White 78 vs Black 126

The two setups

White: setup #78 N N R K Q B B R

King on the d-file, rooks on c, h, queen on the e-file; no bishop starts in a corner; the knights start away from the centre. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 78 gives White +0.21 (Morozov Balance Index, 400M nodes).

Black: setup #126 N Q R N K B B R

King on the e-file, rooks on c, h, queen on the b-file; no bishop starts in a corner; the knights start away from the centre. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 126 gives White +0.27 (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 60.

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 +1 and +24 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 78 gives White +0.21 and setup 126 gives White +0.27: 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 f3, and 3 first moves are within 10 cp of it.

Along the engine's main line (27 moves) the evaluation stayed within ±24 cp the whole way: the balance holds as the pieces come out, not only on move one.

Engine self-play agrees: 10 games, White won 0, drawn 10, Black won 0 (White scored 50.0%).

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: +4

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 +61, Black +9, difference +52. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 0 White wins, 10 draws, 0 Black wins, White scored 50.0%.

Best first moves

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

Main-line play-out

27 moves, 5 000 000 nodes per half-move. Largest |evaluation| 24 cp, mean 2.4 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 0, drawn 10, Black won 0 — White scored 50.0%. Average length 42.5 moves.

1. d4 c5 2. dxc5 f6 3. O-O-O Bxa2 4. Nc3 Be6 5. e4 b6 6. Ba6 Rc6 7. Bb5 bxc5 8. Nb3 Bxb3 9. cxb3 Rd6 10. f4 Rxd1+ 11. Qxd1 Qxf4+ 12. Kb1 Qd6 13. Bxc5 Qxd1+ 14. Rxd1 Nc6 15. Ba4 a6 16. Nd5 e6 17. Bxf8 Rxf8 18. Bxc6 dxc6 19. Nb4 f5 20. e5 Nc7 21. Rd6 Rf7 22. Rxc6 a5 23. Na6 Nxa6 24. Rxa6 g5 25. Ra8+ Kd7 26. Ra7+ Ke8 27. Ra8+ Kd7 28. Ra7+ Ke8

1. e4 f6 2. f3 e5 3. c4 b5 4. cxb5 Bxa2 5. b3 Bxb1 6. Rxb1 c6 7. Qe3 cxb5 8. Qxa7 Nc7 9. g3 Nde6 10. Nc2 Qxa7 11. Bxa7 Ra8 12. Be3 Bc5 13. Kc1 Ra2 14. Bxc5 Nxc5 15. Rb2 Rxb2 16. Kxb2 N5e6 17. h4 Kf7 18. Bh3 Rd8 19. Ra1 d5 20. Ra7 Ke8 21. Kc1 dxe4 22. fxe4 Rd3 23. Ne3 Rxb3 24. Nd5 Kd8 25. Bxe6 Nxe6 26. Ra8+ Kd7 27. Ra7+ Kd8 28. Ra8+ Kd7 29. Ra7+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 78 / 126 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): nqrnkbbr/pppppppp/8/8/8/8/PPPPPPPP/NNRKQBBR w CHch - 0 1

Mirror twin: White 884 vs Black 836 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 344.