Reports · 2026-09-18

Expectimax over sixteen worlds beats greedy on 137 of 200 games

Of the 100 seeds, 58 favoured expectimax, 24 split one game each and 18 favoured greedy. Expectimax won 69 games as Red and 68 as Blue, so move priority did not matter, in line with the Ataraxos observation that first move carries no measurable advantage.

The games were decided by battle, not by stalling

The endings histogram rules out the failure mode the approach page named. 191 of 200 games ended by Flag capture, 5 because a side ran out of legal moves and 4 at the 100-move battleless limit: a draw share of 2%, nowhere near the 40% that would have flagged the result. Games averaged 137 plies, shorter than greedy against random (219), because the search attacks pieces it expects to beat instead of waiting for them.

The replay is the first registered game: seed 0, expectimax as Red, finished in 77 moves by Flag capture.

What this does and does not show

The search sees the same observation as greedy and samples sixteen full states consistent with it; the leaf is greedy's material table plus a few positional terms. Its edge over greedy therefore comes from looking two plies ahead across worlds, not from better information. Sixty of the 200 games still went to greedy, most of them by a Bomb or a Marshal the sample placed wrongly, which is the strategy-fusion weakness of determinization that the concept page describes. The rung above replaces the leaf with a learned one; the search itself stays.

Run record

cd server && cargo run --release -p armies-arena --bin matchup -- --red 'expectimax:{"samples":16,"depth":2}' --blue greedy --games 200 --seed 0 --rules training --threads 32 --moves --out ../research/runs/bbb0214b-63cf-46a3-b5a9-a1a7d322770e/expectimax-vs-greedy.json
cd research && python3 scripts/paired_contrast.py runs/bbb0214b-63cf-46a3-b5a9-a1a7d322770e/expectimax-vs-greedy.json
cd research && python3 scripts/build_experiment_assets.py