Coin Flips

Biased or fair, showing the longest run against the expected log₂ n.

numbers.coin · v1 · renderer text

TTHHTTHTTT HHHHHTHHTH THHHHHTHTH HHTTTHTHHT TTTTTHHHTH THTHTHHTHT THHHTTHTHH THHTTHHHHH THTHTHTTHT HTHTHHHTTH

Controls · from schema()

Flips

1 10000

P(heads)

0 1

A fair coin is 0.5. Bias it and watch the longest run of heads grow much faster than the head count does.

Faces

Group every

0 50

Insert a space every n flips so the sequence can be read. Zero runs them together.

Entropy source

Picking a source changes the story on the receipt, never the quality: anything below class A is mixed with the OS CSPRNG before it reaches you. This result actually came from Operating System CSPRNG.

seed token R866XG43Q8WFZWEJPG6NF7SYXG

Re-render keeps this token. Generate replaces it. That is the whole idea.

entropy in

16 bytes

stream used

700 bytes

entropy out

100.0 bits

rejections

duration

279 µs

heads

tails

heads fraction

0.55

longest head run

longest tail run

expected longest head run

5.98

longest run spread

1.85

alternations

expected alternations

49.50

Seed receipt

Class A · Cryptographic degraded

Drawn from the kernel entropy pool on the server that rendered this page. (The source you picked was unreachable, so we fell back to the kernel.)

source: Operating System CSPRNG
observed: 2026-09-14T17:22:20+00:00
latency: 1505ms
mixed with: nothing — this source stands alone

This source publishes no per-draw proof URL.

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The token is the seed, so this link recomputes the result rather than looking it up. No database, and it works for as long as v1 does.

This page and /api/v1/g/numbers.coin run the same code. There is no private endpoint.

Coin Flips

Result

Measurements

Seed receipt

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