White 12 vs Black 7

The two setups

White: setup #12 Q B N N R K B R

King on the f-file, rooks on e, h, queen on the a-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 12 gives White +0.33 (Morozov Balance Index, 400M nodes).

Black: setup #7 Q N B N R K R B

King on the f-file, rooks on e, 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 7 gives White +0.24 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 55.

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 ±15 cp.

For comparison, in symmetric play setup 12 gives White +0.33 and setup 7 gives White +0.24: 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 (13 moves) the evaluation stayed within ±4 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 16 000 000 000 nodes.

Swap the two setups, giving White the black back rank and Black the white one, and the evaluation jumps to +22. The same two armies dealt the other way round are no longer balanced at all: that is how precisely this pair pays for the first move.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: +9

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 +47, Black +32, difference +15. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 0 White wins, 160 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

13 moves, 5 000 000 nodes per half-move. Largest |evaluation| 4 cp, mean 0.4 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 40.0 moves.

1. c3 g6 2. d4 O-O 3. f3 b6 4. Be3 Bg7 5. O-O Ne6 6. Bf2 c5 7. e3 Nc7 8. e4 cxd4 9. cxd4 Nc6 10. d5 Ne5 11. Ne2 Ba6 12. a4 Qb7 13. Qa2 Nd3 14. Bxd3 Bxd3 15. Bg3 d6 16. Nf2 Bxe2 17. Rxe2 b5 18. Rd1 a5 19. Qb3 Rb8 20. e5 Bxe5 21. Bxe5 dxe5 22. Rxe5 Rfe8 23. Ne4 bxa4 24. Qxb7 Rxb7 25. d6 exd6 26. Rxa5 Kf8 27. Nxd6 Rd8 28. Rxa4 Nb5 29. Nxb7 Rxd1+ 30. Kf2 Rd2+ 31. Kf1 Rxb2 32. Nc5 Rb1+ 33. Kf2 Rb2+ 34. Kf1 Rb1+ 35. Kf2 Rb2+

1. c3 g6 2. e4 b6 3. f3 d5 4. Be3 Bg7 5. O-O Nd7 6. Ne2 e5 7. a4 O-O 8. d3 a5 9. Ba2 dxe4 10. dxe4 Nc5 11. Nf2 Be6 12. Bxe6 Ndxe6 13. Qa2 Qa6 14. b3 Ra8 15. Rb1 Rfd8 16. Nc1 h5 17. Qc2 Kh7 18. Rd1 Rxd1+ 19. Qxd1 c6 20. Ra1 b5 21. Qf1 Qb7 22. axb5 cxb5 23. b4 Na4 24. Ncd3 Qc7 25. Nd1 Bf8 26. bxa5 Rxa5 27. Bd2 Nf4 28. N3f2 Qa7 29. g3 Ne6 30. Kg2 Nb6 31. Rxa5 Qxa5 32. Qe2 Nc5 33. Be1 Nc4 34. Ne3 Qa1 35. Nxc4 bxc4 36. Qd1 Qa8 37. Kf1 Kg8 38. h4 Qa6 39. Qd8 Qb7 40. Qd2 Qa8 41. Qd1 Qc6 42. Qd8 Qb7 43. Qd1 Kg7 44. Qe2 Qa6 45. Qd2 Qf6 46. Qd1 Be7 47. Kg2 Qe6 48. Qb1 Qd7 49. Qb8 Bd6 50. Qb1 Nb3 51. Qd1 Qe6 52. Qc2 Qd7 53. Qe2 Qc6 54. Bd2 Be7 55. Be3 Qb5 56. Qb2 Qa5 57. Nd1

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 12 / 7 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): qnbnrkrb/pppppppp/8/8/8/8/PPPPPPPP/QBNNRKBR w EHeg - 0 1

Mirror twin: White 956 vs Black 946 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 2.