 9,999 | 1 in 10,001 |
| Binary | Choose two digits, then any eight-digit string over them that uses both. C(10,2) × (2⁸ − 2) = 45 × 254 = 11,430 | 11,430 | 1 in 8,749 |
| Trinary | Three digits, inclusion–exclusion to force all three to appear. C(10,3) × (3⁸ − 3·2⁸ + 3) = 120 × 5,796 = 695,520 | 695,520 | 1 in 144 |
| Six of a kind | Choose the repeated digit, choose the two positions that differ, fill them with anything else. 10 × C(8,2) × 9² = 10 × 28 × 81 = 22,680 | 22,680 | 1 in 4,409 |
| Rotator | Only 0, 1, 6, 8 and 9 survive a 180° turn, and each digit in the first half fixes its mirror. 5⁴ − 1 = 624 | 624 | 1 in 160,256 |
| Two-two bookends | The first two digits are fixed by the last two; the middle four are free. 10² × 10⁴ − 1 = 999,999 | 999,999 | 1 in 100 |
Counts overlap, on purpose
A serial can satisfy several definitions at once, and each pattern's count is the number of serials matching that definition — every super radar is also a radar, and is counted in both. The alternative is mutually exclusive counts, where "1 in 10,001" quietly means "1 in 10,001, given it is not also something better". The checker shows the strongest label first and lists every other match with its own figure.
The reference table on the fancy serial number checker is generated at build time by running the detector itself against a real serial for each pattern. The table and the tool are therefore incapable of disagreeing, and the build fails if a pattern exists that no example triggers.
How the value bands are built
Two decisions, both of which put us at odds with most of this niche.
Premiums are added to face value, not multiplied by it. A collector buying a radar is buying the number; the note underneath is a floor. "Worth 5× face" is the standard shorthand and it produces absurd answers the moment you apply it to a $100 bill. Denomination still moves the premium — higher-face notes attract fewer, better-capitalised buyers and get graded more often — but it moves it sub-linearly, so a $100 note carries roughly 2.6 times the premium of a $1, not 100 times.
Condition is applied as a heavy multiplier on the premium, not on the note. A collector holding out for a clean example of a number that exists in nine copies will wait. An about-uncirculated note keeps roughly 60% of the premium, a circulated one 30%, and a worn one 12%. The face value underneath never falls.
The bands are wide because the market is thin. A given pattern may see a few dozen comparable sales in a year, spread across denominations and grades. We will not quote a point estimate, because on this data a single number is a fabrication. Completed eBay sales and the Heritage Auctions archive are where an actionable price comes from, and the tool says so in its own output.
Star note print-run data
Star notes are replacements, printed to replace sheets spoiled during production. Whether a particular star note is scarce depends entirely on how many notes were printed in its run, which the Bureau of Engraving and Printing publishes monthly. The star note lookup is built on the index described below.
| Source | BEP Monthly Production Reports (public domain) |
|---|---|
| Star runs indexed | 582 |
| Denomination + prefix keys | 220 |
| Series covered | 1999–2025 |
| Runs parsed but withheld | 74 |
| Scarcity threshold | 640,000 notes |
BEP output is a US Government work, public domain under 17 U.S.C. §105. The ingest re-runs monthly and fails if parse quality drops below 95% clean, which is how a change to the BEP's report layout surfaces before it corrupts a published serial range. The 74 withheld runs are rows the parser could not read unambiguously. They are dropped rather than guessed at.
Run size alone does not mean scarce
A run of 640,000 notes or fewer is the collector threshold, but a small run is only genuinely scarce if no larger run exists for the same denomination, series and district. When a large run exists alongside it, buyers simply source from the large one and the small run's premium never materialises. Sites that grade on run size alone end up calling a 3,200,000-note run "scarce" — that is the maximum possible run size, which is to say the most common thing there is.
Where the data stops
The BEP's online archive begins with fiscal year 2003, and the indexed data covers series 1999 to 2025. Star runs for series 1976 through 1998 would have to be hand-compiled from printed references, and they are not in this dataset. If you look up an older note the tool will tell you it has no coverage rather than return a confident wrong answer.
Stating this is not modesty. Collectors find gaps like this on their own, and finding it themselves is what destroys a reference site's credibility. The coverage page breaks the boundary down by denomination, district and series, and lists every other gap we know of.
What this site will not do
- Quote a single price. Ranges only, always scaled by denomination and condition, always with the caveat attached.
- Appraise, buy or broker. There is no valuation service here and no dealer relationship behind the numbers.
- Tell you a common note is exciting. When the answer is face value, the tool leads with "worth face value".
- Guess at missing data. Unreadable rows are dropped, and an ambiguous star lookup returns every candidate rather than picking one.
Found an error in a derivation or a print-run figure? Corrections that come with a citation are worth more to this site than any feature, and they get applied in the next build.