White 46 vs Black 643

The two setups

White: setup #46 N N Q R K B B R

King on the e-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 46 gives White +0.19 (Morozov Balance Index, 400M nodes).

Black: setup #643 B R N K R Q N B

King on the d-file, rooks on b, e, queen on the f-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 643 gives White +0.14 (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 -5 and +20 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 46 gives White +0.19 and setup 643 gives White +0.14: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.

The engine's first choice for White is e4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (22 moves) the evaluation stayed within ±18 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 2, drawn 8, Black won 0 (White scored 60.0%).

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: -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 +39, Black +107, difference -68. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 2 White wins, 8 draws, 0 Black wins, White scored 60.0%.

Best first moves

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

Main-line play-out

22 moves, 5 000 000 nodes per half-move. Largest |evaluation| 18 cp, mean 7.2 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 2, drawn 8, Black won 0 — White scored 60.0%. Average length 42.4 moves.

1. f3 f5 2. e4 g5 3. d4 g4 4. fxg4 fxe4 5. Be2 b5 6. Be3 Nd6 7. b3 e6 8. c4 Ne7 9. Nc3 b4 10. Na4 h5 11. h3 a5 12. Nc5 hxg4 13. hxg4 Bc6 14. a3 Nb7 15. axb4 Nxc5 16. bxc5 a4 17. Qc3 axb3 18. Rb1 Ra8 19. Nxb3 Qg7 20. Na5 O-O 21. Rh5 Kf7 22. Rd1 Ba4 23. Ra1 Nc6 24. Nxc6 Bxc6 25. Kf2 Rxa1 26. Qxa1 Qf6+ 27. Kg1 Ra8 28. Qe1 Bg7 29. g5 Qf5 30. g6+ Qxg6 31. Rg5 Qh6 32. Bh5+ Ke7 33. Qg3 Kd8 34. d5 Ra1+ 35. Kh2 Kc8 36. dxc6 dxc6 37. Rxg7 Qxh5+ 38. Qh3 Qe5+ 39. Rg3 Kb7 40. Qg4 Re1 41. Bd2 Rb1 42. Bc3 Qxc5 43. Qxe4 Rc1 44. Re3 Qh5+ 45. Rh3 Qd1 46. Rf3 Rb1 47. Kg3 Rb3 48. Be1 Rxf3+ 49. gxf3 Qd6+ 50. Kg4 Qd7 51. Bc3 Ka6 52. f4 Qf7 53. Kg5 Kb6 54. Qb1+ Ka6 55. Bf6 Qf8 56. Qe4 Qd6 57. Kg6 Qd7 58. Bg5 Ka5 59. Kf6 c5 60. Qe1+ Ka4 61. Qxe6 Qd8+ 62. Kg6 Qd3+ 63. f5 Qc2 64. Kg7 Qg2 65. Kg6 Qc2 66. Qd5 Ka3 67. Kg7 c6 68. Qf3+ Ka2 69. Qf4 Qb1 70. f6 Qa1 71. Qc1 Qe5 72. Qf4

1. f3 b6 2. c4 f5 3. Nc3 g6 4. Bf2 Nd6 5. c5 bxc5 6. Bxc5 a5 7. Nb3 Nf6 8. Nxa5 Qh6 9. Ba7 Rc8 10. d3 Qh5 11. Nc4 Nd5 12. h4 O-O 13. Nxd5 Bxd5 14. Be3 e5 15. Bg5 Be6 16. e4 Nb5 17. Be7 Rfe8 18. Bc5 d6 19. a4 Nd4 20. Bxd4 exd4 21. Be2 d5 22. Na5 c5 23. f4 Qh6 24. e5 g5 25. Nb7 c4 26. dxc4 dxc4 27. Rxd4 gxf4 28. Rxf4 Qg6 29. Nd6 Bxe5 30. Nxe8 c3 31. O-O cxb2 32. Qe3 Bxf4 33. Qxf4 Bd5 34. Bf3 Bxf3 35. Qxf3 Qb6+ 36. Kh2 Qb8+ 37. Kh3 Qe5 38. Qb3+ Kh8 39. Nc7 h6 40. Nd5 Rc1

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 46 / 643 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): brnkrqnb/pppppppp/8/8/8/8/PPPPPPPP/NNQRKBBR w DHbe - 0 1

Mirror twin: White 916 vs Black 211 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 217.