---
title: A learned survival estimate inside the reference search
family: lifetime-objective
summary: Blends a learned survival estimate into the reference board evaluator and tests it under sampled and exact chance handling.
status: completed
evidence: reproduced
reads: public
kind: strategy
technique: nnue
featured: true
---

## The problem

A look-ahead search ends at boards where the game is not over, and it needs an
opinion about each one. That opinion is the [leaf evaluator](/learn/glossary),
and in the [reference policy](/approach/fair-expectimax/reference) it is
nineteen hand-tuned structural terms about height, crowding and chain readiness.
Almost every learning experiment on this site has tried to replace it, and
almost all of them failed the same way, which the
[sibling trap](/learn/concepts/ranking-siblings) page explains.

<GameTreeFigure seed={0x5eed1006} moves={18} caption="The search reaches these boards and stops. Whatever it cannot see beyond them has to be priced by the number on each board, and a learned leaf replaces that number with a prediction of remaining lifetime. The tree is engine output from a scripted round." />

## Proposed solution

Train a small network to predict how many moves a game has left, and mix its
opinion half-and-half into the hand-written scorer. This has an unusual
advantage. A Drop7 Hardcore score is 94.29% the flat bonus for surviving another
row rise, and a game runs at about 3,400 points per move
([finding-01](/docs/exploratory/finding-01-score-is-survival), 64 games), so a
prediction of remaining moves multiplied by 3,400 is already a score in real
points, the same unit the search's own immediate-score term carries. Mixing the
two is mixing two estimates of one quantity. The design is also 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 how many times the leaf is called.

<div style={{ display: "grid", gridTemplateColumns: "repeat(auto-fit, minmax(170px, 1fr))", gap: 12, margin: "1rem 0" }}>
  <Stat label="board scorings per decision" value="615,090" hint="four-move search, five chance samples, counted over 30 real decisions" />
  <Stat label="at seven chance samples" value="2,271,280" hint="same measurement" />
  <Stat label="the trained network costs" value="4,122 µs" hint="per board, in the exported C++ path" />
  <Stat label="so one decision would take" value="2,535 s" hint="against a 0.887 s reference decision: a factor of 2,860" />
</div>

A three-million-parameter convolutional network cannot be the leaf of this
search: one 87-move game would take 6.7 hours of the whole machine and one
64-game arm 18 days
([finding-08](/docs/exploratory/finding-08-learned-leaf)). So the network that
plays is [NNUE](/learn/glossary)-shaped, an "efficiently updatable" network
built from sparse binary features that are gathered and summed, and it runs in
about a microsecond. The prediction written down before any game was played was
that the learned leaf would help more once the search handles luck exactly, with
seven chance samples instead of five.

The policy reads only the visible board, the visible next disc and the moves
until the next rise; at a blend weight of zero the code short-circuits to the
frozen reference before the model is touched.

## How it works

1. Measure the budget first. Nothing on record said how many board evaluations
   a four-move decision 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 on 4,096 real boards at a tolerance declared before the comparison.
   After a surprise (under validity, below) the gate also proves that the
   PyTorch reference repeats bit-for-bit before anything is compared against it.
3. Train the model that can afford to play: 8,902 binary features of which
   exactly 135 are active per board. They 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. The leaf becomes `(1 − w) × hand_written + w × 3400 × predicted_lifetime`.
   At `w = 0` 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, freeze it, and run the 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. The
   output of every arm is a column per position, as in the reference.

## What happened

The learned leaf helped modestly, and it helped most where the prediction said
it would help least. With the reference's five chance samples it added +39,105
points per game on 64 paired development games, with a one-sided bootstrap lower
bound of +1,138, so above zero by very little
([finding-08](/docs/exploratory/finding-08-learned-leaf), run valid, development
tier). With the exact seven-sample chance estimator its gain did not clear its
bound and is unresolved. The preregistered prediction was that the gain would be
materially larger at seven samples; the measured difference between the two
gains was −21,824, the wrong sign, and by the rule fixed in advance that is a
fail. The finding reports it as one.

## What we learned

The refutation has a mechanism. An exact chance estimator and a learned leaf are
both 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 +79,347 with the learned one, the same substitution, 22%
smaller (64 paired games per arm, finding-08). 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 binding constraint is arity. 615,090 board evaluations per decision is a
hard budget, and the 0.008 of held-out correlation between the deployed student
and the network five times its size says a bigger survival model has little
accuracy to offer anyway (finding-08). At equal compute, fixing the chance
estimator is the better purchase: the seven-sample arm costs 3.42× the
reference's CPU per decision and buys +101,171 points, while the learned leaf
roughly doubles the cost of a decision for a gain that clears zero by 1,138.

The move-blind, state-only design is a positive result on its own terms: this
evaluator never sees a move identity and it cleared a paired 64-game lower
bound, which the family's earlier models did not. But every learned arm also
pushed the board away from the 19 to 20 occupied cells where the
[flow ceiling](/approach/lifetime-objective/flow-ceiling) measurement puts the
crossing between achievable clear rate and survival requirement (24.29 to 24.68
cells at five samples, finding-08). A model that predicts remaining lifetime
under the current policy does not steer toward the operating point where
lifetime becomes cheap. Whether aiming the leaf directly at occupancy or at the
clear rate would do so is the open question, and it has not been tested.

<AgentContext summary="Records and provenance">

Source: [`finding-08-learned-leaf`](/docs/exploratory/finding-08-learned-leaf),
a retained exploratory finding measured in this checkout on 2026-08-20; evidence
tier `development` for the gameplay arms and `CHECK` for the export, parity and
feasibility gates. The prediction and pass/fail rule are in `PREREGISTRATION.md`
in this directory, written before any cohort was run. There is no row in the
[experiment index](/docs/research/experiment-index) and no entry in the
[ledger](/docs/research/history).

Verdict as recorded: run validity valid; preregistered prediction fail
(refuted); learned leaf at five chance samples pass; at seven chance samples
inconclusive; evidence tier `development`.

The two-by-two: 64 paired whole games per arm, seeds `0xa51d1000`–`0xa51d103f`,
four-move search, 2,000-move cap; learned arms at `w = 0.50` with the lifetime
head, frozen on a separate 32-game tuning cohort.

</AgentContext>

<AgentContext summary="Full results table">

| arm | mean | median | Q25 | max | moves | games ≥ 1M |
| --- | ---: | ---: | ---: | ---: | ---: | ---: |
| 5 samples, hand-written leaf | 297,327 | 260,415 | 192,352 | 836,427 | 87.16 | 0 |
| 5 samples, learned leaf | 336,432 | 313,730 | 209,914 | 948,586 | 98.28 | 0 |
| 7 samples, hand-written leaf | 398,498 | 344,630 | 212,864 | 1,341,287 | 114.66 | 2 |
| 7 samples, learned leaf | 415,779 | 349,034 | 194,040 | 1,344,732 | 120.75 | 3 |

Paired deltas, one-sided 95% lower bounds, 20,000 percentile-bootstrap
resamples over whole games: learned − hand-written at 5 samples +39,105
[+1,138] points and +11.13 moves, wins–ties–losses 37–0–27; at 7 samples
+17,281 [−55,892], 34–0–30; the difference between those two gains −21,824
[−105,254]; 7 samples − 5 samples with the hand-written leaf +101,171
[+46,730]; with the learned leaf +79,347 [+17,053].

Flow: at five chance samples the learned leaf raises numbered clears by 0.0342
and reveals by 0.0212 per move, consistent with its +11.13 moves of extra
lifetime, and every reported quantile of the score improves. At seven samples
the paired per-game flow changes are slightly negative, an independent reason to
treat the seven-sample gain as unresolved rather than as a smaller real effect.

Occupancy: mean occupied cells moved 24.29 → 24.68 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.

Cost: calling the model at every one of 660,481 leaves roughly doubles the cost
of a decision (2.11× for the learned leaf on top of the exact estimator); the
seven-sample arm costs 3.42× the reference's CPU per decision.

The two models: the convolutional teacher has 3,006,543 parameters, held-out
lifetime correlation 0.8646 and costs 4,122 µs per board. The deployed
NNUE-shaped student has 572,367 parameters, held-out correlation 0.8564 and
costs 1.33 µs: 0.008 of correlation given up for a 3,109× speed-up. Both were
exported and both passed a stated-tolerance parity gate; only the student ever
played a move.

</AgentContext>

<AgentContext summary="Validity, gates and limitations">

Validity gates: both hand-written-leaf arms reproduce the earlier
chance-sampling study's published 64-game cohort to every digit; the `w = 0`
short-circuit matched the frozen reference on 50 of 50 compared moves; 0
score-identity violations in 26,934 decisions; 0 censored games in 256; the
seven-sample arms ran with a raised work bound whose measured 4,956,614 work per
move confirms a completed four-move search rather than a silent degradation to
three.

A host defect found here and not audited generally: the parity gate passed,
then the identical command failed on every output. `torch.nn.Conv2d` on this
host's CPU is nondeterministic: two identical forward passes in eval mode,
single-threaded, differ in 6.25% of output elements, and through the
normalisation layer's group statistics one perturbed activation moves 100% of
the model's outputs. Written up as
[`gpu-03`](/docs/exploratory/gpu-03-onednn-conv-nondeterminism). Any gate in
the repository that compared against a CPU PyTorch convolution may be affected;
that has not been checked.

Limitations the finding states about itself: 64 paired games per arm with a
score standard deviation of 51–67% of the mean, so the +1,138 lower bound clears
zero by very little and wants replication on fresh seeds; the
difference-in-differences interval is wide, so the data refute the predicted
positive interaction but do not establish a negative one; the evaluation cohort
is previously read development data and is now doubly read; the model that was
specified never played a move; the blend weight was tuned only at five chance
samples and the seven-sample tuning confirmation was preregistered and not run;
no timing here is timing-grade; and the mean of 415,779 is far below the
1,050,000 the frozen qualification protocol requires. No protected or final
seed was opened.

Open follow-ups named by the finding: 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.

</AgentContext>