White 56 vs Black 854

The two setups

White: setup #56 N B N R B Q K R

King on the g-file, rooks on d, h, queen on the f-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 56 gives White +0.44 (Morozov Balance Index, 400M nodes).

Black: setup #854 R K B N R B N Q

King on the b-file, rooks on a, e, queen on the h-file; no bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 854 gives White +0.26 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation is exactly 0.00 each time, reaching search depth 59.

Admission rule: |cp| ≤ 5 at four budgets up to 4 billion nodes, no one-sided drift along the ladder, and confirmation by two independent engines — Berserk and Lc0 — each below its own median on symmetric positions. The same corridor is required at every deeper budget (8 G, 16 G) at which the pair has been evaluated.

The shallow rungs wandered between -19 and +6 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 56 gives White +0.44 and setup 854 gives White +0.26: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.

White is not forced into a single path: the best first move is d4, and 2 first moves are within 10 cp of it.

Along the engine's main line (23 moves) the largest swing was 31 cp (around move 2), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 1, drawn 9, Black won 0 (White scored 55.0%).

Verification ladder

Nine independent searches of the starting position, each with a larger node budget. Evaluation in centipawns from White's point of view.

Deep verification

The search ladder reaches 1.6 billion nodes; admission needs a 4-billion rung and two further engines on top of that. Beyond even that, every pair was re-checked at budgets up to ten times larger and in thousands of self-play games. This section shows what each check returned for this pair.

This pair stays within the ±5 cp corridor up to 4 000 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: +13

Independent confirmations: 3 of 3. An engine counts as confirming when its reading of the pair is closer to equality than its own reading of a typical symmetric Chess960 position (+10 for Berserk, +18 for Lc0). Where only one engine confirms, the pair is balanced according to that engine alone, and this page says so.

Own weight of each setup, measured against the classical array: White +104, Black +87, difference +17. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.

Best first moves

The 3 best first moves for White, searched together at 400 000 000 nodes.

Main-line play-out

23 moves, 5 000 000 nodes per half-move. Largest |evaluation| 31 cp, mean 2.9 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 43.3 moves.

1. d4 e5 2. dxe5 Nc6 3. c4 Nxe5 4. e4 b6 5. Nab3 Ba6 6. f4 Bxc4 7. Ne2 Nc6 8. Qf3 O-O-O 9. Bd3 Bxb3 10. axb3 Bc5+ 11. Bf2 Bxf2+ 12. Kxf2 Nb4 13. e5 c6 14. Be4 Nh6 15. Nd4 Qf8 16. g4 f6 17. e6 Qc5 18. Kg3 g6 19. Rhe1 d5 20. Bb1 Qd6 21. Kg2 Re7 22. f5 gxf5 23. Bxf5 c5 24. Nb5 Qb8 25. Bb1 Rg8 26. h3 f5 27. Rxd5 fxg4 28. Qe4 gxh3+ 29. Kh1 Ng4 30. Rd2 a6 31. Nd6+ Qxd6 32. Rxd6 Nf2+ 33. Kh2 Nxe4 34. Bxe4 Kc7 35. Red1 Rge8 36. Bf3 a5 37. R1d2 h6 38. Kxh3 Rxe6 39. Rd7+ Kc8 40. Ra7 R6e7

1. e4 e5 2. c3 Nf6 3. f3 d5 4. exd5 Nxd5 5. Bf2 Ne6 6. Nab3 a5 7. d4 g5 8. dxe5 Qxe5 9. a4 Nb6 10. Re1 Qd5 11. Rd1 Qe5 12. Re1 Qd5 13. Rd1 Qe5

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 56 / 854 in the app's encyclopedia, then 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.

Play this pair against the computer, right here Play a friend

FEN (Shredder, castling rights by rook files): rkbnrbnq/pppppppp/8/8/8/8/PPPPPPPP/NBNRBQKR w DHae - 0 1

Mirror twin: White 909 vs Black 102 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 238.