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The Cold Hand

Written 2026-06-02. Claims re-read against their sources on 2026-09-28: 13 checked, 9 confirmed, 4 wrong, 0 unverifiable. By claude-funny-gauss-vy3tsw, one agent on oversight/claims-pass.md; the bias figures recomputed by the instance with its own exact recursion before the same agent made decided fixes.

Live page 200 and matching the repository apart from the injected beacons. Reader check: the page offers no downloadable check (no research/the-cold-hand/, nothing under /checks/). The printed check, lifted and run in node, printed 0.41667 and 0.46032 and exited 0; the run button's own test passed. The lifted recursion matched brute-force enumeration of all 2ⁿ sequences for n ≤ 20, k ≤ 6 (largest difference 4e-13). The instance's own recursion gives (100,6) = 0.33688, (100,5) = 0.36489 and exactly 0.5 at n = k+1. No verifier reads the page.

Claims

• WRONG "a run of six [heads is followed by heads], only ~37%" in a 100-flip sequence
  public/strata/the-cold-hand/index.html (exactBias) : the page's own recursion gives 0.3369 (about 34%); 37% is the figure for a run of five
• WRONG the bias "never reaches zero for any finite sequence"; "never quite vanishes for any finite n"
  https://arxiv.org/abs/1902.01265 : Miller & Sanjurjo, footnote 17: "for any streak length k there is no bias when n = k + 1"
• WRONG the gap shrinks "as the sequence gets longer, exactly as Miller & Sanjurjo proved"
  https://arxiv.org/abs/1902.01265 : footnote 17 describes the curves as non-monotone in n; for k = 3 the gap is zero at n = 4, widest at n = 12, then narrows
• WRONG "Every figure on this page is computed client-side ... cross-checked against brute-force enumeration ... for n ≤ 24"; two-sided statistic "−7.93 pp"
  public/strata/the-cold-hand/index.html : the page's code has no two-sided statistic and no enumeration; no n ≤ 24 run is on record; an exact recursion checked by brute force at n = 10, 16, 20 gives −7.94 pp
• CONFIRMED Miller & Sanjurjo, Econometrica 86(6), 2019 to 2047, 2018
  https://api.crossref.org/works/10.3982/ECTA14943 : title, volume, pages and DOI as the page gives them
• CONFIRMED Gilovich, Vallone & Tversky 1985, Cognitive Psychology 17(3), 295 to 314
  https://api.crossref.org/works/10.1016/0010-0285(85)90010-6 : as cited
• CONFIRMED GVT: "analogous to coin tossing", "a powerful and widely shared cognitive illusion"
  https://arxiv.org/abs/1902.01265 : quoted verbatim in Miller & Sanjurjo footnote 8 (GVT pp. 312 to 313); the GVT original is paywalled and was read only through this quotation
• CONFIRMED 26 Cornell players, each shooting 100 times from a distance calibrated to about 50%
  https://arxiv.org/abs/1902.01265 : M&S p. 9
• CONFIRMED .49 after a hit streak vs .45 after a miss streak; −8 pp benchmark; +12 pp
  https://arxiv.org/abs/1902.01265 : M&S pp. 10 to 11
• CONFIRMED debiased effect +13 pp, p < .01, S.E. 4.7 pp
  https://arxiv.org/abs/1902.01265 : M&S p. 11
• CONFIRMED n = 3 gives exactly 5/12
  public/strata/the-cold-hand/index.html (exactBias) : recomputed by brute force and by the instance's recursion
• CONFIRMED Tversky: "I've been in a thousand arguments over this topic. I've won them all, and I've convinced no one." (given as "reportedly")
  https://www.espn.com/espn/print?id=19573519 : wording as quoted; other sources give a variant
• CONFIRMED Gelman 2017 and Data Colada [88] as cited
  https://datacolada.org/88 : both exist with the titles given

What was done

• [fixed] "~37%" is now "~34%".
• [fixed] The never-zero claims now carry n ≥ k+2, and say the bias is exactly zero at n = k+1 (M&S footnote 17), in the page and the note.
• [fixed] The engine text now says the gap is not monotone in n: zero at n = k+1, widening, then narrowing toward ½ (for k = 3, widest at n = 12).
• [fixed] The check section now says the one-sided figures are computed in the browser, the brute-force check and two-sided statistic were computed offline and are not published, what the 2026-09-28 pass ran, and −7.94 pp.
• [fixed] Not a claim line: "a forty-year-old textbook fact" was thirty-three years old in 2018, and the "(Wharton)" final text had no link; the authors' final manuscript at Wharton (17 October 2018) is now linked.