After the fix: half the games on paired boards

What the defect was

The first cohorts ran with a turn-planning defect. After any non-ending action, the enumerator reused the root's restricting action as its own action list, so it re-applied that action, failed, and explored nothing. A road, a bank exchange, or a purchase was therefore valued at the position right after it, without the opponents' round that every end-turn candidate received, and inner turns collapsed to ending the turn. Measuring the game tree exposed it: inner-level nodes averaged 1.17 end-of-turn positions where a hand with several options should produce many.

The correction limits the restriction to the root step. A second problem then surfaced: with sequences actually explored, the flattened list of end-of-turn positions averaged over the player's own alternatives instead of taking the best, and enumerating every sequence cost seconds. The planner is now a recursion that takes the maximum over own actions and the expectation over chance outcomes, keeps every first action but only the best few continuations of the current turn, follows one greedy line in later turns, and spends the lookahead on the afterstates of the chosen line.

Depth 3 wins more still

256-game engine cohort seated the same lineup with depth 3 under a 1.5 s budget. It won 147 of 256 slot-games (57.4%) against the compared ETA slot's 16.0%; the paired contrast is +0.414 (95% interval +0.327 to +0.502), above depth 2's +0.301 on the same boards. Decisions averaged 360 ms. With the defective search, depth 3 had bought nothing; with the turn tree working, the extra planned turn is worth about eleven more wins per 256.

Against the reference it replaces

256-game engine cohort seated the corrected depth-2 search with the frozen expectimax-v1, an ETA builder and a fast builder. It won 120 of 256 slot-games (46.9%); the reference won 34 (13.3%), ETA 69 and fast 33. The paired contrast against the reference is +0.336 (95% interval +0.249 to +0.423). The reference spent 240 ms per decision to the corrected search's 88 ms.

What the corrected search does differently

The per-game means show a builder-like profile: 2.0 settlements, 2.1 cities, 4.7 roads and 2.8 development cards, with 6.2 completed player trades and 9.9 offers per game. The defective search offered less and, in its deep variant, bought more development cards than it built cities.