White 103 vs Black 115

The two setups

White: setup #103 Q N B R N K R B

King on the f-file, rooks on d, g, queen on the a-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 103 gives White +0.17 (Morozov Balance Index, 400M nodes).

Black: 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).

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 -18 and +16 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 103 gives White +0.17 and setup 115 gives White +0.10: 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 (27 moves) the evaluation stayed within ±17 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: +5
• Lc0 0.32.1: -1

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 +58, Black +104, difference -46. 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| 17 cp, mean 4.5 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 37.8 moves.

1. b3 g5 2. Bb2 Bxb2 3. Qxb2 b5 4. d4 Nf6 5. Nd3 d6 6. Na3 Bc6 7. O-O h5 8. c4 bxc4 9. bxc4 Be4 10. Nb5 Nbd7 11. Nc3 Ba8 12. d5 Qa6 13. Qb5 Qxb5 14. Nxb5 c6 15. dxc6 Bxc6 16. Nxa7 Be4 17. Nb5 Ra8 18. Ra1 Kg7 19. g3 Rgc8 20. Rfc1 Bxh1 21. Kxh1 Ng4 22. a4 Nc5 23. Nxc5 Rxc5 24. f4 Ra6 25. Ra3 gxf4 26. gxf4 d5 27. Kg2 f5 28. Nd4 dxc4 29. Rac3 Rd5 30. Nf3 Rxa4 31. h3 Nf6 32. Rxc4 Rda5 33. Ng5 Nd5 34. Kf3 Rxc4 35. Rxc4 Ra6 36. Rd4 Ra3+ 37. Kf2 Nf6 38. Rd3 Ra4 39. Rd4 Ra3 40. Rd2 h4

1. g4 c5 2. c4 Nc6 3. b3 b6 4. Bb2 e6 5. Bxc6 Qxc6 6. d4 d5 7. dxc5 bxc5 8. cxd5 exd5 9. b4 cxb4 10. a3 b3 11. Nd2 Qh6 12. Bd4 a5 13. a4 O-O 14. Nef3 Rb8 15. Rb1 Nd6 16. Kg2 Rbe8 17. Rxb3 Rxe2 18. Nf1 Ree8 19. h3 Qf4 20. Ng3 g6 21. Bxh8 f6 22. Qd4 Qxd4 23. Nxd4 Kxh8 24. Rb6 Nc4 25. Ra6 Kg8 26. Rb1 Rf7 27. Nge2 Bb7 28. Ra7 Ba8 29. Ra6 Bb7 30. Ra7 Bc6 31. Ra6

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 103 / 115 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): bnqrnkrb/pppppppp/8/8/8/8/PPPPPPPP/QNBRNKRB w DGdg - 0 1

Mirror twin: White 850 vs Black 835 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 318.