Robber targeting under the learned leaf

The arms and the seats

The baseline seat is the depth-2 search evaluating with the learned tables (ntuple-leaf, artifact hex-portfolio-main.bin). Each arm is that seat plus exactly one switch, and the control is the unchanged baseline. All four switches change candidate generation, so they are active under the tables alone: no arm needed the blended leaf.

The hand-written-leaf numbers above are the swapped-pair corrections from containment/robber-targeting-bias and containment/endgame-seating; the single-seating contrasts that first made these arms look strong were the arena's seating term.

Design

Every contrast is a swapped pair on the same seeds: half A seats the arm in slot 0 with the control in slot 1, half B the reverse, each half a separately registered experiment of 64 deterministic seeds played once per rotation (256 games). The seating-corrected effect is half the per-seed difference of the two slot-0-minus-slot-1 contrasts, the seating term half their sum (analysis/seating_pair.py). Two lineups: builders (slots 2 and 3 are eta and fast, matching the earlier hand-leaf cohorts) and population (slot 2 is a third tables search, slot 3 eta, so robber choices are answered by opponents that trade and block). Three stages ran for every arm: development on seeds 0-63 (builders), confirmation on fresh seeds 800-863 (builders), and population on seeds 800-863. The preregistered extension rule then added seeds 864-927 in both lineups for the arms whose pooled builders effect was positive with its interval coming within 0.03 of zero: need and block_leader. Pooled estimates over stages are after-the-fact pooling, named as such.

Every registered decision rule reads the same: all games complete, and the seating-corrected effect's 95 percent seed interval either excludes zero in the hypothesized direction (support), excludes zero the other way (refutation), or neither (inconclusive). Every pair is inconclusive on its own stages; the one cohort whose interval excluded zero is named below.

The cohorts

All 36 cohorts completed all 256 games: 9,216 games, no invalid moves, stalls, or timeouts. One half (leader, development, half B) was interrupted at 143 of 256 games by a shell timeout on the controlling session and was rerun from scratch; the partial interrupted attempt is filed as interrupted and its games were not pooled.

Seating-corrected effects

The development, confirmation, and extension columns are the builders lineup; the two population columns are the population lineup. The bold cell is the only cohort of the program whose interval excludes zero, on the positive side.

Pooled over stages (after-the-fact pooling, equal weight per seed):

The seating terms of the builders pairs reproduce the known adjacency term (+0.047 to +0.137, each interval containing the values measured by the null pairs); the population pairs measure seating terms near zero (−0.039 to +0.043), consistent with three searches breaking the two-seat adjacency.

Compared with the hand-written leaf

The development stage uses the same seeds 0-63 and the same builders lineup as the first hand-leaf cohorts, so the raw slot-0 contrasts are comparable. With the arm in slot 0, the hand leaf read leader +0.125, need +0.160, threat +0.117, and block leader +0.168; under the tables the same design reads leader +0.117, need +0.105, threat +0.074, and block leader +0.094. Both sets are seating-contaminated, and both shrink to about zero once the pair is swapped: the earlier studies corrected to −0.023, −0.045, −0.033, and +0.012, and this study's builders pools read +0.007, +0.016, −0.005, and +0.011. The pattern that looked like an effect under the hand leaf was the seating term, and under the tables it is the seating term again. One difference is real: the need rule's hand-leaf refutation (−0.045, the only interval excluding zero in the earlier program) does not reproduce under the tables, where its builders pool reads +0.016 (−0.008 to +0.041). Under the learned leaf, choosing the victim by the card this seat needs is not measurably worse than choosing by hand size, but it is not measurably better either.

Where the robber goes

Pooled over both halves of every stage of each arm, the mechanisms do what they claim. The leader arm lands the robber on the points leader's highest-pip hex on 31.1 percent of its robber moves against 27.0 percent for its control seats, and robs the leader on 49.9 percent against 42.2 percent. The threat arm robs the leader on 47.3 percent against 42.2 percent and shifts theft toward the other search (37.2 percent of victims against 34.2 percent), consistent with preferring threatening victims over quiet builders. The need arm barely moves these observables, as expected: it changes which non-leader seat holds the stolen card, a distinction the arena records do not carry. The block leader arm nudges late-game placements (43.2 percent leader victims against 42.3 percent).

Victim distribution by opponent seat, pooled the same way, is nearly flat for every arm and control (about 34 percent each to the other search, the eta builder, and the fast or third-search seat), and the builders themselves land on the leader's best hex on 27.9 percent of their robber moves with 43.0 percent leader victims across all cohorts. The arm seats steal from each opponent category in almost the shares the control seats do; only the leader arm's hex placement and everyone's leader-victim rate move visibly.

The other game statistics agree with no mechanism change: counters (about 2.3 offers countered per game), declines (about 7.6), development bought (2.8 to 2.9), cities built (1.5), roads built (4.5), cards discarded (about 6.0), and player trades (about 4.1) differ between arm and control seats by under a twentieth in every arm.

Decision cost

No switch costs decision time. Within each pair the arm seat and the control seat decide within two percent of each other in every stage (for example 576 against 582 ms for the leader pair under load, 69 against 70 ms for the need extension on an idle machine). The cohorts ran at machine loads from about 150 to 6, so absolute milliseconds are not comparable between stages; the within-pair ratios are. The switches score the same shortlist the search already enumerates, so nothing new is evaluated.

The combination

Need and block leader are the two arms the extension rule marked positive with near-zero intervals, and both read positive in every lineup pooled, so they were combined as a final swapped pair on fresh seeds 928-991 in both lineups. The combination reads +0.035 (−0.015 to +0.085) in the builders lineup and −0.039 (−0.090 to +0.012) in the population lineup. The two readings disagree, both cross zero, and the pooled combination is −0.002. Two small effects that do not individually clear their intervals do not add to one that does.

What could still be wrong

The extension arms were chosen after seeing their first two stages, so their final estimates carry that selection; the block leader population extension that excluded zero is one of ten cells, and the study's own bar asked for the pooled estimate to exclude zero, which it does not. Effects under the tables are development-tier engine evidence at depth 2 against one family of opponents; the tables leaf was trained by self-play against these builders and may already price blocking, which would hide exactly the differences these switches try to create. Population-lineup opponents are three copies of the same search, not distinct retaliators. Decision times are wall-clock and the stages ran at very different machine loads, so only within-pair comparisons are usable. Seeds 0-63 were used by the earlier hand-leaf development cohorts, so the development stage is a comparison on shared boards, not fresh ones, by design.

What this means for the browser

The browser build searches with the hand-written leaf at depth 3 under a one second budget, so the deciding evidence is the hand-leaf measurements: leader −0.023, need −0.045 (refuted), threat −0.033, block leader +0.012, all corrected swapped pairs. The tables evidence agrees: every switch is inconclusive, none reaches +0.03 pooled, and the one positive arm combination disagrees with itself across lineups. Since no switch costs decision time, the reason to keep them off is not cost but the absence of a measured effect in either leaf. None of the four switches is worth enabling in the browser. If one is revisited later, block leader is the candidate: it is the only arm positive in every lineup pooled under the tables and the only cohort to exclude zero, but its hand-leaf reading was +0.012 and its pooled tables effects stay under the bar, so a revisit needs a different mechanism or a sharper lineup, not a bigger cohort of the same one.

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