Coin Flips

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

numbers.coin · v1 · renderer text

HTTHHHHTHT HTHHTTHTHT HTHTTTTHTH THHHHHTHHH TTHTTTTTHT HTTHHTHTTT TTHHHHHTTT HHTHTHHHTH HTHHHHTHTT HTHTTHHHHH

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 Bitcoin Proof-of-Work.

seed token 7FGRHW3EPJ300SCXBB8FMHDKT4

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

391 µs

heads

tails

heads fraction

0.54

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 B · Public beacon

Bitcoin block 973,812 — 19 leading zeros of proof-of-work, found about ten minutes ago.

Published openly — anyone can look this value up after the fact.

source: Bitcoin Proof-of-Work
observed: 2026-10-30T11:15:39+00:00
latency: 978ms
mixed with: csprng — always

https://mempool.space/block/00000000000000000001437feed9aae961c1ad1a4747d5b76de354fe6846c2cf ↗

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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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