Is more computation the answer?

What the evidence says about deeper search, more samples, bigger models, and large training runs, including where more compute improves play and where it does not.

The best policy averages about a third of the target, and computers are fast, so the question is search deeper, sample more, train bigger. The repository has measured each option. It depends entirely on what the compute is spent on. Spent on removing a measured bias in how the search handles luck, it was worth about a third more score and it unlocked a whole extra ply of look-ahead. Spent on more imagined futures for a planner with a broken objective, it made things measurably worse. Spent on bigger models trained on the wrong shape of data, it reproduces the same blind spot with more confidence. Section 4 covers what remains of the proposed learning loop after its first compact students failed their ranking gates.

1. Deeper search

Going from depth 3 to depth 4 helped clearly: on the same eight games, fair D4 outscored fair D3 by a wide margin and won seven of them. That is the evidence that looking ahead matters.

Going from depth 4 to depth 5 has not produced a better policy so far. The status summary records that selective depth 5, full depth 5, and variants that stop at the next row rise "often spent much more work, sampled chance outcomes too noisily, or overrode good D4 actions on unstable estimates."

A later, replicated measurement reframes that conclusion. The earlier depth experiments did not isolate depth from chance-estimator bias. Section 2 covers that bias. Once removed, the fourth ply went from worth almost nothing to worth a great deal:

with the old five-sample estimator, depth 4 trailed depth 3 by about 7,700 points, which the confidence interval could not distinguish from zero;
with an exact seven-sample estimator, depth 4 beat depth 3 by about 86,000 points, and the interval cleared zero comfortably.

In the finding's own words: "With a biased chance estimator, the fourth ply buys nothing. With an exact one, it is worth 86,000 points." Depth and the quality of the chance estimate are complements, not independent dials. That explains the repository's most-repeated conclusion: "deeper is not automatically stronger."

Mean score by search depth on one 64-game development cohort, at five and at seven chance strata. The five-stratum line is flat from depth 3 to depth 5; the seven-stratum line climbs steeply to depth 4. The lone depth-5 seven-stratum point is a stopped arm on the first 32 seeds only and is drawn separately for that reason. Hover or tab to a point for its value, sample size and source record.

Source data

All arms play the same 64-seed development cohort 0xa51d1000-0xa51d103f under corrected 17,000-point Hardcore scoring, except the depth-5 seven-stratum arm, which was stopped by decision after the first 32 seeds (0xa51d1000-0xa51d101f) and is drawn as its own one-point series so the two sample sizes are never joined by a line. Depth 2 was run only at seven strata. No confidence band is drawn on means; the paired contrasts with their bounds are in the companion bar figure. Evidence tier: development / public-development. The historical eight-game D3/D4 cohorts used 7,000-point scoring and are not shown.

Series	Search depth	Mean score	Bounds	n	Source
5 strata (biased next-disc estimate)	3 depth 3, 5 strata	305,051 points	—	64	docs/exploratory/finding-05-chance-strata.md Cost table, mean score
5 strata (biased next-disc estimate)	4 depth 4, 5 strata (frozen reference)	297,327 points	—	64	docs/exploratory/finding-05-chance-strata.md Confirmation cohort detail, mean score
5 strata (biased next-disc estimate)	5 depth 5, 5 strata	288,704 points	—	64	RS-20260821T181917Z-9a34ba02 metrics.d5s5MeanScore (288,703.67)
7 strata (exact next-disc estimate)	2 depth 2, 7 strata	265,294 points	—	64	docs/exploratory/finding-05-chance-strata.md Cost table, mean score
7 strata (exact next-disc estimate)	3 depth 3, 7 strata	312,327 points	—	64	docs/exploratory/finding-05-chance-strata.md Cost table, mean score
7 strata (exact next-disc estimate)	4 depth 4, 7 strata	398,498 points	—	64	RS-20260821T181917Z-9a34ba02 metrics.d4s7ControlMeanScore (398,498.23)
7 strata, first 32 seeds only (arm stopped)	5 depth 5, 7 strata (partial: 32 of 64 planned games)	411,874 points	—	32	RS-20260821T205102Z-d89df4b5 metrics.d5s7MeanScore (411,873.66)

Spec: web/content/figures/score-vs-depth.json · 3 source records

The same factorial as paired contrasts with one-sided 95% lower bounds. Both stratum contrasts clear zero; neither depth-5-minus-depth-4 contrast does, and each sits below the smallest effect its cohort could have detected. The depth-5 question was asked and came back as a non-measurement, which is a different thing from a null.

Source data

Whisker is the one-sided 95% whole-game bootstrap lower bound; the upper end of the whisker is the point estimate itself (no upper bound is drawn). A contrast is significant when its lower bound clears zero: both stratum contrasts (7 minus 5 strata) do; neither depth contrast (5 minus 4 plies) does, and each sits below its own detection floor (47,052 at n=64, 107,988 at n=32). Cohort 0xa51d1000-0xa51d103f; the n=32 contrasts cover its first 32 seeds. Evidence tier: public-development.

Series	Paired contrast (same seeds, whole games)	Paired mean score delta	Bounds	n	Source
Chance resolution: 7 strata minus 5 strata	at depth 4 d4s7 - d4s5, W-T-L 41-0-23, 3.82x work	101,171 points	lower 47,447	64	RS-20260821T205102Z-d89df4b5 metrics.pairedD4s7MinusD4s5 (101,170.8 / 47,446.8)
Chance resolution: 7 strata minus 5 strata	at depth 5 d5s7 - d5s5, W-T-L 19-0-13, 5.85x work	123,613 points	lower 32,575	32	RS-20260821T205102Z-d89df4b5 metrics.pairedD5s7MinusD5s5 (123,612.7 / 32,575.2)
Depth: 5 plies minus 4 plies	at 5 strata d5s5 - d4s5, W-T-L 33-0-31, 23.29x work (below 47,052 floor)	-8,624 points	lower -55,134	64	RS-20260821T205102Z-d89df4b5 metrics.pairedD5s5MinusD4s5 (-8,623.7 / -55,133.7)
Depth: 5 plies minus 4 plies	at 7 strata d5s7 - d4s7, W-T-L 17-0-15, 35.62x work (below 107,988 floor)	23,367 points	lower -83,046	32	RS-20260821T205102Z-d89df4b5 metrics.pairedD5s7MinusD4s7 (23,366.8 / -83,046.2)

Spec: web/content/figures/strata-5-vs-7.json · 1 source record

The depth-5 question was then run, but the result was a non-measurement. At five strata, depth 5 minus depth 4 was −8,624 points over 64 paired games. At seven strata it was +23,367 over 32 paired games, and the estimate changed sign when the cohort grew from 16 games to 32. Both effects were below their detection floors. The supported conclusion is not that the fifth ply helps or does nothing; this complete-game design cannot resolve an effect that small at an affordable cohort size.

Every depth and sampling choice on this page is a work budget:

One decision is one tree, almost all of its nodes are the leaf evaluations at the frontier, and every added ply or sample multiplies that count — which is why the search carries an explicit work cap and why leaf cost multiplies everything.

Source

diagram-work-budget.svg — source and reading guide

Parameter diagram: what "work" counts in the fair expectimax search, why a depth-4 seven-strata decision evaluates ~2.3M leaves, where the work cap stops a search, and why leaf cost multiplies everything. Companion to diagram-chance-strata / diagram-reveal-sampling (the N and M parameters); this one is about the budget the search spends.

What it explains

One decision is one tree: a decision node expands all 7 columns at full width (no pruning — that is what fair D4 is, audit-02 I1), each column leads to a chance node over the N sampled next-disc strata, and the tree repeats per ply down to the frontier leaves.
The census of one depth-4 five-strata decision (finding-13 §2.1): 796,058 nodes, of which 764,899 (96.1%) are fairLeaf leaf calls and 31,159 (3.9%) interior nodes; logical work is 1,560,979 because iterative deepening re-expands plies 1–4. At seven strata, finding-08 §2 measured 2,271,280 leaves per depth-4 decision (615,090 at five strata).
The work cap: the search deepens iteratively — work per completed depth at five strata is 70 / 2,221 / 60,800 / 1,383,207 (finding-13 §4B) — and a declared --max-work budget exhausted mid-ply falls back to the deepest completed ply (finding-13 §8.2). A 3.2M cap sized for five strata silently degrades d4 s7 to depth 3 (finding-05's failure mode, recalled in finding-13 §8); finding-08's seven-stratum arms run --max-work 16000000 and verify completion by work/move = 4,956,614 (finding-08 §7).
Leaf cost multiplies everything: leaves are 96.1% of nodes, so decision cost ≈ leaves × leaf cost. LeafNet (572,367 params, 1.33 µs per state) × 2,271,280 ≈ 3.0 s per d4 s7 decision; the exported CNN teacher (3,006,543 params, 4,122 µs per state) × 2,271,280 ≈ 9,362 s ≈ 2.6 h — gated but never played (finding-08 §2–3, §11).

Element-by-element

Panel 1 (tree): decision node → all 7 column circles (c1, c2, …, c7) → one column's chance node ("?") → the seven possible next discs, of which the chance node samples N = 5 or 7 → dashed "× every ply" → the frontier leaf row. Annotated: leaves are 96.1% of every decision's nodes; branching is 7 × N per ply, worst case 49^d at seven strata.
Panel 2 (census bar): one stacked bar per the finding-13 §2.1 census — 96.1% leaves (accent) vs 3.9% interior (muted) — with the node count (796,058), the logical-work count (1,560,979), and the applied-move count (796,081) spelled out, plus the seven-strata leaf figure.
Panel 3 (work cap): log10-scaled bars of work per completed depth at five strata (d1–d4). The dashed danger outline on the d4 row is the seven-strata requirement (4.96M) crossing the dashed 3.2M cap line; the curved arrow is the fallback to the deepest completed ply (d3). Notes state the finding-05 silent-degradation failure and the 16M s7 budget.
Panel 4 (leaf cost): log10-seconds bars comparing LeafNet (≈3.0 s per d4 s7 decision) against the CNN (≈2.6 h), with the "roughly one microsecond" leaf budget and the frozen-fairLeaf 970 → 279 ns fast-engine figure (3.5×, still 58% of decision time, finding-13 §2.3).
Caption strip: "work counts every node; the cap stops the deepening; the leaf (96.1% of nodes) multiplies everything", plus the NNUE-vs-CNN caption line requested by the owner.
Popovers: what one unit of work is; N strata and the worst-case vs measured gap (10.4×, transpositions, finding-13 §6); why the leaf dominates (Amdahl ≈5×, table = 0.6% of a decision); work-cap semantics including the finding-05 failure; the leaf-cost frontier arithmetic; and a sources/caveats popover on the caption.

Simplifications (stated explicitly)

The tree is schematic. Three of seven columns and three of seven strata arrows are drawn, with ellipses; no real position is implied. No board is drawn, so engine board orientation does not apply here.
Bars are log-scaled (stated under each panel); a linear bar for 70 vs 1,383,207 (or 3 s vs 9,362 s) would be invisible at one end.
The 3.0 s / 2.6 h figures are products of cited numbers (2,271,280 leaves × 1.33 µs / 4,122 µs), not independent measurements; the caption popover says so. finding-08's own wall-clock conclusions come from its cohort runs, not this product.
The d4 five-strata bar (1,383,207) is the search-parity gate's measured work/move; the census decision (1,560,979 work) is a different, larger sample of 24 real decisions. Both are cited with their own contexts; the diagram does not average them.

Sources

docs/exploratory/finding-13-fast-engine.md — §2.1 census (796,058 nodes, 764,899 leaves = 96.1%, 31,159 interior = 3.9%, work 1,560,979, applied moves 796,081), §2.3 attribution (leaf 79.1% → 58%, Amdahl ≈5×, table 0.6%), §4B work per completed depth (70 / 2,221 / 60,800 / 1,383,207 at five strata), §5 ("the last ply is always ~96% of the nodes"), §6 (worst case 582,727,796 vs measured 55.8M at d5 s7, 10.4×), §8 (finding-05's silent degradation; completed-depth fallback).
docs/exploratory/finding-08-learned-leaf.md — §2 (615,090 / 2,271,280 leaves per depth-4 decision at five / seven strata; CNN 4,122 µs per state), §3 (LeafNet 572,367 params, 1.33 µs; "a leaf evaluator has roughly one microsecond"), §5 (tuning cohort), §7 (--max-work 3200000 at s5, 16000000 at s7; work/move 4,956,614), §11 (CNN never played).
docs/exploratory/finding-05-chance-strata.md — the work-bound degradation failure, quoted via finding-13 §8.
Figure spec: runs/RUN-20260823T191900Z-b9f8f80d/kimi-k3-figure-plan.md (parameter-diagrams batch, this diagram = "work budget").

Conventions

Same as the other diagrams in this directory: viewBox="0 0 760 540", width="100%", theme-aware CSS variables with light fallbacks, fig-pt/fig-pop pure-SVG hover/focus popovers with tabindex="0", <title>/<desc> with sources, matching diagram-two-hit-reveal.svg and the .research-fig block of web/app/globals.css. Under 30 KB.

Source: web/content/figures/diagrams/diagram-work-budget.source.md

The technical record

Fair D4 vs D3: 400,675 vs 235,071 mean score over the same 8 corrected-score games (status, evidence snapshot).
The depth × estimator interaction, from finding-05 (evidence tier development, replicated across two independent cohorts, 64 paired games): depth 4 trails depth 3 by 7,723 points with five strata (not significant) and leads by 86,172 with seven (lower bound +26,468, 40–0–24 wins–ties–losses).
The final depth-5 experiment is recorded in RS-20260821T205102Z-d89df4b5: −8,624 at five strata (64 games; detection floor 47,052) and +23,367 at seven strata (32 games; detection floor 107,988). Resolving the latter point estimate would require roughly 684 paired games, about 13 wall-days at the run's measured throughput.
The earlier 19.1 CPU-hour figure was a projection from three roots in finding-13, not the measured cost of the later cohort. The completed run is the authority for what this design costs in practice.

2. More samples of the future

This is where the answer splits in two, depending on what the extra samples are being spent on.

When more samples fixed a real bias, and paid

The reference search does not enumerate every possible next disc. It draws a fixed number of representative samples at each chance node: five, in the frozen reference. But the next disc is uniform over seven values, and five samples cannot represent seven possibilities. An audit measured the consequence: on average 2.41 of the 7 disc values receive zero weight at every chance node, and because the sampling is deterministic the error never averages out. The search was not mis-estimating the future randomly; it was systematically blind to part of it.

The next disc is dealt uniformly from seven values, so a five-sample chance node must leave at least two of them with zero weight every time — the search is not noisy about the future, it is systematically blind to part of it — while seven samples make the average exact.

Source

diagram-chance-strata.svg — source and reading guide

Parameter diagram for the chance-node sample count N, written for the research console. Hand-written, self-contained SVG. The only numbers drawn in the panels are the disc values 1–7, the weights 1/5, 1/7 and 0, and the frozen work bound 3,200,000 with its declared 16,000,000 replacement (a configuration fact, not a measurement). All measured outcomes — the 2.41 zero-weighted values, the paired deltas, the work ratios — appear only inside hover popovers, with their records cited.

What it explains

What a disc stratum is, and why the exact expectation over the seven-point uniform is what unlocks depth:

The chance node has seven atoms. After a drop resolves, the engine deals the next disc uniformly from {1,…,7}. The exact next-disc expectation averages the continuation value over all seven with weight 1/7 each.
N = 5 strata cannot cover seven atoms. The frozen fair-D4 reference draws five stratified samples per chance node, so at least two of the seven values receive zero weight at every node. Audit-02 (H1, quoted in finding-05) measured 2.41 of the 7 values zero-weighted on average, and because which values are missed is fixed by the node's deterministic stream, the error never averages out.
N = 7 is exact. Seven strata put the true 1/7 weight on every atom. Measured at depth 4 on 64 previously unread seeds (finding-05 confirmation cohort): +101,171 mean points (+34%), +27.5 moves, 95% lower bound +47,457.
The interaction is the point. With 5 strata the fourth ply buys nothing measurable (it trails depth 3 by 7,723, n.s.); with 7 strata it is worth +86,172 [+26,468]. Depth and estimator quality are complements, not independent knobs — a deeper ply propagates whatever the chance estimator gives it, bias or signal.

Facts used in the diagram

From docs/exploratory/finding-05-chance-strata.md:

Frozen reference: depth 4, 5 strata; candidate: 7 strata, same everything else (CHECK gate: reproduces the reference at default settings).
Interaction table (64 paired games per arm): d4 7−5 strata +101,171 [LB +47,457], 41-0-23; d3 7−5 +7,276 [−45,961] n.s.; 7 strata d4−d3 +86,172 [+26,468]; 5 strata d3−d4 +7,723 [−42,743] n.s.
Work bound: worst-case depth-4 work with branching b = 7 columns × N strata is 3,134,950 at N=5 (fits the frozen 3,200,000 bound with 2.1% headroom) and 11,892,398 at N=7 (exceeds it 3.7×). A 7-strata run left at the frozen bound silently falls back to a completed depth 3; the 7-strata arms declared 16,000,000. Measured work ratio 3.82× against a predicted 3.79×.
Caveat carried in the N=7 popover: seven strata makes the next-disc expectation exact; covered-disc reveals are still sampled, so the reveal expectation is not exact. That is the separate M knob (finding-09/16), drawn in diagram-reveal-sampling.svg.

Element-by-element

Top row: the seven atoms as accent discs 1–7, each labelled 1/7; the exact-expectation formula to the right.
Left panel (N = 5, danger header): five filled discs (values 1, 2, 4, 5, 7) weighted 1/5; values 3 and 6 dashed and zero-weighted. The estimator line and the "deterministic, never averages out" note.
Right panel (N = 7, accent header): all seven discs filled, each 1/7; "estimate = (1/7)·Σ over all seven = E exactly".
Bottom rows: the interaction as two arrows — flat/muted for "5 strata: depth 3 → 4" (no measurable gain), accent for "7 strata: depth 3 → 4" (the fourth ply pays).
Caption strip: the one-sentence claim, the zero-weight rule, and the work-bound caveat.
Popovers: what a stratum is; the audit-02 H1 measurement; exactness and the confirmation-cohort result; the full interaction table; the work-bound arithmetic.

Simplifications (stated explicitly)

Which two values are missed is illustrative. The panel shows values 3 and 6 unsampled; in the real search the missed set is determined per node by the deterministic stratified stream and varies from node to node. The measured average is 2.41 of 7 (worse than the minimum 2, because draws can repeat), stated in the popover.
Weights are shown as the estimator's weights (1/5 per sampled value, 0 for unsampled), which is exactly how the node average is computed; no claim is made about the internal partition the stratified sampler uses.
The interaction arrows are qualitative. The measured deltas and their intervals live in the popover, per the directory convention that measured numbers carry their record with them.

Sources

docs/exploratory/finding-05-chance-strata.md — strata, exactness, the interaction table, the work-bound analysis, both cohorts.
docs/exploratory/audit-02-fair-d4.md (H1), quoted via finding-05 — the 2.41-of-7 zero-weight measurement.
Companion diagram: diagram-reveal-sampling.svg (the M knob).

Conventions

Same as the other diagrams in this directory: viewBox="0 0 760 540", width="100%", theme-aware CSS variables with light fallbacks, the shared <style> block, fig-pt/fig-pop pure-SVG hover/focus popovers with tabindex="0", <title>/<desc> with sources, marker IDs namespaced cs-. No board position is drawn, so the engine's board-orientation convention does not apply. 16.6 KB, under the 30 KB budget.

Source: web/content/figures/diagrams/diagram-chance-strata.source.md

Raising the sample count to seven makes the next-disc expectation exact. On 64 previously unread paired games that was worth +101,171 mean points (+34%) and +27.5 more moves per game, winning 41 games, tying none and losing 23, with a 95% lower bound of +47,457. The result was replicated on a second independent cohort.

Mean moves survived for the same arms as the score figure. Survival, not scoring rate, is where the seven-stratum fourth ply pays: about 27 more moves per game at depth 4.

Source data

Companion to score-vs-depth: same arms, same cohort 0xa51d1000-0xa51d103f (64 games), same partial depth-5 seven-stratum arm on the first 32 seeds drawn separately. Depth 2 was run only at seven strata.

Series	Search depth	Mean moves	Bounds	n	Source
5 strata (biased next-disc estimate)	3 depth 3, 5 strata	89.84 moves	—	64	docs/exploratory/finding-05-chance-strata.md Cost table, mean moves
5 strata (biased next-disc estimate)	4 depth 4, 5 strata (frozen reference)	87.16 moves	—	64	docs/exploratory/finding-05-chance-strata.md Confirmation cohort detail, mean moves
5 strata (biased next-disc estimate)	5 depth 5, 5 strata	84.69 moves	—	64	RS-20260821T181917Z-9a34ba02 metrics.d5s5MeanMoves (84.6875)
7 strata (exact next-disc estimate)	2 depth 2, 7 strata	79.48 moves	—	64	docs/exploratory/finding-05-chance-strata.md Cost table, mean moves
7 strata (exact next-disc estimate)	3 depth 3, 7 strata	92.27 moves	—	64	docs/exploratory/finding-05-chance-strata.md Cost table, mean moves
7 strata (exact next-disc estimate)	4 depth 4, 7 strata	114.66 moves	—	64	RS-20260821T181917Z-9a34ba02 metrics.d4s7ControlMeanMoves (114.65625)
7 strata, first 32 seeds only (arm stopped)	5 depth 5, 7 strata (partial: 32 of 64 planned games)	117.97 moves	—	32	RS-20260821T205102Z-d89df4b5 metrics.d5s7MeanMoves (117.96875)

Spec: web/content/figures/moves-vs-depth.json · 3 source records

That is the clearest "more compute helped" result in the repository, and what it actually bought was not more search, but an unbiased one. The extra samples removed a defect rather than adding depth.

When more samples made things worse

One family of planners handles uncertainty by imagining many complete futures ("worlds"), planning in each as if the hidden values were known, and choosing the move that does best on average. It is embarrassingly parallel: more worlds, more compute, done.

The repository measured what happens as the number of worlds grows from 1 to 1,024. Quality rose steadily up to 256 worlds, and then fell. At 1,024 worlds the planner survived about half as long and scored about half as much on the same games as it did at 256.

That is not a bug; it is a known property of this kind of planner. Inside each imagined world, the plan knows the answer key. It knows how the hidden discs will turn out, so it systematically overvalues moves that only pay off if the covers happen to be right. With few worlds, sampling noise accidentally protects the planner from its own bias. With many worlds the noise vanishes and the planner converges, faithfully, on the wrong answer. More compute bought a more faithful optimisation of the wrong objective. The finding's own conclusion: improving this planner requires changing the estimator, not spending more on it.

The technical record

Seven strata versus five, from finding-05 (development tier, replicated; the zero-weight measurement is audit-02 H1): at depth 4, +101,171 points / +27.50 moves, 95% lower bound +47,457, 41–0–23. At depth 3 the same change is +7,276 points with a lower bound of −45,961, not significant. The effect is an interaction with depth, not a main effect of sampling.

Clairvoyant (hindsight-optimisation) planner, horizon 7, pooled numbered clears per move on the original eight tapes, from finding-12 §3:

worlds K	1	4	16	64	256	1,024
clears / move	1.5370	1.7095	1.9279	2.1403	2.2309	2.0947 (6 tapes)

Paired on the same six tapes, K = 1,024 vs K = 256: mean moves 100.33 vs 182.00; mean score 347,348 vs 653,644; five of six tapes worse. The arm was stopped at 6 of 8 games. This planner is an oracle because it reads hidden values. Its scores are not policy evidence; the lesson is about the estimator, and it "bounds the whole determinization family."

3. Bigger models and more training

Many learned evaluators were trained here: n-tuple networks, Monte Carlo value models, small neural networks, Q-learning and policy-gradient variants, phase models, fitted policies. Some predicted outcomes well. None displaced fair D4.

The one learned model that has helped so far was placed inside the fair D4 search, as a blend at its leaves, rather than in place of it. On 64 paired games the learned leaf beat the reference leaf at five strata (significant) but not measurably at seven, which refuted the preregistered prediction that it would help more once the chance estimate was exact. Finding-08, development tier; no result record was written for it.

Source data

64 paired whole games per arm on cohort 0xa51d1000-0xa51d103f, corrected scoring, 2,000-move cap. Marker labels are paired wins-ties-losses of the learned leaf against the reference on the same seeds. The learned-minus-reference paired delta is +39,105 at five strata (one-sided 95% lower bound +1,138, significant) and +17,281 at seven strata (lower bound -55,892, not significant); the difference-in-differences is -21,824 (lower bound -105,254), which refuted the preregistered prediction that the learned leaf would help more with the exact estimator. Evidence tier: development (finding-08; no result record was written for this finding).

Series	Chance strata at depth 4	Mean score	Bounds	n	Source
Reference leaf (frozen fair D4)	5 strata	297,327 points	—	64	docs/exploratory/finding-08-learned-leaf.md Section 7 table, d4 s5 reference leaf, mean
Reference leaf (frozen fair D4)	7 strata	398,498 points	—	64	docs/exploratory/finding-08-learned-leaf.md Section 7 table, d4 s7 reference leaf, mean
Learned leaf (LeafNet lifetime, w = 0.50)	5 strata W-T-L 37-0-27 vs reference	336,432 points	—	64	docs/exploratory/finding-08-learned-leaf.md Section 7 table, d4 s5 learned leaf, mean; paired delta +39,105 (lower bound +1,138)
Learned leaf (LeafNet lifetime, w = 0.50)	7 strata W-T-L 34-0-30 vs reference	415,779 points	—	64	docs/exploratory/finding-08-learned-leaf.md Section 7 table, d4 s7 learned leaf, mean; paired delta +17,281 (lower bound -55,892)

Spec: web/content/figures/learned-leaf-arms.json · 1 source record

For most of them the diagnosed reason was not model size and not training length. It was the shape of the data: models were trained on the move that was played and then asked to rank moves that were never played. This is the sibling trap. A bigger model trained on the same data learns the same blind spot with more confidence. The status summary is explicit that students "usually lacked enough diverse successor data, failed held-out sibling ranking, or were too slow to improve complete games."

The first answer to "would a giant training run fix it?" is not if it trains on the same kind of data. A thousand GPUs generating played-move-only labels produce the failure at scale.

The afterstate work did fix the data shape. Its first long-outcome labels were too noisy at low sample counts, but 256 aligned futures made them stable. A later experiment removed that label question by training on exact D4 search values for every legal sibling. The compact student still ranked worse than exact D1. That moves the current obstacle from sibling coverage to what the tested compact evaluators can represent.

4. The proposed learning loop, and where it is blocked

The proposed learning loop was designed to address the diagnosed problem directly:

At every position the actors visit, run a fair search for every legal column under the same random futures, and record all seven values. This is the successor-closed data the sibling page calls for.
Train a public evaluator on those labels.
Put the trained evaluator at the leaves of the search and repeat. Each round's labels come from a stronger searcher than the last.

Steps 1 and 2 have been done at pilot scale in two forms. The first corpus labelled every sibling with long public continuations under shared chance scenarios. Raising the scenario count from 8 to 256 fixed its label-stability failure, but the trained model still lost to fair D4. The second corpus used successor-closed, exact D4 search values: 291,890 labelled afterstates over 8,639 training roots. Its 3.4-million-parameter student reached 0.375 top-1 agreement with D4, below exact D1's 0.486 and the preregistered 0.60 gate.

A later leaf-sized NNUE probe did worse, at about 0.30 top-1. The evidence now blocks the compact leaf form of the loop as tested. More actors would generate more examples of a target that neither tested student could represent well enough. A larger model or a cross-sibling set ranker remains a proposal and must pass an offline ranking gate before it can justify a gameplay or scale-out run.

Step 3 has not been done. No trained evaluator here has passed the gate required to become the search leaf for another label iteration.

Steps 1–3 together are now a registered theory with stated ways to prove it wrong. The next concept page, what a large-scale run would look like, describes the software shape, the order of work, and the gates it must pass. The work starts with a small pilot on a single workstation.

5. The hardware that exists today

This workstation is a 16-core / 32-thread CPU with an integrated GPU that shares system memory. The GPU has been made to work for training and, for the small network sizes tried, runs 1.25–5× faster than the CPU depending on batch size. These lower-bound measurements came from a busy machine. Exact game simulation and tree search remain CPU work; the hardware plan places a full GPU simulator as a research prototype that would have to prove itself move-for-move identical first. Everything in section 4 can be piloted here before it is scaled anywhere.

The technical record

gpu-01 (ROCm enablement, correctness, throughput, two wheel defects and workarounds); amd-ryzen-halo (workload placement and memory policy); fast engine (CPU simulation cost and the batching primer).

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