Hand-built heuristics and shallow search

Give points to the things about a board that a human would notice — low stacks, open columns, gray discs you can reach, numbers that are nearly ready to clear — add them up, and play the column with the best total.

That is the whole family. It is the oldest idea in the repository, the easiest to explain, and the one that everything else is built on top of: these weighted sums are the leaf evaluators at the bottom of every deeper search and the quick continuation policies inside every rollout. When a large learned system fails here, the post-mortem almost always ends with a sentence about features.

The intuition, on real boards

Every figure below is the repository's own rules engine playing a scripted game: the boards, the points, the clears and the reveals are engine output, not drawings. Each one shows a real position and what two of its seven legal columns actually do.

"Open the board"

Twenty-eight of the forty-nine cells are occupied and twenty-three of those are covered gray discs whose numbers nobody can see. Five drops remain before the next rise adds seven more.

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Next disc: 5

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Column 5

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Next disc: 5

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Column 1

Two features do that work: how tall the stacks are, and how many gray discs are still closed. Both are things a human notices in a second, and both are literal terms in the hand evaluator in src/core/typescript/heuristic.ts.

"Prepare useful chains"

Sometimes only one column does anything at all. Here the engine reports that six of the seven legal columns score zero, and the seventh scores 770.

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Next disc: 6

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Column 2

Where the idea starts to strain

The three jobs (stay alive, open the board, prepare chains) pull against each other, and a weighted sum has to settle the argument with fixed numbers. Here is a position where they disagree. It is three drops from a rise.

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Next disc: 7

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Column 5

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Next disc: 7

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Column 4

Which is right? Nobody in this repository knows. The evaluator traded 141 points and one extra reveal for one row of height, because that is what its fixed weights say height is worth. Deciding such trades correctly is the entire research problem, and it is the reason the family's later members stop being pure feature sums and start looking one, two, or several moves ahead.

How a policy in this family works, step by step

1. Read the public position. The visible board, the visible next disc, and the rise clock. Nothing else, not the seed, not the hidden gray numbers, not the score. (One member of the family breaks this and is flagged where it appears: see gray throughput.)
2. Simulate each legal column with the real rules engine. Every disc that clears, every gray disc that cracks or reveals, every wave of the chain.
3. Measure the resulting board. The hand evaluator counts open columns, a squared height load, solid and cracked gray cells, numbered cells, discs that are one addition away from clearing, latent chain potential, gray discs exposed to a future clear, and clogging patterns such as adjacent 1s and triples of 2s.
4. Add it up with fixed weights. Positive for open columns, ready structure and exposed covers; negative for height, buried gray discs and clogs; a flat large penalty for a modelled game over. What such a leaf evaluator can and cannot see is its own subject.
5. Optionally look further. Members of this family extend step 4 in four different directions: average over the possible next discs (sparse expectimax); play the position forward with a quick policy (rollout); commit to a whole sequence of columns before seeing the discs (open loop); or weight the bad outcomes more heavily than the good ones (risk sensitive).
6. Play the winning column. Ties are broken by a fixed order, so the same visible position always produces the same move.

Everything the searching members do at chance points, including averaging rather than hoping — is explained on the choice-and-chance concept page.

What happened

These policies were fast, they were easy to reason about, and several of their features survive today inside the reference search's leaf. As complete policies they were brittle. Weight-fitting runs repeatedly improved the games they were fitted on and then gave the gain back on fresh games, and no hand-built policy tested here displaced the depth-4 reference search (research status, §2 and the compact evidence map in the strategy catalog).

The single most useful thing the family produced is not a policy at all. It is the observation that immediate score is a poor guide: in this mode score is very nearly survival time, and what a long game needs is a steady rate of clearing numbered discs and opening covered ones. Two evaluators in src/core/typescript encode the arithmetic directly — five drops arrive per cycle, a rise adds seven covered discs, so a board that never fills needs about 2.4 numbered clears and 1.4 covered reveals per move.

Technical recordopen ↓close ↑

What is in this family, and how strong the evidence is. Statuses and evidence labels are copied from the experiment index ("Heuristic and rollout search") and, where marked, the experiment history.

Approach	Status	Evidence
Sparse expectimax	completed	task-record only
Open loop	support-only	repository-verified
Phase horizon	rejected	task-record only
Tunneling	completed	task-record only
Virtual ignition	rejected	task-record only
Risk sensitive	rejected	task-record only
Policy comparison	support-only	repository-verified
Gray throughput	rejected	task-record only
Rollout	rejected (planner) / completed (teacher)	task-record only
Cycle abstraction	rejected	task-record only
Edge priority	unknown	repository-verified
Critical risk	unknown	repository-verified
Evolution	rejected	ledger-recorded
Evolved public policy	rejected	ledger-recorded
Exact search	rejected (quadrature, historical D4) / completed (ensemble)	ledger-recorded / task-record only

A scoring caveat that applies to most of the older numbers. A 2026-08-15 audit found that several early experiments had used the 7,000-point level award from the 30-drop Classic/Sequence rules instead of the 17,000-point award of the five-drop Hardcore mode studied here. Runs that record levelBonus: 7000 remain valid evidence that one policy beat another on the same games, and valid evidence about cost, but their absolute scores are not evidence for the Hardcore million-point target (mode-specific scoring correction). Every page in this family says which of its numbers are affected.

The ledger-recorded results in this family, in one place:

• Engineered-feature evolution — three families of evolved one-step action scorers, all rejected. The small nonlinear network fitted 96.86% of 255 training actions but only 43.40% of 235 disjoint teacher actions, then lost its four-game screen 148,349.25 to 307,222.75 points. The phase-weight vector lost its eight-game screen 105,534.875 to 107,709.75. Both are historical 7,000-point Sequence-scored runs.
• Evolved public policy — corrected 17,000-point scoring, and the only member of this family measured under it. It improved its 128-game fitting tournament from 136,169.15 to 157,528.50 points, did not improve lower-quartile survival at all, and its best selective-search wrapper reached 272,605.13 points on eight reused fitting games. Rejected before the probe cohort was opened.
• Exact search: a three-member root-quadrature ensemble passed a four-game screen and then lost its eight-game confirmation 117,066.5 to 162,492.125 while using about three times the work per move; a fully completed extra ply with the older leaf lost its screen 124,172.25 to 149,621.25 at about 24 times the cost. Both historical 7,000-point Sequence-scored runs.

What this taught us, and what is still open

• Interpretable features earned their place as ingredients, not as policies. Height danger, reveal flow, build readiness and the timing of a rise all matter, and all of them survive inside the reference search's leaf. The strategy catalog's recommendation is to keep them as diagnostics and leaf inputs, and not to treat a higher fitting score from another weight sweep as a result without a fresh, paired gate.
• Fitting a weight vector on games is the failure mode, not the method. Every evolution run in this family found plausible directions and then lost them on games it had not been fitted to. That is the same sibling-ranking problem that later defeated much larger learned models, arriving early and cheaply.
• A whole line of this family is unfinished, not refuted. Two labs — edge priority and critical risk — are complete, gated programs with no located outcome at all. The correct label is unknown, and running them is cheap.
• Human strategy advice has never been tested properly here. The strategy catalog's sixth open direction is to turn plausible human rules — high covered discs first, watch the weakly connected edge columns, build simple three- and four-wave chains — into reflection-safe public features and test them on preserved sibling panels before letting any of them control a move. The edge-priority lab is that experiment, waiting to be run.