The opening planner under the learned leaf

The question and the arms

The planner in crates/expectimax/src/v2/opening.rs scores both setup sites as a portfolio with weights calibrated to the hand-written leaf's resource values. The earlier study measured it against the search's own placement under the hand-written leaf and found a match. The leaf has since changed: the learned tables value sites by what wins, and under "search" mode the shortlist is ranked by the lookahead through those tables. Each arm is one switch on the tables baseline seat (v2:{"depth":2,"leaf":{"tables":".../hex-portfolio-main.bin"}}), seated as a swapped pair against the default planner: half A has the candidate in slot 0, half B in slot 1, both on the same seeds, and the effect is half the difference of the two slot-0-minus-slot-1 contrasts with the seating term their half-sum.

Four weight arms were screened first, unregistered, as swapped halves on 16 seeds (928-943, unused by any stage): specialize 0.5 read −0.062 (−0.250 to +0.125), scarcity 0.0 read −0.055 (−0.201 to +0.092), coverage 0.4 with balance 0.5 read −0.023 (−0.144 to +0.097), and expansion 0.5 read −0.055 (−0.185 to +0.076). Screens are screens. The coverage/balance arm had the best point estimate; scarcity tied expansion on the mean and was taken ahead of it for the wider upper interval and because its mechanism, a markup calibrated to the replaced leaf, is the one the tables can plausibly obsolete. Those two arms went through the stages; specialize and expansion stayed screened.

Stages follow the program: development on boards 0-63 with the builders eta and fast (L1), confirmation on fresh boards 800-863, population on 800-863 with a second tables search and eta in slots 2 and 3 (L2), and an extension on boards 864-927 in both lineups for any arm whose pooled L1 effect over 128 seeds was positive with its interval within 0.03 of zero. The search arm (+0.066, +0.001 to +0.132) and the coverage arm (+0.016, −0.025 to +0.056) triggered it; the scarcity arm did not (−0.005, not positive). Every cohort is 256 games (64 seeds, four rotations), all complete in both halves, 26 runs and 6,656 games in total with no incomplete, invalid, or unplayed game.

The search-ranked opening against the planner

Slot 0 of each half holds the candidate named in the row's experiment; the per-slot win rates, mean points, and decision times of every run are in the run records under records/runs/.

The development stage supports the hypothesis and the pooled L1 estimate excludes zero, so the registered rule reads the arm as supported against builders. Two readings temper it. The only cohort whose interval excludes zero is the development one, on boards that many earlier studies used for tuning and where the seating report measured the largest turn order terms; on the 128 fresh L1 seeds alone the effect is +0.024 and crosses zero. And against three searches at the table, where placements are contested by an opponent that trades and blocks, the pooled effect is exactly zero. The search-ranked opening is a bet that pays on builder tables and does not pay on search tables.

The calibration arms

The coverage arm (coverage 0.4, balance 0.5 against defaults 0.15 and 0.2) and the scarcity arm (scarcity 0.0 against the default 1.0) change only the planner's arithmetic, so their decision cost is the control's.

Neither arm separates from zero at any stage. The scarcity markup, tuned to the hand-written leaf's resource values, neither helps nor hurts under the tables, and doubling the coverage and balance weights does nothing either: within the range tested, the planner's choices are insensitive to these weights, or the differences they cause do not convert to wins at depth 2. Both stay at their defaults. The single-seating contrasts in the scarcity rows sit near +0.13 on boards 0-63 and 800-863, the size of the turn-order term there, and the pair removes it.

What the arms chose

Four boards (seeds 0-3, one rotation each) were traced to show what each arm picks; these are traced diagnostics, not measured outcomes, and four boards illustrate rather than establish. Pips are per resource over both chosen sites, computed from the board the trace records and the same planner notes the earlier report read.

On board 0 the search took nine brick pips and five grain, the default spread the same board as five brick, five lumber, four grain, three ore, and the scarcity-off arm concentrated on ten grain. On board 2 the search paired a six-grain site with an eight-ore site and no lumber, the heaviest single-resource bets of the four arms. The coverage arm raised wool the most and covered six distinct numbers on three of the four boards, consistent with its weights, but the cohorts above say those differences do not convert to wins at this depth. The tables' own ranking is visible in the traced setup decision: on board 3 the shortlist's top sites were valued 600.8 and 587.1 leaf units by the tables against 562.6 for the site the planner chose first, and the search took the tables' pick.

The planner keeps one measurable advantage in the aggregates. The search seat lost 1.87 to 2.06 reachable sites per game to 1.60 to 1.79 for the planner seat (a settlement built by another seat within three roads of ground this seat could reach), built about 0.3 fewer roads, and bought about 0.7 more development cards per game: the planner's expansion and draft terms hold ground, and the search converts that ground into cards and purchases instead. Settlement and city counts, trades, and discards move only by tenths.

Decision cost

The search arm's mean decision time runs 25 to 33 percent above the control's (954 against 730 ms in the development half, 690 against 555 on the extension boards), and its nodes per decision 9 to 19 percent higher. The traced games locate the cost: the planner decides setup in about 40 ms, while search mode spent about 2,000 ms per setup decision under this load, four decisions per game, with the mid-game decisions unchanged. The coverage and scarcity arms are arithmetic on the planner and cost nothing. The registered browser rule asks for a mean decision time within 25 percent of the control's; the search arm fails it in every stage.

Comparison with the hand-leaf result

Under the hand-written leaf, the planner study measured the planner against search-ranked placement at −0.017 (−0.075 to +0.042) over 128 boards, with +0.006 (−0.075 to +0.087) on the same boards 0-63 used here: a match. Under the tables the same contrast reads +0.135 on those boards and +0.061 pooled over 192 L1 seeds. The sign flips because only one side of the comparison changed: the planner is the same code with the same hand-leaf calibration, while the search mode now ranks its shortlist with learned site values instead of the hand-written leaf's production-dominated terms. The tables' site values, not the search, are the improvement; the search is just the path through which they reach the placement. That reading also explains the population stage: three seats share the tables, placements are contested, and the planner's draft prediction and ground-holding matter more, so the search mode's edge disappears.

What could still be wrong

The pooled L1 estimate leans on the development boards. Only the 0-63 cohort excludes zero, those boards were used by many earlier studies, and on the 128 fresh L1 seeds the effect crosses zero. A protocol cohort or a fresh-seed-only registration would settle whether the +0.061 is real or a development-board artifact. The population stage ran only 128 seeds against one lineup shape (two focal searches, a third tables seat, one builder); other mixes could read differently. The weight arms were screened at 16 seeds and the tie-break between scarcity and expansion was a judgment call; both screened at −0.055 and either could be the arm that matters at other weights. The planner's draft prediction assumes the other seats use the same planner, which is exact for the builders and the other searches here and not for a person. The traced placements cover four boards and no browser build was run; the WASM cost of searching setup decisions under the one-second budget is inferred from the native traces, not measured in the browser.

What this means for the browser

The browser build runs the hand-written leaf in WASM and cannot load the tables, so the measured gain of "opening":"search" does not exist there: under the hand leaf the two modes measured as equals. The switch also fails the registered cost rule in every stage, 25 to 33 percent more mean decision time, and its true cost is worse in the browser: at depth 3 under a one-second budget, the three or four setup decisions would each consume most of a second before the first roll, against about 40 ms for the planner. Keep "opening":"planner" in the browser. The calibration arms are free but worthless here, so their defaults stand too. On the server, where the tables exist, the search-ranked opening is a modest improvement against builder tables and neutral against search tables; a protocol cohort against the ntuple-leaf baseline would be the next step before changing that default.