Blending the learned leaf, and the endgame switches under it

The arms

The learned tables won their cohort as the only leaf (the learned leaf report); the search can also add the hand-written terms on top of them. LeafConfig exposes two knobs for that. leaf.hand scales the hand-written terms that are added to the tables' value (0 by default), and leaf.scale sets how many hand-written points one win is worth (1000 by default, so a win is ten points). The scale does not change the search's preference between moves; it changes how the tables' win probability compares with thresholds that are fixed in points: the trade margin and threat premium in bargaining, the deepen_gap stop rule, and the hand terms when they are blended.

Both endgame switches are hand-leaf terms, so they are inert under the tables alone; they were measured with leaf.hand 0.25 in both the candidate and the control seat. They were first registered on the hand 1.0 blend; when an unregistered screen showed the full blend much weaker than the tables alone, the unstarted hand 1.0 registrations were withdrawn and the arms were re-registered on the 0.25 blend, which is the configuration a switch must justify itself on. One full-blend pair (hidden points) had already run and is reported below as what it is.

The design

Every contrast is a swapped pair on the same seeds: half A seats the candidate in slot 0, half B seats it in slot 1, and the effect is the per-seed half-difference of the two slot-0-minus-slot-1 contrasts, which cancels the arena's seating term (the seating report); half their sum is the term. The builder lineup L1 puts eta and fast in slots 2 and 3, the population lineup L2 puts the tables baseline in slot 2 and eta in slot 3, so trades, blocks, and robber choices come from opponents that trade and block. Stages: development on seeds 0 to 63, confirmation on 800 to 863 (never used before), population on 800 to 863 in L2, and, when the pooled L1 effect stayed positive with its interval within 0.03 of zero, an extension on 864 to 927 in both lineups. Every cohort is 64 seeds, 4 rotations, 256 deterministic games, and every one completed all 256.

The stage 1 pair of the hand 0.25 arm reproduces the orchestrator's unregistered screen exactly (+0.074, +0.011 to +0.138): the same seats on the same deterministic boards are the same games, so the registered pair confirms the screen's arithmetic rather than independently replicating it. The fresh seeds of the later stages are the test.

The blend arms

Seating-corrected effect per stage, wins per game; pooled rows are named after-the-fact pooling.

The quarter-strength blend is the only arm whose pooled intervals exclude zero, in both lineups. Its stage 2 number (+0.035) crosses zero, and the extension seeds came back at +0.088, so the pooled L1 estimate rests on 192 seeds and the pooled L2 on 128. The dose-response is monotone in the negative direction: the full blend loses to the tables even from the seat that wins the seating term, half strength is inside the noise, and a quarter is a real improvement.

The scale arms

Halving the scale makes every fixed threshold twice as large in win probability, and the arm shows it in play: the halved seat completed 2.3 player trades per game against the control's 3.7 and lost ground everywhere. Doubling the scale makes the thresholds relatively cheaper, the doubled seat traded more (5.1 against 4.1) and bought more development cards (4.07 against 3.88), and the effect on wins never separated from zero in six pairs. The default scale of 1000 is on the right side of both changes; the doubling is free in decision time but buys nothing.

The endgame arms

Both were measured on the hand 0.25 blend in both seats, with the blend alone as the control.

The race leaf, which replaced the opponent terms with the own-minus-leader margin and the leader's expected points, is a small loss under the blend: its stage 1 interval excludes zero on the wrong side and the pooled L1 estimate does too, so the registered rule reads refutation. Under the hand-written leaf the same switch read +0.018 with an interval crossing zero (the endgame report), so the mechanism does nothing there and slightly hurts the blend. Hidden points is the same story at smaller size: nothing under the hand-written leaf, and nothing under the blend either: its extension was triggered by the letter of the rule (pooled L1 +0.008 after two stages) and the extension seeds brought the pooled 192-seed L1 estimate down to +0.003, with the population lineup slightly negative. The hidden-points pair on the full hand 1.0 blend, which ran before the withdrawal, read −0.029 (−0.075 to +0.016), also nothing.

What the blend changes at the table

Per seat per game over both halves of stage 1 (512 games each side):

The hand-written terms push toward cities and settlements, as expected: at a quarter strength the blend builds a quarter more cities and settles more without giving up development cards; at half strength it starts trading development cards for cities; at full strength it abandons the cards the tables were winning with (3.34 against 4.27 for its control) and carries two discards more per game, and the points it gains do not become wins. The quarter-strength blend keeps the tables' style and corrects its build choices.

Decision time is the blend's cost. Compared inside each cohort, where both seats shared the same machine load, the hand 0.25 seat spent 929 ms per decision against its control's 667 ms, about 40 percent more, and the hand 0.5 seat about the same. The two evaluators are both evaluated at every leaf. The scale arms cost nothing (the doubled-scale seat even ran marginally faster, 573 ms against 599 ms, inside noise). The endgame switches cost at most a few percent, and only because the race leaf's tempo estimate runs at the leaf.

Every cohort

All cohorts are 256 deterministic games; every one completed. "Contrast" is the registered slot-0-minus-slot-1 paired contrast of that half; the seating term is half the sum of a pair's two contrasts.

Withdrawn before running, with reasons in the daily log: the hand 1.0 half B (registered protocol) and the race halves on the full blend (registered protocol, registered protocol), because the full blend measured much weaker than the tables alone and a switch on top of it says nothing about a configuration anyone would use; and the scale 500 stage 3 halves (registered protocol, registered protocol), because stage 2 refuted the arm.

What could still be wrong

Everything here is engine-arena evidence at depth 2 on deterministic boards: two fixed builders for L1, one extra search and one builder for L2. No protocol cohort has confirmed the quarter-strength blend, and nothing tests it at depth 3, against negotiating opponents, or with the tables the search would train next. The blend costs about 40 percent more decision time under machine load; the wall-clock numbers are distorted by a machine shared with other agents, and only the within-cohort ratios are meaningful. The 0.25 weight sits between two tested neighbours and was not itself tuned, so it is a coarse reading of where the optimum is; a cheaper subset of the hand terms might buy the same gain for less time. The extension rule was applied by its letter to three arms, and the pooled rows are after-the-fact poolings across stages that were registered separately. The stage 1 pair of hand 0.25 is the same games as the orchestrator's screen by construction.

What this means for the browser

The browser build runs the hand-written leaf in WASM at depth 3 under a one second budget and cannot load the tables, so leaf.hand and leaf.scale are not browser switches; they configure the server-side ntuple-leaf policy, and the quarter-strength blend is a candidate for that policy, worth a protocol cohort against ntuple-leaf before any default changes. The endgame race and hidden-points switches do run under the browser's hand-written leaf, and each now has two swapped-pair readings: under the hand-written leaf +0.018 and +0.006 (seeds 64 to 127), under the tables blend −0.037 pooled over 128 L1 seeds (negative) and +0.003 pooled over 192, all with intervals crossing zero except the race reading under the blend, which is negative. Neither switch reaches the +0.03 wins per game bar under either leaf, so neither is worth enabling in the browser; both stay off. The blend result does say the hand-written terms carry complementary information next to a learned evaluator, which is a reason to keep them sharp in the browser's own leaf, not a change to make today.

All studies · Learned pattern values · Log 2026-09-11