Approaches

Initial placements

How much of a player's strength is decided before the first move, and what is the cheapest way to get a placement that does not lose the game on its own?

Every engine player on the ladder draws its setup uniformly at random (Setup::random, the default of Policy::setup). A uniform draw puts the Flag in the front row in a quarter of all games and gives it no adjacent Bomb in more than half of them. The replay library shows the cost: games that end in seven plies because a Scout walks onto a Flag.

The mechanism

The setup is one decision with about 10^33 legal outcomes, made with no information about the opponent. It is the part of Stratego that is most plainly a mixed strategy: any fixed arrangement can be learned and punished over repeated play, so the object to improve is a distribution over setups, not one setup. Three sources of that distribution, in order of cost:

1. A structured prior. A sampler with a handful of constraints that every strong human setup satisfies (Flag on the back two rows with Bombs or the board edge on its open sides, no Bomb in the front row blocking its own lanes, Scouts forward, Miners kept back, the Spy within two squares of the General). It stays random inside the constraints, costs nothing at play time and runs in the browser.
2. Selection by self-play. A pool of setups drawn from the prior is scored by arena games under a fixed move policy and narrowed by successive halving; survivors are mutated by swapping two pieces. The output is a weighted pool, and it is scored against setups it never met so that a pool fitted to one opponent distribution is caught.
3. The learned setup network of the Ataraxos approach: an autoregressive transformer trained by the game's outcome. It is trained by the scaled run; this approach supplies its baseline and its measurement.

The measurement

A setup-only contrast: both seats play the same move policy with the same parameters and only the setup source differs. Paired seeds, both seats, training rules. The contrast is reported for each ladder policy, because a placement that helps a searching player may not help a greedy one.

Two properties are reported beside the score. Diversity: the entropy of the Flag's square and of each piece type's row over 10,000 samples, since a source that collapses to one arrangement is exploitable however well it scores. Exploitability proxy: the score of the best single opposing setup found by the same selection procedure against the source, with the move policy fixed.

The plan

1. structured-prior: the sampler in the engine's setup module, the setup parameter on every registry policy, and the setup-only contrast against uniform setups for greedy, rollout and expectimax.
2. selection-by-self-play: the pool, successive halving, mutation, the held-out evaluation and the exploitability proxy, with the prior as the baseline.
3. The learned network joins the same contrast when the scaled run files a checkpoint.

Decision rule

The prior replaces uniform setups as the default of every engine player if its setup-only contrast is above zero with a 95% interval for all three policies and its Flag-square entropy stays above 3 bits. Selection is adopted if it beats the prior on held-out opposing setups by an interval above zero and its exploitability proxy is no worse than the prior's.

What could disprove it

The move policies may be too weak to punish a bad setup, in which case the contrast is small for greedy and grows with search depth; that gradient is itself the finding. Selection may overfit the opposing pool: the held-out evaluation exists to show it.

Evidence

Measured September 19, 2026 (report): with the move policy identical in both seats, the structured prior beat uniform setups on 400 paired games per policy under the training rules. Per-seed contrasts with 95% intervals over 200 seeds: 0.430 (0.339 to 0.521) for greedy, 0.630 (0.551 to 0.709) for rollout, 0.670 (0.589 to 0.751) for expectimax at sixteen worlds and depth 2; the uniform-against- uniform null cell read minus 0.033 (minus 0.143 to 0.078), covering zero. The prior keeps 4.14 bits of entropy on the Flag's square over 10,000 samples (uniform: 5.32 bits), and every one of the seventy games that ended within 20 plies in the three treatment cells was lost by the uniform side. The decision rule of the study is met on all three policies; uniform stays the registry default until the user changes it.

Measured September 19, 2026 (report): selection by self-play is adopted. A pool of 32 setups halved from 1,024 prior draws over five rounds and 15,872 games under expectimax at sixteen worlds and depth 2 beat the prior on opposing setups drawn through the arena's evaluation seeds, which the pool never met, with a per-seed contrast of 0.315 (0.223 to 0.407) on 400 paired games, and beat uniform draws by 0.792 (0.728 to 0.857) against the prior's 0.670 on the same seeds. The exploitability proxy went the pool's way: the best single setup the same procedure found against the pool scored 0.150 (0.043 to 0.257) against it, while the prior's exploiter scored 0.458 (0.364 to 0.551) against the prior. A greedy transfer cell held at 0.230 (0.111 to 0.349) with a 34% draw share. The trade is diversity: all 32 Flags sit on the back row for 3.2 bits of Flag-square entropy against the prior's 4.14. The pool is the strongest native setup source and the file content/assets/setup-pool.json backs it; the browser build rejects pool paths, so the prior stays the portable choice and the registry default remains uniform until the user changes it.

Exploratory, measured on September 18, 2026 before any change, on 1,200 unregistered tournament games between random, greedy and rollout under the training rules (raw output, not curated): a side whose Flag stood in the front row lost 61.5% of its games, against 32.7% with the Flag on the back row (49.7% and 46.1% for the two rows between); 107 of the 1,200 games ended within 20 plies. One adjacent Bomb changed the loss rate by about one point, three by eleven points on 24 setups. The curated library's 128 setups place the Flag 30, 32, 32 and 34 times on the four rows, back to front, as a uniform draw would.