THE FOLD / GLITCH / UNDEFINED BEHAVIOR / THE MONTY HALL
THE MONTY HALL
a game show where switching doubles your odds
1 WHAT IT IS · WHAT IT DOES · FACT OR FICTION
The Monty Hall problem is the most famous counter-intuitive result in probability. You pick one of three doors; behind one is a car, behind the others goats. The host — who knows where the car is — opens a different door revealing a goat, then offers you the chance to switch. Should you? Yes: switching wins 2/3 of the time, staying only 1/3. Your first pick is right 1/3 of the time, so the other door hides the car the remaining 2/3 — and the host’s reveal concentrates all of that onto the single unopened door. It scales: with N doors and one goat revealed, switching to a random remaining door wins (N-1)/(N(N-2)).
LIT verified live: a Monte-Carlo simulation gives switch ≈ 2/3 and stay ≈ 1/3 for three doors, and matches (N-1)/(N(N-2)) for four and five doors (window.__montyhall). FIG no framing; the game is simulated with a fair random generator independently in-browser.
LIT verified live: a Monte-Carlo simulation gives switch ≈ 2/3 and stay ≈ 1/3 for three doors, and matches (N-1)/(N(N-2)) for four and five doors (window.__montyhall). FIG no framing; the game is simulated with a fair random generator independently in-browser.
2 HOW IT WAS WEAVED · AI + HUMAN
David (human) seated this at undefined-behavior — the glitch in intuition: the odds seem 50/50 after a door opens, yet switching quietly wins twice as often. AVAN (AI) built the instrument: the three-door simulation, the 2/3-vs-1/3 split, and the N-door generalization.
Credit as content: the Monty Hall problem (Steve Selvin, 1975; popularized by Marilyn vos Savant, 1990). The weave: David names the intuition-glitch; I confirm switching wins 2/3 and the N-door formula.
Credit as content: the Monty Hall problem (Steve Selvin, 1975; popularized by Marilyn vos Savant, 1990). The weave: David names the intuition-glitch; I confirm switching wins 2/3 and the N-door formula.
3 ONE DIMENSION
The three doors: your pick, the host's reveal, and the two outcomes — switch (2/3) vs stay (1/3).
4 TWO DIMENSIONS · INTERACTIVE
Run more trials; the switch-win rate settles on 2/3 (and the N-door rate on its formula).
5 THREE DIMENSIONS + AVAN’S INVERSE
The green forward object: the 2/3 win rate from switching.
AVAN’s addition (the inverse-companion): don’t re-price the two closed doors as 50/50 — track where the 2/3 went. The inverse of ‘your 1/3 first pick’ is ‘the other 2/3, swept by the host onto the one unopened door’. Magenta is the stay probability (1/3); green is the switch probability (2/3) it complements. The host’s reveal hands you the better two-thirds.
LIT Genuine Monty Hall problem (Steve Selvin, 1975; popularized by Marilyn vos Savant, 1990). Verified live: a Monte-Carlo simulation gives switch ≈ 2/3 and stay ≈ 1/3 for three doors, and matches (N−1)/(N(N−2)) for four and five doors (window.__montyhall.ok).
FIG No framing; the game is simulated with a fair random generator independently in-browser. The AVAN inverse is honest — instead of re-pricing the two closed doors as 50/50, track where the 2/3 went: the inverse of 'your 1/3 first pick' is 'the other 2/3, swept by the host onto the one unopened door'. Magenta is the stay probability (1/3); green is the switch probability (2/3) it complements. The host's reveal hands you the better two-thirds.
FIG No framing; the game is simulated with a fair random generator independently in-browser. The AVAN inverse is honest — instead of re-pricing the two closed doors as 50/50, track where the 2/3 went: the inverse of 'your 1/3 first pick' is 'the other 2/3, swept by the host onto the one unopened door'. Magenta is the stay probability (1/3); green is the switch probability (2/3) it complements. The host's reveal hands you the better two-thirds.
◆ sealed .dlw.fold → folded to ROOT_0 · a sphere of UNDEFINED BEHAVIOR · David Lee Wise (ROOT0), with AVAN