Stacking a column for a later chain

Reward the search for building columns that are one quiet drop away from collapsing in several waves. The idea is that a policy which deliberately stores energy — instead of cashing chains as soon as it can — will have something to spend when the board gets tight. A cheap survey said the idea was worth a coefficient; transferring that coefficient to the full search did not work.

Two records sit behind that label: the cheap survey is completed — ledger-recorded diagnostic, and the transfer into the real search is rejected — ledger-recorded.

The intuition, on a real board

A disc clears when the unbroken line through it — along its row or its column — is exactly as long as its number. So a column's height is a trigger: change the height, and different discs in it become live.

Here is a column of three discs that is completely inert. Nothing in it matches its run length, so it can sit there indefinitely. Drop one 4 on top, and it takes itself apart:

That is stored energy: a structure whose value is not visible in the score, only in what one future drop can do to it. The feature tested here measures exactly this, and deliberately measures it conservatively: for each visible column it simulates adding inert discs and repeatedly removes any numbered disc whose value equals the resulting column height, giving a bonus for multi-wave collapses and discounting by how many additions were needed to set them off. It ignores horizontal help and ignores covered-disc reveals — so it never counts energy it is not sure about.

How it works, step by step

1. Compute the ladder feature for the position: for each column, and for each possible number of inert additions, repeatedly remove numbered discs equal to the current column height. Multi-wave collapses get a quadratic bonus; each collapse is discounted by the number of additions needed to reach it.
2. Screen the coefficient cheaply. Add the feature to the evaluator at a range of weights and play 256 complete games with a two-move search, which is fast enough to sweep. This runs only on training seeds.
3. Freeze one weight — the single value that improved score, survival and both flow rates — and change nothing else.
4. Transfer it to the real search. The evaluator becomes the reference leaf plus 500 times the ladder energy; every legal column and every chance branch is still completed at four moves. Nothing is retuned after the transfer.
5. Play eight complete games on a disjoint training-only range against the unchanged search.

The implementation is worth one note: because a column's ladder value depends only on that column, every gravity-valid column state has a shared cache slot — 5,380,840 entries in 21,523,360 bytes — so the exact feature is computed once per distinct column rather than per board. A thousand fixtures proved the cache bit-exact against the direct feature.

What happened, in plain English

The cheap survey was mildly positive. Over 256 two-move games, a weight of 500 raised the average score from 98,642 to 103,467 and average survival from 68.8 to 71.6 moves, with both flow rates improving and both halves of the ordered results improving. But the confidence bounds on the paired difference were still negative, the lower quartile of score actually slipped, and every larger weight tested — 1,000 through 4,000 — was harmful. The ledger is explicit that this was a coefficient-selection signal, not qualification evidence.

The transfer failed. Inside the four-move search on eight fresh training-only games, the unchanged search averaged 124,934 points and 83.9 moves; with the ladder term, 121,849 and 82.1. It won four of eight games on score and four on survival — a coin flip. Its clear and reveal rates per move went up, to 1.933 and 1.061, and that extra throughput simply did not turn into longer games.

That last detail is the interesting one, and it recurs across this family: flow statistics moving in the right direction while survival does not follow. A policy can churn through more discs per move and still be arranging the board worse.

The technical record

Sources. d2-vertical-ladder-probe.cpp (completed — ledger-recorded diagnostic; "the shallow signal motivated a D4 transfer") and fair-vertical-ladder-depth4.cpp (rejected — ledger-recorded; "the shallow benefit did not transfer"), per the experiment index. Ledger section "Literal vertical-ladder energy".

Scoring mode. Neither section carries a scoring label; audit 03 classifies all four means below as historical 7,000-point Sequence scoring. Score and survival regressed together in the transfer, so rescoring widens the gap.

Coefficient sweep — 256 training games 0x3d9e0000...00ff, two-move search, 1,000-move cap:

Arm	Mean score	Mean moves	Clears / move	Reveals / move	Score Q25
No ladder term	98,642.29	68.77	1.84857	1.00034	61,074
Weight 500	103,467.46	71.59	1.87227	1.01855	60,739

Paired 95% lower bounds −3,032 points and −1.995 moves. Weights 1,000–4,000 were harmful. Weight 500 was the unique fixed choice for transfer.

Transfer — eight training-only games 0x3d9f0000...007, full-width four-move search:

Arm	Mean score	Mean moves	Score Q25	Move Q25	Clears / move	Reveals / move
Unchanged reference	124,934.38	83.875	90,673	65	—	—
Reference + 500 × ladder	121,848.63	82.125	82,277	58.75	1.93303	1.06088

Paired change −3,085.75 points and −1.75 moves, 95% lower bounds −56,964.47 and −35.259; 4 of 8 score pairs and 4 of 8 move pairs won. All games uncensored. Four-move work 2.709 million units per candidate move; peak resident memory 37,011,456 bytes under a 128 MiB cap. The D2 audit took 84.230 seconds and the D4 cohort 844.028 seconds. No seed outside these two ranges was opened and no model was retuned after transfer. Artifact /tmp/drop7-fair-vertical-ladder-depth4.json, SHA-256 db6b6b6bb2214317200f4ead1e0243e88da797b0444fac479a79099d21326e93; source hashes a41c6562e1f360a8fde29af2ff74f34b50498f4fec5806bd57e8f539ee4dac8c (probe) and 098f95201d8e8ba3daebe2c75eb4de0d00ff10f120dc1f9ad924efc94dbe15b7 (transfer).

Verification. Optimised strict -Werror builds and the ASan/UBSan self-test passed inherited engine parity, deterministic and reflection-safe actions, metadata blindness, full-width completion, exact cache equality with the direct feature, legality, seed bounds and resource proofs.

What this taught us, and what is still open

The clean lesson is about method, and it is the second time this family learned it: a signal measured with a cheap shallow search does not automatically survive being put inside a deep one. A two-move search has a poor idea of the future, so an evaluator term that supplies some of that idea helps it. A four-move search already simulates two more moves of the same future, so the same term is partly redundant — and where it is not redundant, it competes with what the search actually computed.

The idea being tested is not refuted, only this way of expressing it. The feature is deliberately conservative: it ignores horizontal clears and ignores covered-disc reveals, which are two of the main ways stored energy actually gets released. And the transfer used a coefficient chosen at a different depth, which the machine-tuning experiment also found does not carry across.

Related work elsewhere in the repository points the same direction without resolving it: a constructive planner that builds towards reachable high-number reservoirs across a rise cycle materially beat the one-move fair policy and is a useful fast continuation, but did not beat the four-move search (completed — ledger-recorded, see the experiment index). The status summary records the standing judgement: stored structure looks useful as a feature or an option, not yet as a controller.

Sources

• d2-vertical-ladder-probe.cpp — training-only falsification lab for a literal form of stored chain energy; ignores horizontal help and covered-disc reveals, so it is a conservative description of energy already in the visible column rather than a clairvoyant cascade simulation.
• fair-vertical-ladder-depth4.cpp — the frozen coefficient of 500 inside the four-move search; the leaf is the reference leaf plus 500 times the conservative ladder energy, with every legal action and chance branch completed.