One-ply Q as a pruning prior and a refit leaf
Fit a linear action value to the depth-4 search's own sibling values, then use it not to play but to decide which siblings the search may skip, and separately refit the leaf to the search's own value.
Keep a number for 'how good is it to do this here', play, and after each step nudge that number toward what actually happened plus the best number available next.
On this page
Fit a linear action value to the depth-4 search's own sibling values, then use it not to play but to decide which siblings the search may skip; and, separately, refit the leaf to the search's own value. This page follows the Klein-Friedmann reproduction, whose six-feature policy turned out to be a survival heuristic an order of magnitude below the depth-4 reference, and asks the two questions that were left: can a cheap learned value make the reference search cheaper, and can the search's own value teach its leaf?
Everything here reads the public state: the visible board, the visible next disc and the moves until the next rise. The exact search values used as regression targets are computed from that same public state by the reference search; no seed, hidden disc or future is touched.
The intuition
A depth-4 search is expensive because at every position it tries all seven columns, and for each column all seven ways the chance can fall, four times over. Almost all of that work is spent on continuations the search will not choose. If something cheap could say "these three columns are the only ones worth a look" at each inner position, the search could skip the other four and do a fraction of the work. The thing that says it is a prior: it needs no precision, only recall. It may rank the best column second or third as often as it likes, as long as the best column is rarely outside its top three.
The obvious prior is the search's own one-ply value: play each column under the seven chance outcomes, score the result with the leaf, average. It costs about one hundredth of expanding a column to full depth. The question this page asks is whether a learned linear value, fitted to what the depth-4 search actually concluded about each sibling, can do better than that one-ply value, and whether either is good enough to prune with.
The second question turns the same data around. The depth-4 root value is "expected score over four plies, plus the leaf four plies ahead". Regressing the leaf's own eighteen terms onto that value is one step of bootstrapped value learning: whatever part of the four-ply future is linear in the leaf terms gets folded into the leaf, and a depth-4 search over the refit leaf effectively sees further for that part. Every learned leaf the program has tried so far lost; this one is different in that its target is the search's own value rather than a short-horizon proxy.
How it works, step by step
- Build a sibling-complete panel. Play 48 complete games with the unchanged fair depth-4 search on already-read training seeds. At every position record the exact search value of every legal column at depths one to four, and for every legal column the 32 one-ply numbers: the seven-stratum mean of the eighteen leaf terms after the drop, the mean score gained, the fraction of chance outcomes that end the game, the six Klein-Friedmann drop features, the rise clock and a bias. The one-ply search value is a fixed linear function of those 32 numbers, so a linear fit can only add to it. Split the games 32 for fitting, 16 held out.
- Fit the linear action value by ridge regression to the depth-4 sibling values, choosing the penalty by cross-validation over games.
- Score every ranker on the held-out games against the depth-4 choice: centre-first order, the six-feature policy, the exact one-ply value, the exact depth-two and depth-three values, and the fitted value. Report how often each puts the depth-4 choice first, second, third.
- Prune the search. Inside the depth-4 search, at every inner position with two or more plies still to go, let the prior rank the legal columns and expand only the top w. The root and the last ply stay full width. Chance outcomes and the leaf are untouched, so every pruned value is a lower bound on the full-width value and, with w = 7, the search is the unchanged reference bit for bit. Run it on every held-out position with w of 2, 3 and 4 and each prior; measure how often the decision matches full-width depth 4, how much value it gives up when it does not, and the work.
- Try depth five at depth-four cost. On 128 held-out positions compute exact depth-5 values, then compare pruned depth-5 decisions and full-width depth-4 decisions against them.
- Play games. The best pruned configuration plays 256 complete games on the previously evaluated pilot cohort against full-width depth 4.
- Refit the leaf to the depth-4 root value on positions that are not about to die, check it explains more held-out variance than a rescaled frozen leaf, and play it inside the full-width search on the same 256 games.
What happened
The fitted value is a worse ranker than the one-ply value it contains. On the 2,060 held-out positions, the ridge fit puts the depth-4 choice first on 30.8% of positions and in its top three on 60.4%; the exact one-ply value under the same chance outcomes scores 52.4% and 80.9%. This is not a bug: the 32 features rebuild the one-ply value to eleven decimal places. It is the objective. A death within four plies is worth minus a million points, so least squares halves its held-out error by predicting deaths and, in exchange, ranks the live siblings worse. A post-hoc refit on targets clipped at minus 50,000 recovers exactly the one-ply ranking (53.5%, 80.9%) and nothing beyond it. So the answer to "fit a linear Q to depth 4" is that a linear function of one-ply features cannot beat the one-ply value at reproducing depth-4's choice, and a least-squares fit does not even reach it (RS-20260902T202705Z-75d87947). For scale: the exact depth-3 value ranks depth-4's choice into its top three on 95.0% of positions, depth two on 90.0%, the six-feature policy on 70.1%, and centre order on 40.0%.
The one-ply value prunes depth 4 to a quarter of the work. Expanding only the one-ply value's top three siblings at both interior layers of the depth-4 search reproduces the full-width decision on 92.3% of held-out positions (lower bound 91.8%), gives up 0.87% of the value spread on average when it differs (upper bound 0.98%), and costs 26.4% of the logical work, of which the prior itself is 5.9%; in wall time it is 3.8 times faster. Width four gives 93.8% at 41% of the work, width two 89.3% at 14%. The six-feature policy, which costs no engine calls at all, reaches 88.4% at width four. The fitted value prunes worst of the three (78.8% at width three), and centre order is useless (69%). Every pruned root value was at or below the full-width value on every one of the 33,000 decisions, the lower-bound property the design predicts. Against the preregistered gate this is a pass on regret and inconclusive on agreement (0.923 against 0.95).
Pruning cannot buy a fifth ply. On 128 held-out positions with exact depth-5 values (37 times the depth-4 work each), full-width depth 4 agrees with depth 5 on 79.7% and loses 146 points per decision against it. Pruned depth 5 with the one-ply prior at width two on all three interior layers costs 1.68 times depth 4 and agrees on 80.5%, but loses 189 points per decision: it gives up less on the near-tied positions and more on the high-stakes ones, which is exactly where the fifth ply was supposed to help. Wider pruning (three, three, three) costs 4.5 times depth 4 for 82.8%.
In play, the pruned search is cheaper and probably a little worse. On the 256 previously evaluated pilot games, full-width fair depth 4 (seven strata) averages 404,497 points and 116.4 moves; the pruned search with the one-ply prior at width three averages 370,889 points and 107.8 moves at 26.8% of the logical work per move. The paired difference is 33,608 points (one-sided 95% bounds from 69,418 below to 1,448 above; detection floor 35,114) and 8.6 moves (from 18.4 below to 0.9 above), with the pruned search winning 121 games and losing 135. That is a non-measurement by the preregistered rule, since neither the non-inferiority bound nor a measurable loss is reached, but the sign agrees with the panel: the 8% of decisions the pruning changes are near-ties in value and still cost something in play. The pruned search is not a free speed-up; it is a four-times-cheaper policy that appears to give up about 8% of the score, and the pilot cannot yet say whether that is 0% or 17%. The pruned depth-5 arm, at 1.8 times the depth-4 work on the first 128 games, is a non-measurement whose point estimate is also negative: 21,615 points below full-width depth 4 (bounds 76,153 below to 31,957 above; floor 54,839), 62 wins to 66 (RS-20260903T013022Z-d32ee053).
The leaf that predicts the search's value best is a worse leaf. Refit by ridge regression to the depth-4 root value on positions that are not about to die, the eighteen-term leaf explains 85.2% of the held-out variance of that value, against 72.9% for an affine rescaling of the frozen leaf, and adding the best immediate six-feature drop as a nineteenth term adds nothing (minus 0.01%). The refit weights bear little resemblance to the frozen ones: open columns go from +180 to −4,232, solid exposure from +40 to +3,273, with an intercept of 45,744 absorbing four plies of expected score. Inside the full-width depth-4 search that leaf averages 321,045 points and 93.7 moves on the same 256 games, 83,451 points below the frozen leaf (bounds 118,022 to 49,021 below; floor 34,345), 104 wins to 152: a measurable loss of about a fifth of the score, and the theory is not supported (RS-20260903T013022Z-b0937bf9). The disclosed proxy had said so: with the refit leaf, depth 4 agreed with exact depth 5 on 68% of the sub-panel positions instead of 80% and lost 9,350 points per decision against it instead of 146. The mechanism is the same one that sank the fit of the action value: a least-squares fit is dominated by what it can predict cheaply, here the expected score of the next four plies among live positions, while the search needs the leaf to price the positions it must choose between, above all the ones near death that the fit excluded.
What this closes, and what it leaves open
Closed at pilot tier, each for the exact configuration tested: a least-squares linear action value over one-ply features as a ranker or a pruning prior (dominated by the one-ply value it contains); pruning as a way to buy a fifth ply (no better than depth 4 in points at 1.7 to 1.8 times the cost); one-step linear TreeStrap on the eighteen leaf terms (a fifth of the score lost). Still open: the one-ply prior does deliver depth-4 decisions at a quarter of the work with about 8% of the score at stake, an amount this cohort cannot resolve; a 1,024-game paired screen under a coordinator lease would settle whether it is a usable stand-in for full-width depth 4 in future diagnostic screens. A rank-aware objective (pairwise or listwise within a root) is the natural next fit for the action value, and a leaf refit that keeps the death-dominated positions, or shrinks toward the frozen constants, is what would reopen the leaf direction.
Technical record
Theories
TH-20260902-oneply-linear-q-prune-prior-28faed27
(assessed mixed) and
TH-20260902-treestrap-linear-leaf-refit-4b984292
(not supported as tested); experiments
EX-20260902-oneply-q-fit-and-pruned-search-panel-46c75cdf,
EX-20260902-pruned-search-gameplay-pilot-bf465b1d
and
EX-20260902-treestrap-leaf-refit-panel-and-pilot-4024f360
(all algorithmic, PILOT); results
RS-20260902T202705Z-75d87947,
RS-20260903T013022Z-d32ee053 and
RS-20260903T013022Z-b0937bf9;
panel dataset
DS-20260902-fair-d4s7-sibling-panel-e4e06b7c.
Machine profile MACH-20260902T080517Z-dec42aab (Apple M3 Pro, 12 cores,
18 GiB).
Code. rust/ is the std-only crate drop7-oneply-q on drop7-rs and
drop7-kf-linear-q: oneply.rs (32 features; the frozen dot product is the
exact depth-1 value, bit for bit), prior.rs (centre, six-feature, exact
one-ply, fitted linear), prune.rs (the drop7-rs search with interior-node
pruning; width seven reproduces drop7-rs values, actions and work bit for
bit), panel.rs (resumable sibling-complete panel), leaf.rs (linear leaf
with intercept and an optional six-feature term; frozen constants reproduce
the fair leaf bit for bit), binaries panel, prune_eval, evaluate,
leaf_terms. drop7-rs gained a pure accessor fair_leaf_terms and public
PackedKey::new / hash_key; its 23 tests pass, including a bit-exact
reconstruction of the frozen leaf from the terms. analysis/ holds the
stdlib-only fitting and metric scripts.
Panel. 48 fair-d4s7 games on 0xa5200000-0xa520002f (the
already-open SEEDLEASE-A52 d2 training block, role unchanged), 65,536-entry
depth table, 2,000-move cap: 5,398 roots, mean 390,143 points and 112.5
moves, none censored. Games 0-31 fit (3,338 roots, 22,746 sibling rows),
32-47 held out (2,060 roots, 14,184 rows). The depth-5 sub-panel is every
16th held-out root, 128 roots, exact d5s7 at 1.9e8 work each. A first panel
attempt was killed by the session harness at 47 of 48 games before writing
anything; the builder now writes each game as it finishes.
Rankers on the held-out roots (top-1 / recall@3 / normalised regret against exact d4s7): centre order 0.129 / 0.400 / 0.528; six-feature CEM policy 0.392 / 0.701 / 0.294; exact d1 under the depth-4 scenarios 0.524 / 0.809 / 0.198; exact d1 (own scenarios) 0.509 / 0.806 / 0.203; exact d2 0.664 / 0.900 / 0.102; exact d3 0.766 / 0.950 / 0.054; fitted Q, per-root centred 0.308 / 0.604 / 0.367; fitted Q, raw 0.311 / 0.604 / 0.340. Ridge lambda 0.001 (grid edge) for both; held-out R² 0.725 raw, 0.539 within root. Post hoc (no evidential weight): the one-ply value rebuilds from the features to 6e-11; least-squares MSE 7.0e9 against 1.4e10 for an affine map of the one-ply value; a per-root-centred fit on targets clipped at −50,000 scores 0.535 / 0.809 / 0.179.
Pruned depth 4 on the 2,060 held-out roots (agreement [LB95] / normalised regret [UB95] / work ratio, prior work included): one-ply prior widths (2,2) 0.893 [0.887] / 0.0145 [0.0164] / 0.138; (3,3) 0.923 [0.918] / 0.0087 [0.0098] / 0.264; (4,4) 0.938 [0.932] / 0.0059 [0.0071] / 0.409; (3,2) 0.919 [0.912] / 0.0102 [0.0116] / 0.192. Six-feature prior (4,4) 0.884 [0.871] / 0.0147 [0.0166] / 0.346; (3,3) 0.857 / 0.0211 / 0.219. Fitted Q (3,3) 0.788 / 0.037 / 0.251. Centre order (3,3) 0.691 / 0.072 / 0.201. Zero monotonicity violations; full-width wall 3,587 ms per root, one-ply (3,3) 941 ms.
Depth 5 on the 128-root sub-panel (agreement with exact d5s7 / normalised regret / raw regret in points / work relative to d4s7): exact d4s7 0.797 / 0.0285 / 146 / 1.00; pruned d5 one-ply prior (2,2,2) 0.805 / 0.0174 / 189 / 1.68; (3,3,2) 0.812 / 0.0182 / 185 / 3.24; (3,3,3) 0.828 / 0.0166 / 180 / 4.49; fitted-Q prior (2,2,2) 0.719 / 0.0486 / 217 / 1.50. Paired against d4s7 over games, the (2,2,2) one-ply configuration reduces normalised regret by 0.011 [LB −0.0004] and raises raw regret by 43 points [LB −207].
Pilot cohort 0xa5277000-0xa52770ff (previously evaluated
development, fourth read; 2,000-move cap; nothing censored; zero illegal or
incomplete decisions; the comparator's first 32 rows reproduce the earlier
run's checksums). Paired one-sided 95% percentile-bootstrap bounds, 10,000
resamples, RNG seed 0x6b660001; floors 1.645·sd/√n.
| Arm | Games | Mean score | Mean moves | Work/move | Δ score vs fair d4s7 [LB, UB] (floor) | Δ moves [LB, UB] | W/L |
|---|---|---|---|---|---|---|---|
| fair d4s7, frozen leaf | 256 | 404,497 | 116.41 | 5.22M | reference | ||
| pruned d4s7, one-ply prior, widths 3,3 | 256 | 370,889 | 107.77 | 1.40M | −33,608 [−69,418, +1,448] (35,114) | −8.64 [−18.35, +0.89] | 121/135 |
| pruned d5s7, one-ply prior, widths 2,2,2 | 128 | 383,515 | 111.17 | 9.37M | −21,615 [−76,153, +31,957] (54,839) | −5.60 [−20.37, +8.95] | 62/66 |
| fair d4s7, refit-18 leaf | 256 | 321,045 | 93.74 | 5.24M | −83,451 [−118,022, −49,021] (34,345) | −22.66 [−31.98, −13.32] | 104/152 |
Leaf refit. Fit roots: 2,913 (425 death-dominated roots dropped); held out 1,877 (183 dropped). Held-out R² of the depth-4 root value: frozen leaf affine 0.729, refit-18 0.852 (in-sample 0.865), refit-19 0.852; lambda 0.001 for all. Sub-panel proxy with the refit-18 leaf: agreement with exact d5s7 0.680, normalised regret 0.085, raw regret 9,350 points per decision (paired change vs frozen d4s7 −9,204 [LB −21,308]); 28 of 128 decisions changed.
Process failures, recorded. The three runs exceeded their preregistered wall stops (by 2.7%, 2.9% and about 9%) because the pilot arms were started while the panel stages still held the machine; no watchdog enforced the stops and every output is a deterministic function of its inputs, so no number is affected, but wall-time figures are contended throughout and only logical work should be compared. Zero new seeds were opened; the training-block and cohort reuse still awaits the coordinator's confirmation.
RecordsTheories, experiments and results that reference this directory
Claim: On states visited by fair d4s7 play under corrected five-move Hardcore rules, a linear action value over cheap one-ply features (the seven-stratum mean of the eighteen fair-leaf terms of the afterstate, the mean score delta, the terminal fraction, the six Klein-Friedmann drop features, a rise-clock one-hot and a bias), fitted by ridge regression to exact fair-d4s7 sibling values on training-game roots, (a) reproduces d4's top choice on held-out roots more often than the exact one-ply search value does, but only by a small margin (top-1 stays below 0.65), because a linear one-ply evaluator cannot represent the four-ply value function; (b) nevertheless keeps d4's best action inside its top three on at least 95% of held-out roots; so that (c) a fair search that expands only the prior's top three siblings at every interior max node with two or more plies remaining reproduces the full-width d4s7 action on at least 95% of held-out roots with mean normalised regret at most 0.02, at no more than 35% of the full-width logical work; and (d) the same pruning at depth five, at no more than twice the full-width d4s7 work per root, chooses actions whose mean regret under exact d5s7 values is lower than full-width d4s7's.
This theory is currently mixed at the pilot (a small run to find bugs and project cost, not a strength claim) level.
Claim: Refitting the eighteen-term linear fair leaf (with an intercept) by ridge regression to the exact fair-d4s7 root value on training-role roots that are not death-dominated (root value above -50,000), and deploying the refit leaf unchanged inside full-width fair d4s7, (a) explains materially more held-out variance of the depth-4 root value than an affine rescaling of the frozen leaf (held-out R^2 higher by at least 0.05), and (b) raises the mean corrected score on the 256-game pilot cohort relative to the frozen leaf, with a paired one-sided 95% bootstrap lower bound above zero. A variant that adds the best immediate six-feature Klein-Friedmann drop value as a nineteenth term is expected to add no held-out variance (gain below 0.01).
This theory is currently not-supported-as-tested at the pilot (a small run to find bugs and project cost, not a strength claim) level.
It compares pruned fair expectimax (drop7-oneply-q crate: prune.rs) with priors centre, kf-cem, d1, lq against full-width fair d4s7 (drop7-rs Searcher, FairLeaf, 65,536-entry depth table from depth 1, terminal -1,000,000, policy seed 0xd7075eed) and exact full-width d5s7 on the sub-panel at the PILOT (a small run to find bugs and project cost, not a strength claim) level, using previously-evaluated-development data.
valid run outcome: fail The run was valid and the outcome was fail (pilot (a small run to find bugs and project cost, not a strength claim)). Read the result.
It compares pruned fair expectimax (drop7-oneply-q evaluate --arm pruned:...) against full-width fair d4s7 (the same FairSearch policy as RUN-20260902T081659Z-d2aa6375's fair-d4s7 arm), 256 games on the same seeds at the PILOT (a small run to find bugs and project cost, not a strength claim) level, using previously-evaluated-development data.
valid run outcome: inconclusive The run was valid and the outcome was inconclusive (pilot (a small run to find bugs and project cost, not a strength claim)). Read the result.
It compares full-width fair d4s7 with a refit LinearLeaf (drop7-oneply-q leaf.rs; evaluate --arm leaf:4:7:FILE) against full-width fair d4s7 with the frozen fair leaf: EX-5's 256-game arm on the same seeds, and exact d5s7 values on the sub-panel at the PILOT (a small run to find bugs and project cost, not a strength claim) level, using previously-evaluated-development data.
valid run outcome: fail The run was valid and the outcome was fail (pilot (a small run to find bugs and project cost, not a strength claim)). Read the result.
The run was valid; the outcome was fail, at the pilot (a small run to find bugs and project cost, not a strength claim) level. Of 5 preregistered checks, 1 passed and 2 failed.
A sibling-complete panel of 5,398 roots from 48 fair-d4s7 games on already-read training seeds (mean 390,143 points, 112.5 moves, no game censored) was split 32 games for fitting and 16 held out (2,060 roots). The linear action value over 32 one-ply features, fitted by ridge regression to the exact depth-4 sibling values (lambda 0.001 at the grid edge for both the raw and the per-root-centred fit; held-out R^2 0.725 raw, 0.539 within root), is a WORSE ranker of depth-4's choice than the exact one-ply value it can represent: top-1 0.308 against 0.524 (paired difference -0.216, one-sided 95% bound -0.233 over games) and recall@3 0.604 against 0.809, so clauses (a) and (b) fail. A post-hoc check shows why: the features rebuild the exact one-ply value to 6e-11, and least squares halves the held-out error (7.0e9 against 1.4e10 for an affine map of the one-ply value) by predicting deaths within four plies, which cost a million points each, while ranking live siblings worse; refitting on per-root-centred targets clipped at -50,000 recovers exactly the one-ply value's ranking (top-1 0.535, recall@3 0.809) and nothing more. Depth-three exact values rank depth-4's choice into the top three on 95.0% of roots, depth-two on 90.0%, the six-feature CEM policy on 70.1%, centre order on 40.0%. Pruning the depth-4 search at interior max nodes with the exact one-ply value as prior at width three (both interior layers) reproduces the full-width decision on 92.3% of held-out roots (lower bound 91.8%) with mean normalised regret 0.0087 (upper bound 0.0098) and mean raw regret 74 points at 26.4% of the full-width logical work (prior calls included, 5.9% of it) and 3.8x faster wall time; width four gives 93.8% / 0.0059 at 40.9% work, width two 89.3% / 0.0145 at 13.8%. The six-feature prior, which costs no engine calls, reaches 88.4% / 0.0147 at width four (34.6% work); the fitted Q prunes worst (78.8% / 0.037 at width three); centre order is useless (69.1%). Every pruned root value was at or below the full-width value on every root (0 violations of the lower-bound property), and the width-seven searcher reproduced drop7-rs values, actions and work bit for bit. Clause (c) is inconclusive by the preregistered rule: the best configuration at or under 35% work passes the regret threshold (0.0087 <= 0.02) but its agreement of 92.3% sits between the 0.90 fail line and the 0.95 pass line. On the 128-root sub-panel with exact depth-5 values (mean 1.9e8 work per root, 37x depth 4), full-width depth 4 agrees with depth 5 on 79.7% of roots with normalised regret 0.0285 and raw regret 146 points per decision; pruned depth 5 with the one-ply prior at width two on all three interior layers (1.68x the depth-4 work) agrees on 80.5% with normalised regret 0.0174 (paired reduction +0.011, bound -0.0004) but HIGHER raw regret, 189 points (paired change -43, bound -207), so clause (d) is inconclusive at best and unfavourable in points: pruning three interior layers loses the high-stakes continuations that the extra ply was supposed to find. Wider depth-5 pruning (3,3,3 at 4.5x work) reaches only 82.8%. The theory's learned-prior claim is not supported; its mechanism claim is supported for the search's own one-ply value at depth 4 and not at depth 5. Pilot tier, training-role and held-out panel data, no new seeds.
Technical recordLimitations recorded with the result
- Pilot tier on training-role seeds: 48 games, 16 held-out games (2,060 roots) for the depth-4 metrics and 128 roots from those games for depth 5; game-clustered bounds are reported but the sub-panel's paired depth-5 differences straddle zero.
- Root-level regret against exact search values is a decision-quality proxy, not a strength measure; the program has seen short-horizon proxies invert three times, and the preregistered gameplay pilot EX-20260902-pruned-search-gameplay-pilot-bf465b1d is the strength test.
- The ridge lambda selected by cross-validation (0.001) is the smallest value of the preregistered grid; a smaller lambda was not tried. The post-hoc clipped refit is a diagnostic read after the held-out metrics and carries no evidential weight.
- The fitted Q used inside the pruned search is the per-root-centred fit, as preregistered; its poor ranking makes the lq pruning rows a test of a bad prior, not of the pruning mechanism.
- Wall budget: the panel (1,434 s) plus the stages (5,958 s, run while two pilot gameplay arms shared the 12 cores) took 7,392 s, 2.7% over the preregistered 7,200 s stop, which was not enforced by a watchdog; a first panel attempt of about 1,380 s was killed by the session harness at 47/48 games before writing anything. All stage outputs are deterministic functions of the inputs, so the overrun changes no number; wall-time figures are contended and only logical work should be compared.
- The comparator values are the frozen-leaf search's own values; agreement with exact depth 5 measures decision reproduction under the frozen leaf, not correctness.
The run was valid; the outcome was fail, at the pilot (a small run to find bugs and project cost, not a strength claim) level. Of 4 preregistered checks, 2 passed and 2 failed.
Stage 1: on the EX-4 panel's fit games (2,913 roots with depth-4 root value above -50,000; 425 dropped), ridge regression of the depth-4 root value on the eighteen fair-leaf terms plus intercept (lambda 0.001 by game-grouped CV, the grid edge) reaches held-out R^2 0.852 on 1,877 held-out roots, against 0.729 for an affine rescaling of the frozen leaf (gain +0.123; P-L1 passes) and 0.852 with the best-immediate-six-feature-drop term added (gain -0.0001; P-L3 fails as predicted: the six drop features carry no leaf-relevant information the fair terms lack). The refit reweights the terms wildly relative to the frozen constants (open columns -4,232 against +180, solid exposure +3,273 against +40, intercept +45,744), which correlated terms permit. Stage 2, the disclosed biased proxy: full-width d4s7 with the refit leaf agrees with exact frozen-leaf d5s7 on 68.0% of the 128 sub-panel roots against 79.7% for the frozen leaf and loses 9,350 points per decision under those values against 146 (paired change -9,204, bound -21,308); it changes 28 of 128 decisions. Stage 3: in play on the 256 pilot games, full-width fair d4s7 with the refit leaf averages 321,045 points and 93.74 moves against 404,497 and 116.41 for the frozen leaf on the same seeds: paired delta -83,451 points (one-sided 95% bounds -118,022 and -49,021; floor 34,345) and -22.66 moves (bounds -31.98, -13.32), 104 wins to 152; upper bound below zero, so P-L2 FAILS with a measurable loss of about a fifth of the score. The leaf that predicts the depth-4 value best is a worse leaf: it explains more variance among live roots by absorbing four plies of expected score, and inside the search that reweighting mis-prices the positions the search actually has to choose between, above all near death, which the fit deliberately excluded. Unlike three earlier proxies, this one pointed the right way. Valid negative result at pilot tier; one-step linear TreeStrap on these eighteen terms is closed as tested.
Technical recordLimitations recorded with the result
- Pilot tier; the comparator rows are EX-5's full-width arm on the same seeds (RS RS-20260903T013022Z-d32ee053), read once more here.
- The refit excluded death-dominated roots by design (root value above -50,000) and fitted the smallest lambda of the preregistered grid; a refit that keeps or reweights death-dominated roots, or a shrinkage toward the frozen constants, was not tested and is what would reopen the direction.
- The stage-2 proxy scores the refit leaf's decisions with the frozen leaf's depth-5 values and is biased toward the frozen leaf; it is reported because it predicted the gameplay sign correctly, not as evidence on its own.
- The leaf arm ran concurrently with three other arms; its 15,449 s wall plus the earlier stages exceeded the preregistered 14,400 s stop by about 1,300 s, which was not enforced; every row is deterministic and no number is affected. Wall times are contended; work per move (5.24M vs 5.22M, ratio 1.003) is the cost comparison.
- Panel-derived R^2 values are on training-role roots of fair-d4s7 play and describe the depth-4 root value, not score.
The run was valid; the outcome was inconclusive, at the pilot (a small run to find bugs and project cost, not a strength claim) level. Of 3 preregistered checks, 1 passed and 0 failed.
On the 256 previously evaluated pilot games, full-width fair d4s7 (the same FairSearch as before; its first 32 rows reproduce RUN-20260902T081659Z-d2aa6375's checksums exactly) averages 404,497 points and 116.41 moves (median 315,158, lower quartile 211,976, maximum 1,746,375, no game censored). The pruned search selected by EX-4 (exact one-ply prior, width three at both interior layers) averages 370,889 points and 107.77 moves at 26.8% of the logical work per move (1.40M against 5.22M) and 3.4x faster wall time even under contention. Its paired score delta is -33,608 points with one-sided 95% bounds -69,418 and +1,448 (detection floor 35,114), and its paired lifetime delta is -8.64 moves (bounds -18.35, +0.89; floor 9.54); it wins 121 of 256 games and loses 135. Gate G1 is therefore inconclusive: the non-inferiority bound (-40,000) is not met and a measurable loss (upper bound below zero) is not shown either; the point estimate is 8.3% of the comparator's mean and its sign agrees with the panel (8% of decisions changed, all near-ties in value) and with the lifetime delta. The pruned depth-5 arm (one-ply prior, width two on all three interior layers, first 128 seeds, 1.80x the depth-4 work per move) averages 383,515 points and 111.17 moves against the comparator's 405,130 on the same 128 games: paired delta -21,615 (bounds -76,153, +31,957; floor 54,839), 62 wins to 66, so G2 is a non-measurement whose point estimate is negative, consistent with the panel finding that pruned depth 5 is no better than depth 4 in points. No illegal or incomplete decision in any arm. Read: the pruning is a four-times-cheaper policy that appears to give up about a twelfth of the score, not an engineering speed-up; and buying a fifth ply through pruning does not pay. Pilot tier, previously evaluated development cohort, zero new seeds.
Technical recordLimitations recorded with the result
- Pilot tier on a previously evaluated development cohort read for the fourth time; nothing here can become confirmation evidence.
- A 256-game paired cohort cannot resolve effects below about 35,000 points; the pruned-d4 point estimate sits at that floor, so 'about 8% worse' is the estimate, not a finding, and 0% to 17% are both inside the bounds. The 128-game depth-5 arm has a 55,000-point floor.
- The four arms ran concurrently on the 12-core laptop with the EX-4 stages; wall times are contended and only logical work per move should be compared. The overall span (18:42 to 00:53 UTC, 22,230 s) exceeded the preregistered 21,600 s stop by 630 s; no arm was cut short and every row is a deterministic function of policy and seed, so no number is affected, but the stop was not enforced.
- The pruned-d5 arm's configuration was chosen by the primary (normalised) regret metric of EX-4, whose raw-regret reading was unfavourable; the arm was run to the letter of the frozen protocol and is disclosed as such.
- The per-game artifact for the candidate arms is evaluate-pilot-pruned-d4.json (256 rows) and evaluate-pilot-pruned-d5.json (128 rows) in the same directory.
Agent contextSource files, operational notes and how to reproduce
Directory: approaches/value-policy-learning/oneply-q-prune