Hand management under the learned leaf

The arms

The baseline seat is the arena's tables configuration, v2:{"depth":2,"leaf":{"tables":".../hex-portfolio-main.bin"}}, and each candidate adds one switch. spend_down and discard_projection act on the candidate lists, so they run under the tables alone. spend_down offers up to three bank trades and two roads chosen only to shed cards when the hand is over the discard limit; discard_projection ranks each legal discard by the build deficits of the kept hand plus the production expected before the next own turn.

The third arm is the leaf's seven-risk pricing, weights.hand_risk 0 against the default 1. A leaf term is inert under the tables alone (leaf.hand 0 skips the hand-written terms), so it must be measured on a blend. The program first registered it on the full blend (hand 1.0 in both seats), then a program-wide screen measured the full blend itself at −0.207 wins per game against the tables alone (95% interval −0.284 to −0.130) while the quarter blend read +0.074 (+0.011 to +0.138). A switch measured on a configuration that much weaker than the baseline says little about anything anyone would run, so the six full-blend registrations were withdrawn before running and the arm was re-registered on the quarter blend (hand 0.25 in both seats). The withdrawn registrations are listed in the AgentContext.

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 swaps them, and the effect is the per-seed half-difference of the two slot-0-minus-slot-1 contrasts (the seating term is their half-sum), computed by analysis/seating_pair.py from the retained games. Each half is 64 seeds played once per rotation of the four slots, 256 games, deterministic. The builders lineup puts an ETA and a fast builder in slots 2 and 3, matching the hand-leaf cohorts; the population lineup puts the tables baseline seat in slot 2 and ETA in slot 3, so three searches sit at the table. Stages: development on seeds 0 to 63, confirmation on seeds 800 to 863 (unused by any earlier experiment), population on seeds 800 to 863, and an extension on seeds 864 to 927 in both lineups only when the pooled builders-lineup effect over 128 seeds is positive with its interval's lower bound within 0.03 of zero. The registered decision rule for every pair: the seating-corrected effect's 95% seed interval excludes zero in the hypothesized direction (support), excludes it the other way (refutation), or neither (inconclusive). Pooled estimates across stages are after-the-fact pooling.

All 22 cohorts completed 256 of 256 games. One earlier attempt at the first cohort was interrupted after 3 games by an operator mistake (the queue driver was not session-detached) and is filed as interrupted; its games were not pooled and the cohort was rerun from scratch.

spend_down

Pooled over the two builders pairs (after-the-fact): −0.006 (−0.042 to +0.030), so the extension was not triggered. The population pair leans negative; with the interval's upper end at +0.004 the switch is at best neutral there, and it costs about a fifth more decision time (814 ms against 682 ms per decision, ratio 1.19 pooled over stages).

discard_projection

The pooled builders reading over 128 seeds was +0.011 (−0.018 to +0.040): positive with the lower bound inside 0.03 of zero, so the extension ran. With it, the builders estimate over 192 seeds is +0.012 (−0.010 to +0.034) and the population estimate over 128 seeds is −0.002 (−0.023 to +0.019), both after-the-fact pooling. The switch costs nothing measurable in decision time (ratio 1.00). The builders intervals still allow a small gain, up to about +0.03 wins per game; the population interval caps it at +0.019.

hand_risk 0 on the quarter blend

Pooled over all three stages (after-the-fact): −0.001 (−0.029 to +0.028) over 192 seeds. The term's presence or absence is invisible at this scale, in either lineup.

The mechanisms fire, and it does not matter

Per-game means for the candidate against the control, pooled over each arm's stages. Hand size at the roll is the arena's new per-seat counter, the hand summed over the game's rolls before each roll's production and discards.

The switches move the counts they target. Spending down ends fewer turns over the limit (0.40 against 0.47) and discards less; removing the risk term on the blend raises discards a little; the projection changes which cards go without changing the counts. None of it moves the win rate.

The comparison with the hand-written leaf explains why. Under that leaf the control discarded 8.6 to 9.2 cards per game and ended about 1.0 turn per game over the limit; under the tables the control discards about 5 and ends 0.4 to 0.5 turns over the limit, holding 4.8 cards at the roll. The tables were trained by self-play with the same fixed discard rule, so they already value a held card by what it becomes, and the play they induce rarely reaches eight cards. The situation all three mechanisms address comes up half as often, and the earlier study had already shown pricing it differently buys nothing at this depth even when it does come up: under the hand-written leaf on the same development seeds, spend_down read +0.066 in one seating (the size of the seating term), discard_projection corrected to −0.029 (−0.073 to +0.015), and the hand_risk sweep over 0, 2, and 4 was flat (hand-management report).

What could still be wrong

Everything here is engine-arena development tier at depth 2 on deterministic boards, with two fixed lineups. The projection's builders-lineup intervals do not exclude a gain under +0.034, so a small effect there is possible; the population lineup and the pooled 320-seed reading make anything at or above the +0.03 browser threshold unlikely. The blend the risk arm sits on was chosen by a screen, and the quarter strength also quarters the term's influence, so the arm answers "does the term matter at the strength anyone would run it" rather than "does seven-risk pricing matter at full strength"; at full strength under the hand-written leaf the sweep was already flat. Decision times were measured on a heavily shared machine, so the absolute milliseconds are inflated and only the within-run ratios carry meaning. The seating terms these pairs measured (+0.03 to +0.12) match the null pairs in the seating report, so the correction is behaving as expected. Finally, the tables were trained with the fixed discard rule; a leaf trained with a different rule could price these situations differently.

What this means for the browser

The browser build runs the hand-written leaf at depth 3 under a one-second budget, and the program's rule for adopting a switch there is a pooled effect of at least +0.03 wins per game with the interval excluding zero and a decision cost within 25% of the control's. No arm comes close. spend_down is at best neutral under the tables, leans negative at a search-heavy table, and costs 19% more decision time; under the hand-written leaf its only reading was the seating term. discard_projection is free and never negative, but its best pooled reading is +0.012 and the population lineup caps it at +0.019. The hand_risk weight was flat across 0, 1, 2, and 4 under the hand-written leaf the browser actually runs, and removing it on the blend under the tables is worth −0.001. Enable nothing; keep hand_risk at 1.