THE FOLD / BOSS / THE GAUNTLET / THE NEWTON–PEPYS
THE NEWTON–PEPYS
the shortest gauntlet
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
In 1693 Samuel Pepys — diarist, Navy man, gambler — wrote to Isaac Newton with a wager question: which is likeliest, at least one six in 6 dice, at least two sixes in 12, or at least three in 18? Intuition says they’re equal (each asks for the ‘fair share’ of sixes) or that more dice help. Newton answered: the first, and it isn’t close — P = 31031/46656 ≈ 0.665 vs 0.619 vs 0.597. The mean number of sixes scales perfectly, but the variance spreads the larger pools across more failing configurations. Pepys, betting on the third option, reportedly disliked the answer.
LIT verified live: all three probabilities computed as exact rationals with BigInt binomials — P(A) = 31031/46656 exactly; A > B > C by exact cross-multiplication, no floats in the verdict; 200k-roll Monte Carlo agrees within 0.005 (window.__pepys). FIG the correspondence is documented (three letters, 1693); Stigler’s analysis argues Newton’s reasoning was partly wrong even though his answer was right — we cite that honestly rather than polishing the legend.
LIT verified live: all three probabilities computed as exact rationals with BigInt binomials — P(A) = 31031/46656 exactly; A > B > C by exact cross-multiplication, no floats in the verdict; 200k-roll Monte Carlo agrees within 0.005 (window.__pepys). FIG the correspondence is documented (three letters, 1693); Stigler’s analysis argues Newton’s reasoning was partly wrong even though his answer was right — we cite that honestly rather than polishing the legend.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at the-gauntlet — the boss: three doors, each a longer corridor demanding proportionally more hits — and the SHORTEST corridor is the softest boss, because long corridors let variance drown you. AVAN (AI) built the instrument: the BigInt exact-rational engine and the dice-roller cross-check.
Credit as content: Samuel Pepys & Isaac Newton (1693 letters); Stephen Stigler (the modern audit of Newton’s reasoning). The weave: David names the gauntlet; I count every one of the 6¹⁸ corridors exactly.
Credit as content: Samuel Pepys & Isaac Newton (1693 letters); Stephen Stigler (the modern audit of Newton’s reasoning). The weave: David names the gauntlet; I count every one of the 6¹⁸ corridors exactly.
3 ONE DIMENSION
Three wagers, exact rationals — the short gauntlet wins.
4 TWO DIMENSIONS · INTERACTIVE
Roll the three pools; the tallies track the exact values.
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the three corridors, doors thinning with depth.
AVAN’s addition (the inverse-companion): don’t scale the target with the army — count the ways to miss. The inverse of ‘fair share’ thinking is variance thinking: doubling dice doubles the expected sixes but more than doubles the arrangements that fall short of quota. Magenta is the intuition that all three are equal; green is the exact count that says take the short fight. When a wager scales ‘proportionally,’ audit what the variance did.
LIT Verified live: all three probabilities as exact BigInt rationals — P(A) = 31031/46656 exactly; A > B > C by exact cross-multiplication, no floats in the verdict; 200k-roll Monte Carlo agrees within 0.005 (window.__pepys.ok).
FIG The three 1693 letters are documented; Stigler's analysis argues Newton's reasoning partly wobbled even though his answer was right — cited honestly, not polished. The AVAN inverse — count the ways to miss, not the fair share: doubling dice more than doubles the arrangements below quota. Magenta is the equal-odds intuition; green is the exact count. Take the short fight.
FIG The three 1693 letters are documented; Stigler's analysis argues Newton's reasoning partly wobbled even though his answer was right — cited honestly, not polished. The AVAN inverse — count the ways to miss, not the fair share: doubling dice more than doubles the arrangements below quota. Magenta is the equal-odds intuition; green is the exact count. Take the short fight.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of THE GAUNTLET · David Lee Wise (ROOT0), with AVAN