White 321 vs Black 901

The two setups

White: setup #321 B N R B Q K R N

King on the f-file, rooks on c, g, queen on the e-file; one 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 321 gives White +0.27 (Morozov Balance Index, 400M nodes).

Black: setup #901 R K B B Q R N N

King on the b-file, rooks on a, f, 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 901 gives White +0.21 (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 61.

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 ±6 cp.

For comparison, in symmetric play setup 321 gives White +0.27 and setup 901 gives White +0.21: 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 O-O, and 3 first moves are within 10 cp of it.

Along the engine's main line (14 moves) the evaluation stayed within ±6 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 +90. 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: -17

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 +86, Black +80, difference +6. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 3 White wins, 150 draws, 7 Black wins, White scored 48.8%.

Best first moves

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

Main-line play-out

14 moves, 5 000 000 nodes per half-move. Largest |evaluation| 6 cp, mean 0.2 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 43.0 moves.

1. e3 e5 2. b4 d5 3. O-O Ng6 4. f4 f5 5. fxe5 Nxe5 6. Nf2 Nf6 7. a4 a5 8. b5 b6 9. Nd3 Nc4 10. Nb2 Ne5 11. Nd3 Nc4 12. Nb2 Be7 13. Nxc4 dxc4 14. Bf3 Bd6 15. Qe2 Ng4 16. h3 Ne5 17. Bxa8 Kxa8 18. d4 cxd3 19. cxd3 g5 20. Nd2 Bb7 21. Bxe5 Qxe5 22. Nf3 Qf6 23. Nd4 Qe5 24. Nf3 Bxf3 25. Qxf3+ Kb8 26. g3 g4 27. hxg4 fxg4 28. d4 Qe6 29. Qe2 Re8 30. Rc3 h5 31. e4 Qxe4 32. Qxe4 Rxe4 33. Rd3 Re2 34. Rf2 Re1+ 35. Rf1 Re2 36. Rf2 Re1+ 37. Rf1

1. O-O Ng6 2. c4 f5 3. b4 e5 4. e3 Nf6 5. f3 d5 6. Nf2 a5 7. bxa5 Rxa5 8. cxd5 Nxd5 9. Nc3 Nf6 10. Rb1 Qe7 11. Qe2 Nd7 12. a4 Nb6 13. Bb2 Rf6 14. Bc2 Bd7 15. Kh1 Qe8 16. Nd3 Be7 17. e4 Rc6 18. Bb3 Nf4 19. Nxf4 exf4 20. e5 Be6 21. Bxe6 Rxe6 22. d4 Nxa4 23. Qc2 g6 24. Ra1 Rea6 25. Nxa4 Rxa4 26. Rac1 Qc6 27. Qb3 Qe6 28. d5 Qb6 29. Qc2 Ra2 30. d6 cxd6 31. Qc8+ Ka7 32. Bc3 dxe5 33. Bxe5 Bd6 34. Bg7 Rd2 35. Bc3 Rd5 36. Qg8 Rd3 37. Qxh7 Ba3 38. Rb1 Rxc3 39. Rxb6 Rxb6 40. Qg7 Bb2 41. Qe7 Rc4 42. h3 Rc1 43. Rg1 Rxg1+ 44. Kxg1 Bd4+ 45. Kf1 Ra6 46. Qg5 Be3 47. h4 Ra1+ 48. Ke2 Ra2+ 49. Kd1 Ra1+ 50. Kc2 Ra2+ 51. Kb1 Ra6 52. g4 fxg4 53. fxg4 Bf2 54. h5 f3 55. Qf4 Bh4 56. Qxf3 gxh5 57. gxh5 Bg5 58. Qf2+ Rb6+ 59. Kc2 Bh6 60. Kd3 Bc1 61. Qc5 Bh6 62. Kc2 Bg7 63. Kd3 Bh6 64. Qd4 Bf8

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 321 / 901 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): rkbbqrnn/pppppppp/8/8/8/8/PPPPPPPP/BNRBQKRN w CGaf - 0 1

Mirror twin: White 347 vs Black 58 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 56.