True randomness clumps; evenness is the fingerprint of design.
Precise claimIndependent fair random trials are expected to clump: in 100 fair coin flips a run of 6 or more of the same face appears with probability about 81% (exactly 80.68%), so a sequence with no long runs is evidence of editing rather than proof of it.
Applies
Exact probabilities for independent fair Bernoulli trials, recomputed independently; the page's live sequences come from crypto.getRandomValues and a documented streak-suppressing algorithm, and the same statistics are applied to the visitor's own typed sequence.
Does not prove
Streak statistics cannot prove a particular sequence is random or rigged — short-run sequences occur by chance — and the page makes no claim about any specific commercial shuffle algorithm's current implementation.
Portable rule
If a sequence is claimed to be random, then check its clumps before its averages — long runs point to chance, suspicious evenness points to an editor.
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randomness-illusion
Can You Tell Real Randomness From Fake?
Two coin-flip sequences: one truly random, one arranged to look random. Call which is real, then type your own flips and let the streak statistics judge whether you faked randomness convincingly.
Two coin-flip sequences, 60 flips each. One was generated by a true random number generator in your browser the moment this page loaded. The other was arranged to look random. Which one is truly random?
Sequence ASequence B
One pick locks it in. No “can’t tell” on this page — the streaks are the test.
The reveal
Independent fair random trials are expected to clump: in 100 fair coin flips a run of 6 or more of the same face appears with probability about 81% (exactly 80.68%), so a sequence with no long runs is evidence of editing rather than proof of it.
Your call and the truth appear here the moment you commit above.
Sequence ASequence B
If you picked the even one, you did what almost everyone does: you read “no pattern” as “no clumps.” But clumps are exactly what independent chance produces.
In 60 fair flips a run of 4 or more of the same face appears 99.19% of the time. In 100 fair flips a run of 6 or more of the same face appears 80.68% of the time (heads alone: 54.61%). The arranged sequence caps its runs at 2 — that cap is the fingerprint.
True randomness clumps. Evenness is the fingerprint of design.
The random side is redrawn live from crypto.getRandomValues — never prerecorded. Your original pair above stays as you judged it, and which side holds the true random sequence was reassigned at random when this page loaded.
The rebuilt model
You assumed:
A genuinely random sequence should look evenly spread — no long streaks, frequent alternation, roughly half and half.
The actual model:
Chance has no memory and no editor: each flip is independent, so long runs occur with high, exactly computable probability; suppressed runs and over-frequent alternation are signatures of a generator that edits out clumps.
The variable that failed you:
Who generated the sequence — independent chance, or a process (a person or an algorithm) that edits out clumps.
Change one variable
One variable changes: the generator. The page’s two generators step aside — your own fingers type 40 flips that you think look random.
Everything else stays fixed: the same longest-run and alternation measures, with chance thresholds corrected for the shorter length. Fair 40-flip sequences show a run of 4 or more 95.66% of the time and top 60% alternation only 9.98% of the time.
Click this pad or tab to it, then type: H heads · T tails · ⌫ undo. The buttons below work too.
0 of 40 flips
Longest run
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Alternation
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Balance (heads : tails)
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Boundary: this detector flags editing; it never certifies a single sequence. Fair 40-flip sequences fail the run check 4.34% of the time and the alternation check 9.98% of the time. Streak statistics describe generators, not people.
The run-length mathematics of fair coin sequences, including detecting an invented sequence by its too-short longest run; page probabilities were recomputed independently from this model.
The documented default misperception of random sequences — people expect more alternation and fewer streaks than independent chance produces.
paper — checked 2026-07-20.
Scope: Exact probabilities for independent fair Bernoulli trials, recomputed independently; the page's live sequences come from crypto.getRandomValues and a documented streak-suppressing algorithm, and the same statistics are applied to the visitor's own typed sequence.
Does not prove: Streak statistics cannot prove a particular sequence is random or rigged — short-run sequences occur by chance — and the page makes no claim about any specific commercial shuffle algorithm's current implementation.