White 109 vs Black 54

The two setups

White: setup #109 Q N R B N K B R

King on the f-file, rooks on c, h, queen on the a-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 109 gives White +0.10 (Morozov Balance Index, 400M nodes).

Black: 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).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±4 centipawns of equality, reaching search depth 55.

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 -18 and +13 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 109 gives White +0.10 and setup 54 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 c4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (18 moves) the largest swing was 33 cp (around move 3), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 1, drawn 9, Black won 0 (White scored 55.0%).

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: -9
• Lc0 0.32.1: 0

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 +32, Black +133, difference -101. 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, 9 draws, 0 Black wins, White scored 55.0%.

Best first moves

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

Main-line play-out

18 moves, 5 000 000 nodes per half-move. Largest |evaluation| 33 cp, mean 8.5 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 39.5 moves.

1. f4 e5 2. fxe5 c5 3. b4 d6 4. exd6 cxb4 5. Bxa7 Nc6 6. Bc5 Bxd6 7. Bxd6 Rxd6 8. Nf3 O-O 9. a3 Bg4 10. e3 bxa3 11. Qxa3 Rh6 12. O-O Qb8 13. Rf2 Bxf3 14. gxf3 Nc7 15. Nc3 Qd8 16. f4 Rg6+ 17. Kf1 Qh4 18. Bf3 Rd8 19. Qb2 Qh3+ 20. Ke1 h6 21. Ne2 Ne8 22. Rb1 Rgd6 23. Ng3 R6d7 24. Qc3 Rc7 25. Qa1 Nd6 26. Be2 Kh8 27. Bf1 Qe6 28. Bd3 b5 29. Rg2 f6 30. Qc3 Qc8 31. Qa1 Ra7 32. Qb2 Na5 33. Qd4 Qa8 34. Re2 Nac4 35. Qc5 f5 36. Bxf5 Nxf5 37. Qxf5 Ra2 38. d4 Na3 39. Rc1 b4 40. Kf2 Rc8 41. h4 Rc3 42. d5 Rc5 43. Qe4 Qxd5 44. Qxb4 Nxc2 45. Qe4 Qxe4 46. Nxe4 Rc6 47. h5 Kh7 48. Rd2 Rc4 49. Kf3 Rc8 50. Ng3 Rc5 51. Kf2 Rc3 52. Ne2 Rc5 53. e4 Rc7 54. Ng3 Rc4 55. Re2 Rc5 56. Nf5 Rc3 57. Rd2 Rc4 58. Nd6 Rc6 59. e5 Nb4 60. Rxa2 Rxc1 61. Ra7 Nd5 62. f5 Rc2+ 63. Kf3 Rd2 64. Ne8 Rb2 65. f6 Kg8 66. Rxg7+ Kf8 67. Nd6 Rb3+ 68. Ke4 Nxf6+ 69. exf6 Re3+ 70. Kf5 Rf3+ 71. Ke5 Re3+ 72. Ne4

1. f3 b6 2. Nd3 h5 3. c4 c5 4. a3 h4 5. b4 d6 6. Nc3 f5 7. Be3 e5 8. Bg5 Be7 9. Ba4 Bd7 10. Bxd7 Nxd7 11. Bxe7 Qxe7 12. O-O O-O 13. Nf2 Nc7 14. Nh3 Nf6 15. Qb1 Qd7 16. e3 g6 17. Rcd1 Qg7 18. bxc5 dxc5 19. a4 Ne6 20. a5 bxa5 21. Qa2 Qc7 22. d3 Rd7 23. e4 Nd4 24. Kh1 Qd8 25. Rb1 Rg7 26. Nd5 Kh7 27. Rfe1 f4 28. Nf2 Rff7 29. h3 Rb7 30. Kh2 Rb4 31. Ra1 Rf7 32. Qxa5 Qxa5 33. Rxa5 Rbb7 34. Nxf6+ Rxf6 35. Rea1 Rff7 36. R1a2 Nb3 37. Ra6 Nc1 38. Rd2 Nb3 39. Rda2 Nc1 40. Ra1 Nb3

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 109 / 54 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): nnbrqbkr/pppppppp/8/8/8/8/PPPPPPPP/QNRBNKBR w CHdh - 0 1

Mirror twin: White 856 vs Black 902 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 444.