Search settings under the learned tables

What each arm changes

The baseline seat is v2:{"depth":2,"leaf":{"tables":"artifacts/ntuple/hex-portfolio-main.bin"}}, the depth-2 search that evaluates with the learned n-tuple tables. Each candidate is that seat plus one switch, played against the unchanged baseline. The same nine switches were measured under the hand-written leaf in the ablation program, in one seating; the seating diagnosis later showed those contrasts carry a turn-order term of +0.05 to +0.18 wins per game, so they are quoted here with that caveat.

The design

Every contrast is a swapped pair on the same seeds: half A seats the candidate in slot 0 and the control in slot 1, half B seats the control in slot 0 and the candidate in slot 1, and the seating-corrected effect is the per-seed half-difference of the two slot-0-minus-slot-1 contrasts, with the seating term their half-sum (analysis/seating_pair.py). Development played seeds 0 to 63 against the eta and fast builders, the boards of the hand-leaf ablations; confirmation played fresh seeds 800 to 863, which no earlier experiment used; population played seeds 800 to 863 with the tables baseline in slot 2 and eta in slot 3, so three searches share the table. Arms whose pooled effect over the 128 development-plus-confirmation seeds is positive with an interval reaching within 0.03 of zero extended to seeds 864 to 927 in both lineups. Each half is 256 games (64 seeds, four rotations, deterministic tapes); every cohort completed all games with no invalid moves, stalls, or search errors. Decision times are wall-clock under a machine shared with other research (load 80 to 160 on 32 cores), so the candidate-to-control ratio inside the same games is the cost reading, not the absolute milliseconds.

The cohorts

Every run in the program, half by half. Half A seats the candidate in slot 0; half B seats it in slot 1. Slot 0 and slot 1 wins are out of 256.

The effects

Pooled rows pool the per-seed effects of both halves over stages; they are after-the-fact poolings of preregistered cohorts. The two arms whose pooled 128-seed effect was positive with an interval reaching within 0.03 of zero (samples 8 and leaf opponents) extended to seeds 864 to 927 in both lineups, so their L1 estimates rest on 192 seeds and their L2 estimates on 128.

Bold intervals exclude zero. Stage by stage: scenarios 4 read −0.416 (−0.490 to −0.342) on the development boards and −0.367 (−0.443 to −0.291) on the confirmation boards; samples 1 read −0.109 twice; counts only read −0.141 and −0.145; no proposals read −0.143 and −0.201; reciprocity read −0.070 and −0.076; samples 8 read +0.057 (−0.007 to +0.120), +0.025 (−0.029 to +0.080), and +0.053 (−0.016 to +0.121) at the builder table and −0.010 (−0.064 to +0.045) and −0.004 (−0.057 to +0.049) at the population table; leaf opponents read +0.041 (−0.020 to +0.102), +0.016 (−0.054 to +0.086), and +0.037 (−0.024 to +0.098) against the builders and +0.012 (−0.049 to +0.073) and +0.055 (−0.003 to +0.112) at the population table. The seating terms measured by the pairs land between −0.018 and +0.146, in line with the seating report; the inner_scenarios:2 pair, whose two halves play identical lineups, measures the term directly: +0.098 (+0.006 to +0.189) on seeds 0 to 63 and +0.078 (−0.028 to +0.184) on seeds 800 to 863.

Dice scenarios

Four scenarios cost −0.392 wins per game, roughly what removing six of the eight scenarios cost under the hand-written leaf (−0.410 single-seating on the same boards, corrected for the +0.176 term of that design, about −0.59). The diagnostics say why the loss is so large: the four-scenario seat ends turns over the seven-card limit constantly, discarding 13.9 cards per game against the control's 5.5, buying 2.75 development cards against 4.25, and finishing 2.4 points behind. Its imagined opponents' rounds are too coarse to see when holding cards is safe. Sixteen scenarios are the mirror image: a null effect (−0.026, interval crossing zero) at 2.7 times the decision cost. Averaging the opponents' round over eight scenarios is close to the right operating point under the tables; the eight default scenarios buy almost all of the available strength, and doubling the count buys nothing the games can see.

Sampled hidden worlds

One sampled world costs −0.109 and cuts decision time to about a third: the belief average over four worlds is real strength, not noise. Eight worlds are the one switch in the program that gains strength, and only where the other seats are builders: +0.045 (+0.009 to +0.081) pooled over the 192 L1 seeds, with every one of the three pairs landing between +0.025 and +0.057. At the population table the gain is gone, −0.007 (−0.045 to +0.031) pooled over 128 seeds, so the extra belief averaging buys nothing when the opponents model the search right back. The cost is 1.8 times the control's decision time, so the switch fails the browser rule on cost even before the population reading. Under the hand-written leaf one world read −0.051 single-seating (−0.012, crossing zero, on 192 fresh seeds): the sampled-world average matters more under the tables leaf than it did under the hand-written terms.

Deeper-level scenarios

inner_scenarios sets the scenario count for the opponents' rounds after deeper planned turns, and at depth 2 there are none: the leaf is evaluated at the end of the second planned turn, before any deeper round. The arm cannot change a decision, and the cohorts confirm it: both halves of both stages played byte-identical games (the effect is exactly zero by construction, and the pair's seating term is the null term for those boards). This switch first binds at depth 3, the browser's depth, where it has not been measured.

Leaf-guided opponents

Letting the opponents inside the lookahead choose by the tables leaf instead of the fixed builder leans positive everywhere and resolves nowhere: +0.031 (−0.006 to +0.068) over the 192 L1 seeds and +0.033 (−0.009 to +0.075) over the 128 population seeds, five pairs all positive, no interval excluding zero, at 1.8 times the control's decision time. The mechanism does change the search's picture of the future: the candidate accepts more offers from others (1.3 against 1.1 per game) and declines fewer, because the opponents it imagines now trade toward their own best builds. Under the hand-written leaf the same switch read −0.008 (single seating); under the tables it is a plausible small gain that this budget, even after the extension, cannot confirm.

Event knowledge

counts_only drops the event history and samples hidden hands from public counts alone, the one belief mechanism confirmed under the hand-written leaf (−0.066 when removed, 192 seeds). Under the tables it costs twice that: −0.143 (−0.188 to −0.097), and −0.053 (−0.107 to +0.002) at the population lineup. The seat with counts-only beliefs proposes less (11.9 offers per game against 14.9) and misprices the trades it is offered; event knowledge is worth more, not less, to the stronger leaf.

Proposals

Turning proposals off costs −0.172, the largest social effect in the study, and it holds at the population table (−0.143, −0.197 to −0.089) where another search answers offers. The diagnostics show the mechanism: the silent seat falls from 14.2 offers per game to 4.6 (the residue is counters to others' offers), closes 2.7 player trades per game against 3.9, and finishes 1.1 points behind. Under the hand-written leaf the same switch read −0.027 single-seating (interval crossing zero): proposals were worth little to the weaker search and are worth a seventh of a win to the tables search.

Reciprocity

Scaling each partner's modeled willingness by their observed acceptance rate of this seat's offers is the one arm whose interval excludes zero in the wrong direction: −0.073 pooled over the 128 L1 seeds, −0.082 (−0.141 to −0.023) against the population lineup. The mechanism explains the loss: against the builders and the baseline search, whose acceptance rules are fixed, a partner that has refused the seat's offers is not a partner that will keep refusing, so the seat with the scaling stops asking. It offers 9.8 times per game against the control's 14.7, counters half as often, declines more, and finishes 0.4 points behind. Under the hand-written leaf the same switch read −0.031 (interval crossing zero); under the tables it is confirmed harmful and stays off.

Against the hand-written leaf

Six of the nine arms have hand-leaf readings on the same development boards, all in one seating with the candidate in slot 0, so each carries the +0.176 seating term of that design in the candidate's favor; the corrected hand-leaf estimate is roughly the published contrast minus that term. The table compares each hand-leaf contrast with the seating-corrected tables effect.

The pattern is one-directional: every information input to the search is worth as much or more under the learned leaf. The stronger evaluator does not absorb the value of the belief machinery; it leans on it. Only the opponent-model switch (leaf-guided opponents) moved toward the tables leaf, from roughly zero to a small unconfirmed positive.

What could still be wrong

These are engine-arena games at depth 2 on two lineups; strength through the protocol arena, at other depths, or against humans is not established. The decision times are wall-clock under heavy shared load, so only their ratios are comparable; the ratios themselves are stable across halves and stages. The population lineup seats three copies of the same search family, so the social arms (proposals, reciprocity) are measured against opponents whose acceptance behavior is fixed or search-like, not human. The two positive-mean arms (samples 8, leaf opponents) were extended after their pooled intervals reached toward zero, so their final estimates rest on 192 seeds but the extension was chosen after seeing the first 128; both poolings are named as after-the-fact wherever they appear. The inner_scenarios arm is simply untested at the depth where it binds. Every arm was tested alone; combinations were not.

What this means for the browser

The browser build runs WASM, the hand-written leaf, depth 3 under a one-second budget, so a switch is worth enabling there only if it adds strength within the cost rule (pooled effect at least +0.03 with an interval excluding zero and decision time within 25% of the control), saves time without losing strength, or buys a depth the budget would otherwise deny. No switch meets the strength and cost rule together: eight sampled worlds reach the strength half against builders (+0.045, interval excluding zero) but cost 1.8 times the control's decisions and lose the gain at the population table, and the leaf-guided opponents stay unresolved at the same cost. Everything else loses strength. The defaults are right for the browser too, with three cost readings worth keeping:

• scenarios:4 cuts decision time to 68% but loses 0.39 wins per game under the tables and about as much under the hand leaf (−0.410 published, worse corrected). It is not a browser lever; halving the dice average is the one setting both leaves agree is catastrophic.
• samples:1 cuts decision time to about a third for −0.109 under the tables (the hand leaf's fresh-seed reading was −0.012, crossing zero). This is the one genuine trade on the table: if the one-second budget cannot finish depth 3 in the browser, one sampled world is the setting most likely to buy the missing depth for a strength price of roughly a tenth of a win per game, and it should be measured there in WASM before any decision. It is not worth enabling while depth 3 fits the budget.
• inner_scenarios:2 is free at depth 2 because it cannot bind there, but at the browser's depth 3 it does bind and its cost and strength there are unmeasured. It is the natural next measurement for the browser budget: if two deeper-level scenarios hold strength at depth 3, they shorten exactly the part of the tree the browser pays most for.

Everything else stays at its defaults: event knowledge and proposals are worth more under both leaves than any browser saving from dropping them, sixteen scenarios cost time for nothing, the reciprocity scaling is refuted, and the two unresolved positives (eight sampled worlds, leaf-guided opponents) cost 1.8 times the control's decisions, which the one-second budget cannot afford. If the browser budget ever loosens or the tables leaf reaches the browser, eight sampled worlds against builders is the one measured strength gain worth revisiting.

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