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>
Playing on a phone, the boards read as a grid of long straight lines crossing
everywhere — "一看到这个画面，我脑袋就大". The cause is one line in the filler.
Each family lays its signature routes over part of the board and leaves the rest
to completePorts, which paired every leftover port with the one straight across.
On a switchback board that made 76% of all track pairs diameters and left 43 of
61 cells containing nothing but diameters. Two diameters in one cell always
cross, so the straightness and the crossings were never two problems.
Preferring a bend halves both, in every family: switchback 76% → 40% straight
and 2.38 → 0.92 crossings per cell, crossing 86% → 10%, weave 37% → 5%.
It was also quietly suppressing 反差, the swing between a piece looking hopeless
and becoming trivial, which the design brief calls the point of the game.
Straight routes barely change between orientations. With bends, petals goes from
4.2 to 14.0 and crossing from 4.8 to 28.8 — both had been failing the ≥12 gate
and were absent from the level pool entirely. Petals is the family the user
singles out as the good-looking one. Generation yield rises with it: four seeds
now grow 24 playable levels against 3, at greater rotation depth.
createRouteBoard keeps 'straight' as its default so nothing already built moves;
the sweep opts in. labs/route-gallery draws both, with the real renderer, so the
choice is made by looking rather than by reading a number.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
