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Do Random Events Cluster?

By Alex Korablev · Statistics · Probability Simulation · Graduate · Simulation of a known property · version 4

Students test Pinker's claim that random events cluster through a star-field game, coin-flip streaks, sample-size histograms and a kidney-stone Simpson's paradox case.

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Licence: CC BY 4.0

Topicsclustering illusionruns in coin flipslaw of small numberssimpson's paradox

Assumption ledger

  • parameterStar fields have 85 points in a 300 x 300 square; the fake field enforces a minimum spacing of about 26 units, relaxed if stuck
  • distributionCoin flips are independent fair Bernoulli(0.5) draws; star positions are uniform
  • parameterStreak experiment uses 100 flips per experiment; histogram uses 1,000 samples of n from 5 to 500
  • dataKidney stone counts are the classic published study figures (273/350 vs 289/350 overall)
  • simplificationAll randomness is seeded: star fields, coin experiment number k and each histogram draw are pure functions of the shared seed and the counters in state (round, flips, n, draws), so every teammate sees the same results
  • interpretationShared state holds only inputs: seed, round, star-field picks, coin-run guess, number of coin experiments run, sample size n, histogram redraw count, kidney-stone pick and written answers. Scores, averages, verdicts, grids and histograms are derived on every render

Breakout check

Not checked yet.

Built-in checks 8 of 8 pass

  • sideFor is deterministic for a seed and round (passes)
  • random field falls on side A about half the time (passes)
  • picking the right side scores every round, the wrong side scores none (passes)
  • setState(getState()) leaves state unchanged (passes)
  • seeded random field has 85 points inside the square (passes)
  • longest run of a known sequence is 3 at positions 2 to 4 (passes)
  • coin experiment k is a deterministic function of seed and k (passes)
  • histogram draw is deterministic and has 1,000 samples (passes)

Cite this

Alex Korablev (2026). Do Random Events Cluster? [Interactive model], version 4. Ideas at Play. https://ideasatplay.org/play/do-random-events-cluster-9f6544?v=4 (CC BY 4.0)

History

  1. v4Coin flips, the histogram redraw button and the sample-size slider are now seeded and stored in shared state (new keys flips, n, draws), Reseed resets them, and written answers remain in state as before. (generated, Oct 20, 2026)current
  2. v3Star-field picks, score, kidney-stone pick, coin guess and written answers now live in one shared state (with seeded star fields, a reseed control and the window.artifact interface), so teammates see the same answers and feedback; browser storage was removed. (generated, Oct 20, 2026)View
  3. v2Darkened the faint text colour to meet 4.5:1 contrast and added an aria-label to each star-field SVG; nothing else changed. (generated, Oct 19, 2026)View
  4. v1Imported; lineage before import is not available. (imported, Oct 19, 2026)View

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