Reading the next build

The mechanism

expectimax-v2 models other seats one way: inside the lookahead they follow a fixed builder on sampled hands, and outside it the bargaining threats read points and a shared frontier scan. The study added one predictor and three switches, each off by default, in crates/expectimax/src/v2/predict.rs:

The predictor itself runs the builders' own greedy target choice on a hand and the public board: the next piece the line completes (the first road toward the expansion site, the site settlement, a city, or a development card), the site that line ends up taking, and the turns until the piece and the whole line are affordable. Inside the search the hand is the seat's sampled hand, so every prediction is an expectation over the searcher's belief; the arena diagnostic replaces it with a public-knowledge estimate. The deployable policy never reads a hidden hand: its samples come from its own observation and event history.

How the cohorts were run

Each arm ran as a mirrored pair of registered deterministic cohorts, 64 seeds and four rotations (256 games) each: treatment slot 0 against the unchanged depth-2 control in slot 1, and the same two searches with the slots swapped. The average of the two order-paired per-seed contrasts is the mechanism estimate, because slot 1 always sits immediately after slot 0 in engine seat order and that order alone moves wins. An ETA and a fast builder held the other two seats. All 3,072 games completed; there was no censoring or invalid game.

Only the denial term met its development rule, and its fresh-seed reading refutes the development estimate rather than confirming it: over both seed sets the pooled estimate is about +0.018, indistinguishable from zero at this scale. The predicted opponent model and the predicted threat stay inconclusive in both directions. No default changes; the switches remain research knobs. The depth-2 hand-written leaf, the fixed builders, and the single lineup bound every number here, and the twin search in slots 0 and 1 is the strongest rival at the table, which is exactly the opponent the predictor reads worst.

Does the prediction read opponents?

The arena measured the predictor honestly from one observer seat's public knowledge: at each opponent's first main-phase decision of a turn it recorded the predicted next build and compared it with the first build that seat actually completed in the same turn, over 64 games (seeds 0 to 15, --predict-diag 0).

The predictor reads builder-like opponents well and searches badly, which explains the result: the seat that wins these tables is the other search, whose next build depends on trades, development cards, and blocking choices no greedy line predicts. Builder-directed terms can only matter against the builders, who are the weakest seats at this table.

One mechanism signal did move. The denial seat lost about 0.1 fewer frontier sites per game than its control in all four denial cohorts (1.75 against 1.85 or so, from the new sites_lost counter, which counts opponent settlements built on a vertex the seat could reach within three roads). The term changes the board in the direction it claims without changing who wins measurably.

The slot-order asymmetry

A control cohort of two identical depth-2 searches, ETA, and fast on seeds 0 to 63 split 129 to 85 for slot 0: +0.172 wins per game (95% interval +0.083 to +0.261) for the seat that always acts immediately before its twin, with identical policies. On seeds 64 to 79 the same pair split 30 to 29. The asymmetry is a property of the board lottery on the development seed set, not of any policy: the four rotations seat slot 1 immediately after slot 0 in engine seat order in every one of them.

This matters beyond this study. The single-order ablation contrasts reported earlier, all on seeds 0 to 63 with the same lineup shape, carry the same slot bonus; a treatment that did nothing would have shown about +0.17 there. The near-zero ablation arms were likely slightly negative, and the decisive levers stand well above the bonus. Future paired contrasts should either run mirrored pairs, as here, or report the twin-seed slot baseline alongside. This cohort is an unregistered diagnostic; the registered evidence in this report is the twelve mirrored cohorts.