---
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: development-tier exploratory finding, with mechanics gates
reads: public
---

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.

<EvidenceLabel status="completed" evidence="development-tier exploratory finding" reads="public" />

## 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](/learn/glossary), 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](/learn/concepts/ranking-siblings) 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.

<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 — measured, not estimated" />
  <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>

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.

<GameTreeFigure seed={0x5eed1006} moves={18} caption="The leaf's job in one picture: the search reaches these boards and stops; whatever it cannot see beyond them has to be priced by the number on each. A learned leaf replaces that number with a prediction of remaining lifetime." />

## 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](/learn/glossary)-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 reports it without 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](/approaches/lifetime-objective/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.

<TechnicalDetails title="The record: the two-by-two, the gates, and the host defect">

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`, 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.** 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.

| 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]**,
37–0–27; at 7 samples +17,281 [−55,892], 34–0–30; the difference between those
two **−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].

**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.

**Validity gates.** Both hand-written-leaf arms reproduce the earlier
chance-sampling study's published 64-game cohort **to every digit**, which is
what makes the comparison sound; 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; and 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, 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 separately as
[`gpu-03`](/docs/exploratory/gpu-03-onednn-conv-nondeterminism). Any gate in this
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.**

</TechnicalDetails>

## 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](/approaches/lifetime-objective/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.