dice · φ⁻4 · hue 2 · 6

Monty Hall — switching wins 2/3

discoveredTheoremsWaveThirtyEight · src/9/1 · finite-complete

9/1 finite-complete self-contained anim/dice

Theorem.Monty Hall — switching wins 2/3 — P(win | switch) = 2/3 and P(win | stay) = 1/3.

Proof.exhaustive over the 9 equally-likely (car, pick) pairs: switching wins precisely when the first guess was wrong (2/3), staying 1/3 — the counterintuitive result computed, with the correct probability model.

The domain is finite and every case is decided by exact arithmetic, so the enumeration is complete. ∎

src/9/1/index.ts#discoveredTheoremsWaveThirtyEight

1 · Classification

finite-complete — self-contained computation, no external lean

2 · Provenance

Documented theorem re-derived by exhaustive computation (humanityNovel=false); first-in-this-registry is the only sense of discovered.

Acknowledgment

"Monty Hall — switching wins 2/3" is a re-derivation, acknowledged to documented mathematics — the original proof is the prior art this re-derivation acknowledges; not new to humanity — the contribution is the reproducible computation discoveredTheoremsWaveThirtyEight.

Prior art: documented mathematics — the original proof is the prior art this re-derivation acknowledges
Novelty: not new to humanity — a re-derivation (humanityNovel = false)
Contribution: a reproducible computation (discoveredTheoremsWaveThirtyEight @ src/9/1) that re-derives the result at zero tokens — the contribution is the verifiable recomputation, NOT the theorem

3 · Reproducibility

Recompute from source: npm run theorems:verify recomputes discoveredTheoremsWaveThirtyEight (src/9/1/index.ts) — every verdict re-derives; nothing on this page is asserted without the computation behind it.