White 54 vs Black 116

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 #116 N B B Q R N K R

King on the g-file, rooks on e, h, queen on the d-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 116 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 56.

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 54 gives White +0.20 and setup 116 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.

White is not forced into a single path: the best first move is d4, and 2 first moves are within 10 cp of it.

Along the engine's main line (26 moves) the evaluation stayed within ±17 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 3, drawn 7, Black won 0 (White scored 65.0%).

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: -8
• Lc0 0.32.1: +6

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 +132, difference +1. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 3 White wins, 7 draws, 0 Black wins, White scored 65.0%.

Best first moves

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

Main-line play-out

26 moves, 5 000 000 nodes per half-move. Largest |evaluation| 17 cp, mean 2.3 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 3, drawn 7, Black won 0 — White scored 65.0%. Average length 49.4 moves.

1. d4 c6 2. e4 e5 3. dxe5 Bxe5 4. Nb3 Ne6 5. g3 Bc7 6. f4 O-O 7. Bg2 a5 8. Be3 Nb6 9. Nxa5 d5 10. O-O Nd7 11. Nb3 dxe4 12. f5 Ng5 13. N1d2 Qe7 14. Bf4 Nb6 15. Bxg5 Qxg5 16. Nxe4 Qh6 17. Qd2 Qxd2 18. Nexd2 Re5 19. Rde1 Rxe1 20. Rxe1 Rd8 21. Be4 Na4 22. Nc4 g6 23. fxg6 hxg6 24. Bf3 Be6 25. Nba5 Ra8 26. Rxe6 fxe6 27. Nxb7 Ra6 28. Be4 Kf7 29. Kg2 Nb6 30. Bd3 Nxc4 31. Bxc4 Rb6 32. Nc5 Rxb2 33. Bxe6+ Kf6 34. Bb3 Rb1 35. h4 Re1 36. Kf3 Rg1 37. Kf2 Ra1 38. Kf3 Rf1+ 39. Kg4 Re1 40. Kf3 Rf1+

1. d4 c6 2. c4 d5 3. cxd5 cxd5 4. Nc3 Nb6 5. g3 Bf5 6. Bg2 e6 7. Nb3 h5 8. h4 Ng6 9. e4 dxe4 10. Nc5 Qc8 11. Bxe4 Nd5 12. Bf3 Bg4 13. Qe2 Nxc3 14. bxc3 e5 15. Qd3 b6 16. Ne4 exd4 17. cxd4 Qf5 18. Bxg4 hxg4 19. Re1 Re6 20. Bg5 f6 21. O-O O-O 22. Bd2 Rd8 23. Qc4 Kh8 24. Ng5 Rxe1 25. Nf7+ Kh7 26. Rxe1 b5 27. Qc3 Rd7 28. Qc8 Nxh4 29. Qh8+ Kg6 30. Qxh4 Rxf7 31. Re8 Rb7 32. Qh8 Bd6 33. Rg8 Qh5 34. Rxg7+ Rxg7 35. Qe8+ Rf7 36. Qg8+ Rg7 37. Qe8+ Rf7 38. Qg8+ Kf5 39. Qc8+ Kg6

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 54 / 116 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): nbbqrnkr/pppppppp/8/8/8/8/PPPPPPPP/NNBRQBKR w DHeh - 0 1

Mirror twin: White 902 vs Black 846 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 232.