Encyclopedia of balanced asymmetric Chess960

What an asymmetric pair is

In ordinary Chess960 both sides start from the same shuffled back rank, and White keeps the usual first-move edge. In an asymmetric pair each side has its own setup from the same list of 960. Black's setup can then compensate White's first move — and for some pairs the compensation is exact.

All 460 800 distinct pairs were screened by a staged engine search; the most even ones were deepened step by step. A pair enters this encyclopedia only when it holds |cp| ≤ 5 at 400 million, 800 million, 1.6 billion and 4 billion nodes without drifting to one side, and when Berserk and Lc0 — engines of different architectures — each place it closer to equality than their own typical symmetric position. Castling for each side remains Chess960 castling on its own back rank.

How every pair was checked

1. Verification ladder: nine searches with a growing node budget (100k → 500k → 2M → 8M → 32M → 128M → 400M → 800M → 1.6B), Stockfish 17.1, one thread, last completed iteration — reproducible bit for bit.
2. Admission criterion: |cp| ≤ 5 at all four deepest rungs, no one-sided drift along the ladder, and confirmation by two further engines. Shallow rungs are shown as they are — their drift is part of the record.
3. First moves: the 3 best first moves for White at 400M nodes — how many equivalent ways to start the game exist.
4. Main-line play-out: the engine plays its own main line for 30 moves at 5M nodes per half-move; the evaluation is recorded after every half-move.
5. Engine self-play: 10 games per pair at 500k nodes per move; the first 4 half-moves are picked at random among moves within 15 cp of the best (seed published), so the games differ.

Across the whole composition: 1550 self-play games, White won 27, drawn 1458, Black won 65 — White scored 48.8%.

Engine: Stockfish 17.1. Composition updated 2026-10-05 05:01:52; checks completed 2026-10-08 08:32:47. Search methodology

How the composition was verified

Beyond the admission rule, the whole composition went through an evidence programme: deeper budgets, reversed pairs, two independent engines, measured setup weights and mass self-play.

Doubling the budget: at 4 billion nodes 142 of 155 pairs still read exactly 0.00, at 8 billion 27, at 16 billion 27. Those that move scatter to both sides of zero, and the spread keeps shrinking.

Independent engines agree. Berserk 14 puts the pairs at 0 and symmetric Chess960 positions at +10; Lc0 v0.32.1 (net 791556) puts them at +1 and +18. Neither engine found a single symmetric position that favours Black.

Reversed pairs: all 30 of them favour White, median +69. The compensation works in one direction only.

Setup weights: 960 arrays measured against the classical one. The classical array itself weighs +11, which matches its known symmetric evaluation.

Mass self-play: 6450 games, White scored 49.2%, 6114 draws.

Agreement across the composition of 155 pairs: all three independent engines confirm 155, two confirm 0, one confirms 0, none confirms 0.

History of the composition

• 2026-09-21 — 52 pairs: the first composition, under an earlier rule — evaluation exactly 0.00 at three budgets, one engine.
• 2026-10-03 — 174 pairs: the base had grown, but it was split in two by two different admission rules.
• 2026-10-05 — 155 pairs: one base, one rule. Pairs admitted by the earlier rule that do not meet it: 19; they left the composition.

What left the composition

When the base became one, the stricter rule was applied to everything in it. 19 pairs admitted by the earlier one-engine rule do not meet it. Their data stays published — below is each pair with the condition it failed, so the decision can be checked instead of taken on trust.

• 7-676 — Berserk no better than its symmetric median, Lc0 no better than its symmetric median
• 25-902 — Lc0 no better than its symmetric median
• 41-928 — Lc0 no better than its symmetric median
• 61-620 — Berserk no better than its symmetric median
• 66-138 — ladder outside ±5 cp, one-sided drift, Berserk no better than its symmetric median, Lc0 no better than its symmetric median
• 85-256 — ladder outside ±5 cp
• 106-955 — Lc0 no better than its symmetric median
• 143-885 — Lc0 no better than its symmetric median
• 188-896 — ladder outside ±5 cp, one-sided drift
• 196-480 — Berserk no better than its symmetric median
• 198-819 — Lc0 no better than its symmetric median
• 223-767 — Lc0 no better than its symmetric median
• 303-48 — Lc0 no better than its symmetric median
• 303-823 — Lc0 no better than its symmetric median
• 317-934 — ladder outside ±5 cp, one-sided drift, Berserk no better than its symmetric median
• 335-829 — Lc0 no better than its symmetric median
• 466-726 — Berserk no better than its symmetric median
• 473-353 — ladder outside ±5 cp
• 495-851 — Berserk no better than its symmetric median

The 155 pairs

Play it in the CH960 app

Every pair of the encyclopedia can be started in the free CH960 app (Android): open Encyclopedia of balanced pairs, pick a pair and choose how to play.

• Local game — two players on one device, with a clock.
• With a mentor — a clearly labelled training bot with hints, at your level.
• Challenge a friend — an online game by link; both players get the same pair, colours swap on rematch.

Open data

asym_encyclopedia.json · CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)

Morozov R. Encyclopedia of balanced asymmetric Chess960. ch960.com/asym/encyclopedia, 2026. CC BY 4.0.