White 54 vs Black 117

The two setups

White: setup #54 N N B R Q B K R

King on the g-file, rooks on d, h, 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 54 gives White +0.20 (Morozov Balance Index, 400M nodes).

Black: setup #117 N Q B B R N K R

King on the g-file, rooks on e, h, queen on the b-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 117 gives White +0.20 (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 58.

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 -20 and +15 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 54 gives White +0.20 and setup 117 gives White +0.20: 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 d4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (30 moves) the largest swing was 67 cp (around move 12), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 0, drawn 8, Black won 2 (White scored 40.0%).

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: -5
• Lc0 0.32.1: +13

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 +133, Black +93, difference +40. 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, 8 draws, 2 Black wins, White scored 40.0%.

Best first moves

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

Main-line play-out

30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 67 cp, mean 25.8 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 0, drawn 8, Black won 2 — White scored 40.0%. Average length 62.4 moves.

1. c4 d6 2. d4 e5 3. dxe5 dxe5 4. c5 c6 5. Nd2 Be7 6. b4 b6 7. Nab3 Ne6 8. Ba3 O-O 9. Nc4 Rd8 10. e3 e4 11. Be2 Nac7 12. Ne5 Qb7 13. Rc1 Bf6 14. Nc4 Qa6 15. Nbd2 Nb5 16. Nxe4 Nxa3 17. Na5 Nb5 18. Nxc6 Rde8 19. Nd6 Nec7 20. cxb6 axb6 21. Qd1 Qa3 22. Nxb5 Nxb5 23. Bxb5 Rxe3 24. O-O Ree8 25. Qd6 Ba6 26. Qd5 g6 27. Bxa6 Qxa6 28. Rc2 Qa4 29. Qb3 Qxb3 30. axb3 h5 31. g3 h4 32. Rd1 h3 33. Kf1 b5 34. Rd3 Re4 35. Re2 Rxe2 36. Kxe2 Ra8 37. Kf3 Ra6 38. Nb8 Ra2 39. Nd7 Be7 40. Nc5 Rb2 41. Rd7 Kf8 42. Rb7 Bf6 43. Kg4 Bd4 44. Kxh3 Bxf2 45. Nd3 Re2 46. Rxb5 Bg1 47. Rd5 Rxh2+ 48. Kg4 Re2 49. Kf3 Rc2 50. Nf4 Rc3+ 51. Rd3 Rxd3+ 52. Nxd3 Ke7 53. Kf4 Ba7 54. Kg5 Bb8 55. g4 Ba7

1. h4 d5 2. h5 h6 3. e4 dxe4 4. Qxe4 Nd7 5. d4 c6 6. Nd2 Nab6 7. Nf3 Bc7 8. c4 Nf6 9. Qc2 Bg4 10. Be2 Bxh5 11. b4 Nbd7 12. Nb3 Bg6 13. Bd3 Bxd3 14. Qxd3 e5 15. dxe5 Nxe5 16. Nxe5 Rd8 17. Qf3 Rxd1+ 18. Qxd1 Bxe5 19. a3 O-O 20. Qf3 Qc8 21. g3 Qe6 22. Rh4 b6 23. Kg2 Re8 24. Be3 h5 25. Bg5 g6 26. Bxf6 Qxf6 27. Re4 Qxf3+ 28. Kxf3 f6 29. Nd4 Rc8 30. c5 Kf7 31. Ke3 bxc5 32. bxc5 a6 33. Kf3 g5 34. a4 Kg6 35. a5 g4+ 36. Kg2 Kf7 37. Kf1 Ke7 38. f3 gxf3 39. Kf2 Kd7 40. Nxf3 Bc3 41. Rh4 Bxa5 42. Rd4+ Ke6 43. Rd6+ Kf7 44. Rd7+ Ke8 45. Rh7 Bc3 46. Rxh5 Kd7 47. Rh4 Ke6 48. Rc4 Bb2 49. Ra4 Ra8 50. Ke3 a5 51. g4 Kd5 52. Kd3 Be5 53. g5 fxg5 54. Nxg5 Kxc5 55. Kc2 Kb5 56. Re4 Bd6 57. Nf3 Bc5 58. Nd4+ Kb6 59. Kb3 Rg8 60. Nc2 Rg3+ 61. Ka4 Rc3 62. Re2 Bd6 63. Re6 Bc5 64. Re2 Kc7 65. Rg2 Rc4+ 66. Kb3 Re4 67. Rg8 Bd6 68. Ka2 a4 69. Kb2 Be5+ 70. Ka2 Re2 71. Kb1 Rf2 72. Re8 Bf6 73. Kc1 Bc3 74. Kd1 Rd2+ 75. Kc1 Rh2 76. Kd1 Rh1+ 77. Ke2 Rh4 78. Kd3 Bb2 79. Ne1 Rh3+ 80. Kc2 Rh2+ 81. Kb1 Bc3 82. Nc2 Rh1+ 83. Ka2 Rc1 84. Re7+ Kb6 85. Re2 Kb5 86. Ka3 c5 87. Rf2 Bd4 88. Rh2 Rf1 89. Re2 Rf3+ 90. Ka2 Kc4 91. Re8 Rf2 92. Kb1 Kc3 93. Nxd4 Rf1+ 94. Ka2 cxd4 95. Rc8+ Kd2 96. Ka3 Rc1 97. Rb8 Rc4 98. Kb2 d3 99. Rd8 Ke2 100. Re8+ Kd1 101. Rg8 d2 102. Rg2 Rb4+ 103. Ka3 Rf4 104. Kb2 a3+ 105. Kc3 Rf3+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 54 / 117 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): nqbbrnkr/pppppppp/8/8/8/8/PPPPPPPP/NNBRQBKR w DHeh - 0 1

Mirror twin: White 902 vs Black 842 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 233.