No level in this project is more than a third pieces — 13% to 28% across the
shipping fifty, and the thousand-level set that preceded it peaks at 32% with
exactly one level above 30%. Clearing a full board is the satisfying part of a
clearing game, and it has never been on offer.
It was not a design choice. deadTurnAudit walks the reachable state space with a
20000-state budget, and the endgame gate read its answer. Past about eleven
pieces that budget is gone long before the walk reaches any state with three
pieces left, so the audit returned `endgameMinOpen: null` — and the gate,
written `endgameMinOpen >= 2`, compared null and got false. Every denser level
was thrown out for a bad endgame that was never looked at. `exhausted` was right
there in the audit's return value and nothing consulted it.
Endgames are now enumerated outright rather than walked to: C(26,3) is 2600
subsets, so it finishes on any board this game will ever have. The statistic is
the SHARE of endgames that are tight, not the minimum over them, because a
minimum over more subsets falls for arithmetic alone — the same confound that
made doubleDead look eight times worse for deep levels when the rate was 2%
against 5%. By share, crowded boards are the better ones: worst 0.33% against
1.73% for sparse.
With the gate measuring something, density inverts. At eight pieces per
orientation: 44% density, 18 of 23 candidates passing the whole chain, and not
one failing the dead-turn gate. At two: 19% density, 9 of 23, with eleven
failing on dead turns. perTurn becomes a swept dial, and the hard piece ceiling
that truncated the placement schedule regardless of it is gone.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Round 1 played all fifty levels and came back with the mechanics clean and one
complaint repeated across the reports: 短暂以为转错了方向 — a turn that changed
nothing. That one is mechanical rather than perceptual, so it can be gated.
The first attempt gated `doubleDead`, and it was wrong. That counts dead states,
which scales with the state space: three-turn levels have ~187 reachable stuck
states and five-turn ones ~739, so a raw count made deep levels look eight times
worse when the rate is 2% against 5%. It would have erased every level past
three turns — the opposite of the brief, where turning is the signature and is
not to be rationed. The gate is `maxDeadTurns`, the longest run of turns before
something opens, at 1: one beat of suspense, then a release. Eleven of the fifty
shipped at 2.
Selection could not express the curve either. Spreading picks evenly over the
ranked pool returns whatever the pool is made of, and the pool is 88%
three-turn, so no weighting moved the distribution off {3: 46}. A quota per
depth states the curve outright, deepest first so the scarce end picks before a
family cap is spent on levels the shallow end has hundreds of.
Same rule bot, both sets: blind rotations 0.24 → 0.12, worst blind streak 4 → 1,
decisions unchanged at 10.3. The same amount to do, half the wasted motion.
Rotation now runs 1.8 / 3.0 / 4.1 across the bands against 1.8 / 3.0 / 3.5.
Verdicts are keyed by the board rather than by its id, because a reselect
re-issues ids from the ordinal and `c50-01-v05` is not the same board before and
after — the review sheet was one reselect away from printing one level's verdict
under another's thumbnail.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
