White 115 vs Black 124

The two setups

White: setup #115 B N Q R N K R B

King on the f-file, rooks on d, g, queen on the c-file; one 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 115 gives White +0.10 (Morozov Balance Index, 400M nodes).

Black: setup #124 N B Q R N K B R

King on the f-file, rooks on d, h, queen on the c-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 124 gives White +0.19 (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 58.

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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±7 cp.

For comparison, in symmetric play setup 115 gives White +0.10 and setup 124 gives White +0.19: 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 b3, and 3 first moves are within 10 cp of it.

Along the engine's main line (19 moves) the evaluation stayed within ±8 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: +6
• Lc0 0.32.1: +10

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 +81, difference +23. 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

19 moves, 5 000 000 nodes per half-move. Largest |evaluation| 8 cp, mean 0.9 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 38.4 moves.

1. c4 c6 2. O-O d5 3. cxd5 cxd5 4. Qxc8 Rxc8 5. g3 f6 6. Nc3 e6 7. f4 Nd6 8. e4 a6 9. Bf3 Ba7+ 10. Kg2 Nb6 11. e5 Nf5 12. Bg4 Bf7 13. exf6 gxf6 14. Bxf5 exf5 15. Nf3 Nd7 16. b3 d4 17. Ne2 d3 18. Ned4 Bxd4 19. Nxd4 Bd5+ 20. Kf2 Be4 21. Rfe1 h5 22. Rc1 Kf7 23. Rxc8 Rxc8 24. Bb2 Nb6 25. Rc1 Rxc1 26. Bxc1 Ke7 27. a4 Nd5 28. Ba3+ Kd7 29. a5 Nc7 30. Ke3 Nd5+ 31. Kf2 Nc7 32. Bc5 Nd5

1. b3 f6 2. g3 c6 3. d4 d5 4. Nd2 h5 5. e4 dxe4 6. Nxe4 h4 7. Nf3 hxg3 8. fxg3 Bd5 9. Qe3 Qe6 10. Re1 Nd6 11. Nc5 Qxe3 12. Rxe3 Nf5 13. Re2 b6 14. Ne6+ Bxe6 15. Rxe6 Bd6 16. g4 Nh4 17. Nxh4 Rxh4 18. Bxc6 Rc8 19. Bb7 Rxc2 20. Bxa8 Rhxh2 21. O-O Rh4 22. Bf3 Bh2+ 23. Kh1 Bg3+ 24. Kg1 Bh2+ 25. Kh1 Bd6+ 26. Kg1

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 115 / 124 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): nbqrnkbr/pppppppp/8/8/8/8/PPPPPPPP/BNQRNKRB w DGdh - 0 1

Mirror twin: White 835 vs Black 844 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 467.