A learned survival estimate inside the reference search

Train a small network to predict how many moves a game has left, mix its opinion half-and-half into the reference search's hand-written board scorer, and test the prediction — written down in advance — that it would help more once the search handles luck exactly.

Why anyone expected this to work

A look-ahead search ends at boards where the game is not over, and it needs an opinion about each one: how promising is this? That opinion is the leaf evaluator, and in the reference policy it is nineteen hand-tuned structural terms about height, crowding and chain readiness. Almost every learning experiment in this repository has been an attempt to replace it — and almost all of them failed in the same way, which the sibling trap page explains.

This attempt has an unusual advantage. Because a Drop7 Hardcore score is 94% the flat bonus for surviving another row rise, and runs at about 3,400 points per move, a prediction of "how many moves are left" multiplied by 3,400 is already a score in real points — the same unit the search's own immediate-score term carries. Mixing it with the hand-written score is mixing two estimates of one quantity, not a score with an arbitrary index. The design is also deliberately blind to which move was played: the same function scores every legal successor inside the existing search, so it cannot take the shortcut that sank earlier models.

The catch is arity, and it turned out to be the whole story.

One 87-move game would take 6.7 hours of the entire machine and one 64-game arm would take 18 days. The premise that a three-million-parameter convolutional network can be the leaf of this search is false by three orders of magnitude, and that is the first result here.

How it works

1. Measure the budget first. Nothing in the repository recorded how many board evaluations a four-move decision actually performs, so a probe counted them over 30 real decisions before anything was trained.
2. Train the network that was specified anyway, export it to a versioned binary that runs with no PyTorch, no BLAS and no allocation on the hot path, and gate it: 4,096 real boards, a tolerance declared before the comparison, and — after a nasty surprise — a proof that the PyTorch reference repeats bit-for-bit before anything is compared against it.
3. Then train the model that can afford to play. A leaf has roughly one microsecond. That is an NNUE-shaped budget, so the student is NNUE-shaped: 8,902 binary features of which exactly 135 are active per board, gathered and summed rather than multiplied through a dense matrix. The features include 84 adjacent-pair features, because a disc clears when its number matches the length of the run it lands in, and a per-cell bag of features cannot see a run at all.
4. Blend, do not replace. The leaf becomes (1 − w) × hand_written + w × 3400 × predicted_lifetime. At w = 0 the code short-circuits to the hand-written leaf before the model is touched, so the comparison arm is the frozen reference bit-for-bit and costs exactly what the reference costs.
5. Choose w on a separate 32-game cohort, then freeze it and run the real comparison as a two-by-two: hand-written versus learned leaf, at five and at seven chance samples, 64 paired games each, on a cohort that tuning never touched.

What happened

The learned leaf helps — modestly, and where it was predicted not to. With the reference's five chance samples it is worth +39,105 points and +11.13 moves, winning 37 of 64 paired games, with a one-sided 95% bootstrap lower bound of +1,138: above zero, but only just. With the exact seven-sample chance estimator it is worth +17,281 points with a lower bound of −55,892 — unresolved.

The preregistered prediction is refuted, on its own stated rule. The prediction, written before any game was played, was that the learned leaf would help materially more at seven chance samples than at five, and the pass/fail rule was written with it. The measured difference between the two gains is −21,824 with a lower bound of −105,254: the effect is smaller where the prediction said it would be larger. By the rule fixed in advance this is a FAIL, and the finding says so plainly rather than reframing it.

The mechanism explains the refutation. Both an exact chance estimator and a learned leaf are ways of knowing more about what happens after the current move, and having bought that knowledge once, buying it again returns less. Seen from the other axis: making the chance estimator exact is worth +101,171 points with the hand-written leaf and only +79,347 with the learned one — the same substitution, 22% smaller. Extra look-ahead is processed through the chance average, so a biased average corrupts it; a leaf value is terminal, so it inherits the bias of the path that reached it but does not compound it.

The flow rates back the five-sample result and not the seven-sample one. At five chance samples the learned leaf raises numbered clears by 0.0342 and reveals by 0.0212 per move, which is what its +11.13 moves of extra lifetime predicts, and every reported quantile of the score improves. At seven samples the paired per-game flow changes are slightly negative. That is an independent reason — beyond its own confidence bound — to treat the seven-sample gain as unresolved rather than as a smaller real effect.

The most useful result is the one that points the wrong way. Every learned arm pushed the board away from the 19–20 occupied cells where the flow ceiling measurement says the achievable clear rate crosses the survival requirement: 24.29 → 24.68 cells at five samples, 23.15 → 23.87 at seven, and 25.53 for the pure learned leaf with the hand-written one switched off entirely. A model that predicts remaining lifetime accurately still does not steer the policy to the operating point where lifetime becomes cheap, because remaining lifetime under the current policy is not the same target as remaining lifetime under a policy that holds flow balance.

And as a purchase it is poor. Calling the model at every one of 660,481 leaves roughly doubles the cost of a decision. Spending the same compute on the chance estimator instead — the seven-sample arm, at 3.42× the reference's CPU per decision — buys +101,171 points. At equal compute, fixing the chance estimator is the better buy, and it is not close.

What this taught us, and what is still open

• The binding constraint is arity, not capacity. 615,090 board evaluations per decision is a hard budget. A model five times more accurate that costs five times more is unplayable — and the 0.008 of correlation between the small student and the network five times its size says the accuracy is not there to be had anyway. "Train a bigger survival model" is not the next experiment.
• Do not buy both axes. The cheapest strong configuration on this evidence is the hand-written leaf with an exact chance estimator; adding the learned leaf on top costs 2.11× for a gain that does not clear its bound.
• This is a positive result for the state-only, move-blind design. The repository's repeated failure mode is a model that learns the outcome of the move that was played and is then asked to rank moves it never saw. This evaluator never sees a move identity at all, and it cleared a paired 64-game lower bound. The design is worth keeping even though its magnitude is modest.
• Still open, and the finding names it as the more actionable question: predicting lifetime under the current policy is the wrong target. Aiming directly at occupancy or at the clear rate — the quantity the flow ceiling work identified — is a different and untested objective.
• Still open: a fresh-cohort replication of the +39,105, and a blend weight re-tuned at seven chance samples, which would say whether the seven-sample number is an underestimate.