Reports · 2026-09-19

Search does not separate from the network on the small checkpoint

Every game here is a game the checkpoint itself decides to draw. The network against itself on 200 paired games drew 159 of 200 into the quiet limit, so most seeds in every cell contribute a zero contrast (9 of 12 in the search cell, 10 of 12 in the ablation, 72 of 100 in the null pair), and a cell that wins every decisive game still moves its interval by only so much. That is the honest reading of the 60.4%: the search side won all five games of its cell that ended in a flag capture, and 12 seeds cannot lift an interval clear of zero against a 79.5% draw rate. The 1,000-rollout depth-40 cell, which the paper's Table 17 has at the top of its budget ladder, stays registered and unrun: one search move at that budget costs 8.4 s on this machine (measured on a middlegame probe under shared load), about 90 hours for its 100 paired seeds, which is a user-scale run, not an afternoon.

The value head has nothing to say

The mechanism the search updates with is the value estimate q, the move network's outcome prediction averaged over belief-sampled rollouts. On 2,000 positions from the checkpoint's own self-play (16 games, seed 0, mean 747.8 plies, 12 draws and 4 blue wins), the value head's expected value correlates with the eventual outcome at Pearson -0.19, and every one of the 2,000 predictions falls in the middle fifth of the scale:

The predictions never leave the middle fifth of the scale, and what wiggling they do inside that band ranks the positions slightly backwards against the realised outcomes. The search diagnostics agree from the inside: across the 6,092 search moves of the first cell the q values of the legal moves spread by 0.019 on average, and the tabular update's top share of 0.103 is a near-uniform policy only mildly sharpened, with the beta-zero cell's amplified noise pushing its top share to 0.218 and its score nowhere. The paper's search needs a value head that ranks continuations and a belief that samples plausible opponents; on this checkpoint the value head carries no ranking (above) and the belief network was already shown worse than the counting prior (the learned-belief report).

Costs, measured while the machine was shared

All three were measured while other delegated agents used the machine, so they are upper bounds, not alone-on-the-machine numbers. The paper reports 1.26 s per move at 1,000 rollouts and depth 40 on one H100; this machine's 8.4 s per move at that budget is the cost the unrun cell is registered with.

Run records: the 200-by-10 cell, the beta-zero cell, the null pair.

What this bounds

These cells bound the search at this rung of the ladder, not the method in the paper: both search settings played a checkpoint thirty small iterations old whose value head is uninformative and whose belief sampler was rejected the same day, so the paper's Elo gains had neither of their two engines to run on. The point estimates lean the paper's way (search 0.208 above beta-zero 0.083, both above the null pair's 0.015) with no loss in 48 search games, which is a reason to retest rather than retire. The retest belongs on the scaled run's checkpoint, where the milestones measure a policy that beats greedy before search is asked to add to it, and the 1,000-by-40 cell needs a user-scale budget or a batched GPU rollout implementation before its 90 hours become an afternoon.

.venv/bin/python -m armies_train match \
  --red run:runs/belief-policy:search=200,depth=10,alpha=0.002,beta=0.02 \
  --blue run:runs/belief-policy --games 24 --seed 0 --rules training \
  --out runs/ue-cell-a.json
.venv/bin/python -m armies_train match \
  --red run:runs/belief-policy:search=200,depth=10,alpha=0.002,beta=0 \
  --blue run:runs/belief-policy --games 24 --seed 0 --rules training \
  --out runs/ue-cell-c.json
.venv/bin/python -m armies_train match \
  --red run:runs/belief-policy --blue run:runs/belief-policy \
  --games 200 --seed 0 --rules training --out runs/ue-cell-d.json
.venv/bin/python -m armies_train calibrate \
  --run runs/belief-policy --positions 2000 --games 16 --seed 0 \
  --out runs/ue-calibrate.json