Approaches

Expectimax over sampled worlds

Does a shallow search over sampled hidden configurations beat a one-ply heuristic, and at what cost per move?

The mechanism

For each decision, sample sixteen full states consistent with the observation using the engine's determinizer, run alpha-beta to depth two (plus captures) in each, score leaves with material, advancement, Flag safety and mobility, and average the root values per move. The concept page covers the method and its strategy-fusion flaw.

The plan

Two registered comparisons. First, expectimax against greedy on 200 paired games under the training rules with a two-second move budget. Second, a sweep over samples (4, 16, 64) and depth (1, 2, 3) against greedy on 100 paired games each, recorded as a plot of effective win rate against milliseconds per move, so that the cost of the strength is visible before the leaf is replaced.

Decision rule

Promote if the per-seed contrast against greedy has a 95% interval above zero on all 200 games and the mean time per move is under two seconds on this machine. Either failure keeps greedy as the reference and sends the search back for profiling or a better leaf.

Evidence

Run on September 18, 2026: expectimax with sixteen sampled worlds at depth 2 won 137, drew 4 and lost 59 of 200 paired games against greedy, 69.5% effective (62.8% to 75.5%), per-seed contrast 0.39 with a 95% interval of 0.24 to 0.54, at 9.8 ms per move; 191 games ended by Flag capture. Both conditions of the decision rule hold and expectimax is promoted. See the report and the run record.

The samples-by-depth sweep ran the same day: nine cells of 100 paired games against greedy. Every cell beat 50% by the point estimate; the best was sixteen worlds at depth 2 at 67.5% (57.8% to 75.9%) and 9.5 ms per move, and neither more worlds nor deeper search separated from it, so the browser keeps that cell. See the sweep report and its record. Belief rollouts with random playouts, the flat Monte Carlo alternative, scored 19% against that cell on 100 paired games and stay a baseline; see the rollout report and its record.

What could disprove it

A search that wins mainly by stalling into battleless draws against a greedy that attacks too eagerly would show up as a high draw share with few Flag captures. The endings histogram is part of the decision. A search that loses on time is recorded as a loss of budget, not of strength.