Opening portfolios

Should you maximize production, diversify, or commit to a powerful specialization?

The decision at the table

Two opening settlements give you both an income stream and a set of constraints. Lots of cards can still leave you waiting for the same missing resource. An ore-and-grain plan can be strong with space for cities; a wood-and-brick plan needs settlement sites that will remain reachable.

Treat the two placements as a portfolio. Compare expected production, which resources arrive together on the same roll, access to scarce inputs, conversion through ports, and the next reachable site. A diversified set of numbers changes the variability of income; it does not automatically increase its mean.

The mechanism to test

Score opening pairs by the builds they can fund and the routes they preserve. During the snake draft, predict which sites may disappear before your second placement. A slightly weaker first spot may leave a much better pair. Compare specialization with diversification conditional on the island, rather than declaring either universally best.

Proposed experiment

Compare production-only placement, build-aware resource coverage, and coverage plus contested-site lookahead. Keep the later-game policy identical. Hypothesis: valuing missing inputs and accessible expansion improves completed-game win rate over production alone.

Record production by resource, turns to first new settlement and city, unspent cards, and loss of reachable sites. Stratify by opening seat and a board-scarcity definition frozen before evaluation. A useful exhibit is a scatter plot of expected income against time to the first point-producing build.

First ablation

Placing the opening with the builder heuristic instead of the search changed the contrast by -0.035 wins per game (95% interval -0.133 to +0.062) on 64 deterministic boards: search placement is worth little at depth 2, if anything. Details and every run ID are in the ablation report; this is a development-tier result on one lineup.

Second round: a draft-aware planner

The setup is now placed by a planner that scores the two sites as a portfolio and predicts the intervening draft picks (the server's docs/expectimax.md, Opening placement). Its first draft valued pips with a player's sense of balance and lost 0.30 wins per game to the search's own placement; calibrated to the leaf's resource values it appeared to win single-seating screens by +0.09 to +0.12, but swapped-seating pairs on 128 boards put the planner effect at −0.017 (−0.075 to +0.042) with a seating term of +0.063: as strong as the search's placement, not stronger, with balanced and explained placements. Five discrete strategies hurt at every blend strength and stay off. The opening planner report has the sweep and the cohort.

Third round: the planner under the learned leaf

The leaf changed to the learned n-tuple tables, so the comparison ran again: with "opening":"search" the search ranks its shortlist with learned site values, against the same hand-leaf-calibrated planner. Swapped pairs through development, confirmation, and population stages put the search-ranked opening ahead against builders (+0.061 wins per game, 95% interval +0.009 to +0.113, pooled over 192 boards) but only the reused development boards exclude zero, and against a table with a third search the effect is zero (+0.001). Doubling the coverage and balance weights and removing the scarcity markup are both nulls. The switch costs a full search on every setup decision, about 2 s each against the planner's 40 ms, so the browser keeps the planner and the server default waits for a protocol cohort. The opening planner tables report has the cohorts and the traced placements.

What could disprove it

More production without faster conversion or a win-rate improvement does not support the mechanism. Opening scores can also overfit specific boards. Do not choose a scarcity threshold after seeing which games the candidate won.

All approaches · Player’s guide · Experiment program

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