White 444 vs Black 637

The two setups

White: setup #444 R B N N Q K B R

King on the f-file, rooks on a, h, queen on the e-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 444 gives White +0.13 (Morozov Balance Index, 400M nodes).

Black: setup #637 R N K B Q R B N

King on the c-file, rooks on a, f, queen on the e-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 637 gives White +0.21 (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 53.

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 shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±6 cp.

For comparison, in symmetric play setup 444 gives White +0.13 and setup 637 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.

The engine's first choice for White is f4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (24 moves) the evaluation stayed within ±19 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 1, drawn 4, Black won 5 (White scored 30.0%).

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 held exactly 0.00 up to 1 600 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: -14

Independent confirmations: 2 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 +54, Black +95, difference -41. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 1 White wins, 4 draws, 5 Black wins, White scored 30.0%.

Best first moves

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

Main-line play-out

24 moves, 5 000 000 nodes per half-move. Largest |evaluation| 19 cp, mean 1.7 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 4, Black won 5 — White scored 30.0%. Average length 71.6 moves.

1. e4 f5 2. exf5 g6 3. f4 gxf5 4. Bd4 Bc4+ 5. d3 Ba6 6. O-O Ng6 7. c4 b6 8. Ne2 c5 9. Bf2 Nc6 10. Ndc3 e6 11. Nb5 Be7 12. d4 cxd4 13. a4 Bb4 14. Qc1 Qe7 15. Nexd4 Bb7 16. Nc2 Bc5 17. Qd2 a6 18. Bxc5 Qxc5+ 19. Nbd4 a5 20. Ra3 Rg8 21. g3 e5 22. fxe5 f4 23. Rb3 fxg3 24. Rxg3 Ncxe5 25. Ne3 O-O-O 26. Nb3 Qc6 27. Qg2 Qxa4 28. Be4 Bxe4 29. Qxe4 Kb8 30. Nd2 Qb4 31. Rd1 Rge8 32. Nd5 Qc5+ 33. Kh1 Re6 34. Rf1 Nc6 35. Qg4 Nce5 36. Qg5 Rf8 37. Rxf8+ Qxf8 38. Rg1 Qc8 39. b3 Qc6 40. Qg2 Ne7 41. Nc3 Nd3 42. Qxc6 dxc6 43. Rg7 h5 44. Kg1 Re3 45. Nf1 Re5 46. Nd2 Nc5 47. Nf3 Re3 48. Nd4 Kc8 49. Rg3 Rxg3+ 50. hxg3 Kd7 51. Kg2 Kd6 52. Kf2 Ne6 53. Nf3 Kc5 54. Na4+ Kb4 55. Nxb6 Kxb3 56. Ke2 a4 57. Nd2+ Kb4 58. Nxa4 Kxa4 59. Kf3 Kb4 60. Ke4 Kc3 61. Nf1 Kxc4 62. Nd2+ Kc3 63. Nb1+ Kc2 64. Na3+ Kb3 65. Nb1 Kc2 66. Na3+ Kb2 67. Nc4+ Kc3 68. Nd6 Ng7 69. Kf3 Kd4 70. Ne4 c5 71. Nd2 Kd3 72. Ne4 Ne6 73. Nf2+ Kd4 74. Ne4 c4 75. Nd2 Kd3 76. Nb1 Ng5+ 77. Kf2 Ne4+ 78. Kg1 Nd2 79. Na3 c3 80. Kf2 Nc4 81. Nxc4

1. e4 f5 2. exf5 g6 3. f4 gxf5 4. Bd4 Bc4+ 5. d3 Ba6 6. O-O Ng6 7. c4 b6 8. Ne2 c5 9. Bf2 Nc6 10. Ndc3 e6 11. Nb5 Be7 12. d4 cxd4 13. a4 Bb4 14. Qc1 Qe7 15. Nexd4 Bb7 16. Nc2 Bc5 17. Qd2 a6 18. Bxc5 Qxc5+ 19. Nbd4 a5 20. Ra3 Rg8 21. g3 e5 22. fxe5 f4 23. Rb3 fxg3 24. Rxg3 Ncxe5 25. Ne3 O-O-O 26. Nb3 Qc6 27. Qg2 Qxa4 28. Be4 Bxe4 29. Qxe4 Kb8 30. Nd2 Qb4 31. Rd1 Rge8 32. Nd5 Qc5+ 33. Kh1 Re6 34. Rf1 Nc6 35. Qg4 Nce5 36. Qg5 Rf8 37. Rxf8+ Qxf8 38. Rg1 Qc8 39. b3 Qc6 40. Qg2 Ne7 41. Nc3 Nd3 42. Qxc6 dxc6 43. Rg7 h5 44. Kg1 Re3 45. Nf1 Re5 46. Nd2 Nc5 47. Nf3 Re3 48. Nd4 Kc8 49. Rg3 Rxg3+ 50. hxg3 Kd7 51. Kg2 Kd6 52. Kf2 Ne6 53. Nf3 Kc5 54. Na4+ Kb4 55. Nxb6 Kxb3 56. Ke2 a4 57. Nd2+ Kb4 58. Nxa4 Kxa4 59. Kf3 Kb4 60. Ke4 Kc3 61. Nf1 Kxc4 62. Nd2+ Kc3 63. Nb1+ Kc2 64. Na3+ Kb3 65. Nb1 Kc2 66. Na3+ Kb2 67. Nc4+ Kc3 68. Nd6 Ng7 69. Kf3 Kd4 70. Ne4 c5 71. Nd2 Kd3 72. Ne4 Ne6 73. Nf2+ Kd4 74. Ne4 c4 75. Nd2 Kd3 76. Nb1 Ng5+ 77. Kf2 Ne4+ 78. Kg1 Nd2 79. Na3 c3 80. Kf2 Nc4 81. Nxc4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 444 / 637 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): rnkbqrbn/pppppppp/8/8/8/8/PPPPPPPP/RBNNQKBR w AHaf - 0 1

Mirror twin (the same position mirrored): White 716 vs Black 232.