Reference
Evidence boundary
Measured
The training loop's collection throughput on this workstation, measured
September 18, 2026 with stage timers and matched ten-iteration runs
(report): the move network's forward
pass is 96% of a collection step on the small preset, and enabling the
ROCm build's experimental attention kernels (now the training package's
default) lifts collection from 4,300 to 10,100 environment steps per
second and halves iteration wall time from 73.5 to 35.0 seconds. The
environment's share of collection is 2.0% before and 5.4% after;
torch.compile of the forward is recorded as unsafe on this inductor
build (NaN rows on a quarter to a half of real batches).
The engine's throughput on this workstation, in release mode on
September 18, 2026: 17 ns per applied move including the end-of-game check,
71 ns per legal-move generation, 4.5 million random plies per second on one
core with the competitive rules, and 84 million random plies per second on
all 32 threads. The state is 440 bytes. These numbers are from
cargo run --release -p armies-engine --bin bench and are repeatable.
The engine's rules are covered by tests in ../server/crates/engine/tests:
movement, battles, the two-square rule including the Scout extension, the
continuous-chase rule with a twelve-threat lap around a lake, the draw
rules, and generator-checker agreement over thousands of random positions.
Three registered experiments were run on September 18, 2026, each with a record and a report:
- Baseline arena: greedy scored 90.2% effective against random on 200 paired games (Wilson 85.4% to 93.6%); the random self-match covered 50%. Decision rule met. Report.
- Expectimax (16 worlds, depth 2) scored 69.5% against greedy on 200 paired games, per-seed contrast 0.39 (0.24 to 0.54), 9.8 ms per move. Decision rule met; expectimax is the current top of the measured ladder. Report.
- Self-play smoke: twenty iterations trained without entropy collapse, but the network's 60% against random (44.6% to 73.7%) covers 50% and it stalls into battleless draws. Decision rule not met. Report.
Two more registrations ran later the same day, each with records in the replay library:
- Expectimax samples-by-depth sweep: 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. Neither the depth claim nor the worlds claim reached separated intervals. Report.
- Rollout rung: flat Monte Carlo with the registry defaults scored 19% (12.5% to 27.8%) against that expectimax cell on 100 paired games, per-seed contrast minus 0.62 (minus 0.81 to minus 0.43). Not promoted. Report.
In the evening the first delegated study ran: knowledge-limited subgame solving (theory T1) against the 16-world depth-2 expectimax cell, 200 paired games at each of two budgets. The kluss searcher (64 worlds, 4 shadows per world, one-sided GT-CFR, predictive CFR+) scored 26.8% (21.1% to 33.3%) at 5,000 expansions per move and 33.5% (27.3% to 40.3%) at 10,000, with per-seed contrasts of minus 0.465 (minus 0.607 to minus 0.323) and minus 0.330 (minus 0.467 to minus 0.193). The hypothesis is disproved as registered at both budgets; the solver converged and priced hidden information but the tree it can afford is too shallow. Report.
On September 19, 2026 the learned-belief study measured both of its
quantities and both are negative at the scale it could train
(report,
record):
a belief network trained on thirty small-preset self-play iterations
scored 2.29 nats per hidden piece on the replay library's held-out games
against the counting prior's 2.10 (top-1 21.4% against 24.2%), worse in
every phase and for every acting player, and expectimax at 16 worlds and
depth 2 sampling from it scored 45.25% (38.5% to 52.2%) on 200 paired
games against the same expectimax sampling from the prior, per-seed
contrast minus 0.095 (minus 0.217 to 0.027), inconclusive. The decision
rule is not met and the learned belief is not the sampler; the retest
belongs to the scaled run's checkpoint. The measurement bridge is on
main: a Searcher class in the Python bindings whose two entry points
agree bit for bit on the same worlds.
Later on September 19 the opponent-portfolio study (theory T2) measured
OLSS-II against full KLUSS at equal wall clock
(report, five records from
2436cdbe
to
4ffa3c2f):
with a portfolio of one strategy (greedy) the olss2 player scored 61.0%
(54.1% to 67.5%) at 50 ms, with two strategies (greedy plus the
searcher's leaf policy at temperature 0.3) 60.5% (53.6% to 67.0%) at
50 ms and 62.0% (55.1% to 68.4%) at 200 ms, all on 200 paired games with
contrast intervals above zero, and at 1 s 55.0% (45.2% to 64.4%) on 100
paired games with the interval covering zero, so no crossing budget was
found between 50 ms and 1 s. The 200 ms portfolio player lost to
expectimax at sixteen worlds and depth 2, 38.0% (31.6% to 44.9%),
contrast minus 0.240 (minus 0.390 to minus 0.090): limiting the opponent
beats the free-opponent subgame at equal cost but does not catch plain
search. The kluss registry policy now has the mode parameter
(kluss or olss2) and the portfolio list, documented in the
server's docs/search.md.
The same day the update-equivalence study ran its cells on the small checkpoint with its belief network (report, records): search at 200 rollouts and depth 10 scored 60.4% effective against the network itself (per-seed contrast 0.208, minus 0.016 to 0.433, inconclusive) and the beta-zero ablation scored 54.2% (0.083, minus 0.027 to 0.194, inconclusive), no search loss in 48 games, the null pair covering zero (0.015, minus 0.054 to 0.084) and three quarters of every cell drawn by the checkpoint itself. The paper's beta-zero catastrophe did not appear; the value head's calibration explains both null results (all 2,000 of its predictions on the checkpoint's own self-play inside the middle fifth of the outcome scale, Pearson minus 0.19 against the realised outcomes), so search has no signal to update with at this scale and the retest belongs to the scaled run's checkpoint too.
The ladder asset carries the earlier games and an Elo fit over the pairwise scores with random anchored at 1000 (greedy 1393, expectimax 1535, rollout 1283, the smoke network 1090); kluss is measured only against expectimax and stays out of the Elo fit, and the n-tuple rung is unmeasured.
Setups were uniform draws for every engine player until September 19,
2026, and the measured cost is now registered: with the move policy held
fixed, the structured prior of the
initial placements approach beat uniform
setups on 400 paired games per policy under the training rules, per-seed
contrasts 0.430 (0.339 to 0.521) for greedy, 0.630 (0.551 to 0.709) for
rollout and 0.670 (0.589 to 0.751) for expectimax at sixteen worlds and
depth 2, with a uniform-against-uniform null cell covering zero
(report). The sampler keeps 4.14 bits of
entropy on the Flag's square, and every registry policy now accepts a
setup parameter (uniform, structured, or forty glyphs); the default
stays uniform until the user changes it. The earlier exploratory number
stands beside it: on 1,200 unregistered tournament games a side with a
front-row Flag lost 61.5% against 32.7% with the Flag on the back row.
Selection by self-play was measured the same day
(report): a pool of 32 setups halved
from 1,024 prior draws over 15,872 selection games under expectimax at
sixteen worlds and depth 2 beat the prior on held-out opposing setups
with a per-seed contrast of 0.315 (0.223 to 0.407) on 400 paired games,
and its exploitability proxy, the score of the best single setup the same
procedure finds, read 0.150 (0.043 to 0.257) against the pool while the
prior's own exploiter read 0.458 (0.364 to 0.551) against the prior. The
pool is adopted for native players as the strongest measured setup source
("setup":"pool:<path>", the committed
pool file); the browser build rejects
pool paths and the registry default stays uniform pending the user's call.
The replay library (records/games/, 80 records, 2.2 MB) holds six games
for every pair of random, greedy, expectimax and rollout, seed 0
from both seats for every sweep cell, seeds 0 to 4 from both seats of
the rollout match, seed 0 from both seats of both kluss cells, seed 0
from both seats of the three structured-against-uniform cells, and seed 0
from both seats of the pool-against-prior and both exploiter cells. Every
record replays through the engine.
Registered, not run
Two registrations of the scaled self-play run, prepared on September 19,
2026 with the scaled preset sized at the paper's per-GPU numbers (135.4 s
per iteration, 12.14 GiB, report); the
multi-day training run is launched by the user and the matches play at
the wall-clock milestones:
- The 48-hour milestone: the checkpoint nearest hour 48 of
runs/scaled-1againstgreedy, 200 paired games, seeds 2000 to 2099, training rules, decided by the per-seed contrast. - The 96-hour milestone: the same against
expectimaxat sixteen worlds and depth two, same seeds and rule.
The 1,000-by-40 cell of the update-equivalence study is registered and
priced, not run: one search move at that budget costs 8.4 s on this
machine under shared load, about 90 hours for its 100 paired seeds, a
user-scale run rather than an agent session; the registration
(experiments/40af5091-8456-47e8-88ba-a74a6f3002ba) records the
pricing and the study's
report carries the three cells
that did run.
Planned
The n-tuple rung, the full Ataraxos preset and the DeepNash comparison are described on their approach pages with decision rules but have no registration. The research program adds nine proposed studies on the evening of September 18, 2026: knowledge-limited subgame solving against expectimax, the opponent portfolio, the learned belief as a sampler, update-equivalence search on the small checkpoint, the scaled run, the training loop's throughput, the run layout and the monitor, and the NashDreamer infoset model. Each is delegated to an agent that registers before it runs; the scaled run, the learned belief, the opponent portfolio and the update-equivalence study have since filed and run (above) and the rest have no registration yet. The monitor study is complete the same evening as an engineering deliverable: armies-watch with its tests, no player strength measured.
Numbers from the papers
Every figure or table transcribed from the Ataraxos or DeepNash papers says so in its caption. The setup heatmap on the setup-network page is illustrative and encodes only the paper's qualitative description.