White 15 vs Black 658

The two setups

White: setup #15 Q N N R K R B B

King on the e-file, rooks on d, f, 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 15 gives White +0.27 (Morozov Balance Index, 400M nodes).

Black: setup #658 B R N K R B N Q

King on the d-file, rooks on b, e, queen on the h-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 658 gives White +0.35 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation never left ±1 centipawns of equality, 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 wandered between -15 and +19 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 15 gives White +0.27 and setup 658 gives White +0.35: 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 g3; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (14 moves) the evaluation stayed within ±16 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 5, Black won 5 (White scored 25.0%).

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: 0
• Lc0 0.32.1: -2

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 +11, Black +88, difference -77. 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, 5 draws, 5 Black wins, White scored 25.0%.

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| 16 cp, mean 0.9 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 0, drawn 5, Black won 5 — White scored 25.0%. Average length 61.6 moves.

1. Nd3 b6 2. b4 h5 3. f3 h4 4. e4 f6 5. a4 e5 6. Bf2 Nge7 7. g4 hxg3 8. hxg3 Nc6 9. b5 Na5 10. Nc3 Nd6 11. Nb2 f5 12. O-O-O O-O-O 13. d3 g5 14. Kb1 Kb8 15. Qa2 f4 16. Be1 Qh3 17. Bd2 Qxg3 18. Rg1 Qh4 19. Bg2 Qh2 20. Bh1 Be7 21. Nd5 Bxd5 22. Qxd5 Ndb7 23. Qxe5 Bc5 24. Qxg5 Bxg1 25. Qxg1 Qh6 26. d4 Rg8 27. Qe1 Rdf8 28. e5 Qg6 29. Qf2 Qf7 30. Nd3 Qc4 31. Nb2 Qd5 32. Nd3 Qc4 33. Nb2 Qd5 34. Bc1 d6 35. Qe1 dxe5 36. dxe5 Qe6 37. Qb4 Qxe5 38. Nd3 Qd5 39. Bxf4 Nc5 40. Nb2 Qe6 41. Bc1 Rd8 42. Re1 Qh3 43. f4 Rh8 44. Bd2 Rhe8 45. Bc1 a6 46. bxa6 Ka7 47. Rxe8 Rxe8 48. Bd5 Rd8 49. Be4 Nxe4 50. Qxe4 Qd7 51. Qe2 Qd5 52. Nd3 Qc6 53. f5 Qxa4 54. Qe5 Rd7 55. f6 Nc4 56. Qf5 Nd6 57. Qd5 Qc4 58. Nf4 Rf7 59. Qxc4 Nxc4 60. Nh5 Kxa6 61. Ka2 Kb7 62. Bf4 Kc6 63. Kb3 Nd6 64. Be5 Rh7 65. Nf4 Nf7 66. Bd4 Rh4 67. Be3 Rh6 68. Bd4 Rh4 69. Be3 Rg4 70. Kc3 Rg5 71. Ne2 Rd5 72. Ng3 Kd7 73. Kb3 Nd6 74. Bf4 Rd1 75. Ka2 Rd4 76. Be5 Rd5 77. Bf4 Ke6 78. Be3 Kxf6 79. Ne2 Rf5 80. Nf4 c5 81. Nd3 Ke6 82. Nf4+ Ke5 83. Nd3+ Kd5 84. Bh6 Ne4 85. Ka3 b5 86. Kb3 c4+ 87. Kb4 cxd3 88. cxd3 Nd6 89. Ka5 Rf3 90. d4 Kc4 91. Kb6 b4 92. Bg5 b3 93. Bc1 Rd3 94. Kc6 Rxd4 95. Kd7 Rd1 96. Bb2

1. g3 e5 2. b3 g6 3. Nd3 Bg7 4. e4 d5 5. f3 b6 6. O-O-O Nge7 7. Rde1 c5 8. a4 O-O 9. exd5 Bxd5 10. Nc3 Bb7 11. Qa3 Re8 12. Qa2 Nd6 13. Ne4 Rbd8 14. f4 Bxe4 15. Bxe4 f5 16. b4+ c4 17. fxe5 Nxe4 18. Qxc4+ Nd5 19. Nf4 Bh6 20. Rxe4 fxe4 21. Nxd5 Qxe5 22. Nf4+ Kh8 23. c3 Bg7 24. Be3 Rc8 25. Qb3 b5 26. Kd1 Rc4 27. h4 Rec8 28. Ke1 a5 29. Kf2 axb4 30. cxb4 bxa4 31. Qxa4 Qd6 32. Kg2 Rxb4 33. Qa3 Rcb8 34. Qa2 Qc6 35. Qe6 Qxe6 36. Nxe6 Bb2 37. Rf7 R4b7 38. Rf4 Re7 39. Rxe4 Bf6 40. Kf3 Rbe8 41. Nc5 Rxe4 42. Nxe4 Be5 43. d4 Bg7 44. Ng5 Kg8 45. Kf2 Bf6 46. Kf3 Bd8 47. Bf4 Bf6 48. Be3 Bh8 49. Nh3 Bg7 50. Ng5 h5 51. Nh3 Kf7 52. Nf4 Rd8 53. Ke4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 15 / 658 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): brnkrbnq/pppppppp/8/8/8/8/PPPPPPPP/QNNRKRBB w DFbe - 0 1

Mirror twin: White 944 vs Black 199 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 3.