White 58 vs Black 547

The two setups

White: setup #58 N N R Q B B K R

King on the g-file, rooks on c, 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 58 gives White +0.19 (Morozov Balance Index, 400M nodes).

Black: setup #547 B R N K N Q R B

King on the d-file, rooks on b, g, queen on the f-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 547 gives White +0.10 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 63.

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 -27 and +33 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 58 gives White +0.19 and setup 547 gives White +0.10: 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 e3, and 3 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the largest swing was 32 cp (around move 7), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 3, drawn 6, Black won 1 (White scored 60.0%).

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 16 000 000 000 nodes.

Swap the two setups, giving White the black back rank and Black the white one, and the evaluation jumps to +42. The same two armies dealt the other way round are no longer balanced at all: that is how precisely this pair pays for the first move.

Independent engines, run on the same position:

• Berserk 14: +1
• Lc0 0.32.1: +8

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 +33, Black +140, difference -107. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 35 White wins, 123 draws, 2 Black wins, White scored 60.3%.

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| 32 cp, mean 7.8 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 3, drawn 6, Black won 1 — White scored 60.0%. Average length 46.4 moves.

1. d4 g5 2. c4 f5 3. Nc3 b6 4. e3 e6 5. b4 Nf6 6. b5 Ne7 7. Qa4 f4 8. Qxa7 Rc8 9. Nc2 Qh6 10. h3 Nf5 11. Qa3 fxe3 12. Nxe3 Nxd4 13. Rd1 Nh5 14. Ne2 Nxe2+ 15. Bxe2 Nf4 16. Bf1 d6 17. c5 bxc5 18. Qxc5 O-O 19. Qc2 Qg6 20. Qxg6+ Nxg6 21. a4 Rf4 22. a5 Rcf8 23. b6 cxb6 24. Rxd6 bxa5 25. Rxe6 Bd4 26. Be2 Re4 27. Ra6 Nf4 28. Bc4+ Kh8 29. O-O Bxe3 30. fxe3 Rxc4 31. exf4 gxf4 32. Bd2 Rg8 33. Rxf4 Rxg2+ 34. Kf1 Rxf4+ 35. Bxf4 Bf3 36. Rxa5 Kg7 37. Rg5+ Rxg5 38. Bxg5 Bc6 39. Kf2 Kg6 40. h4 Kf5 41. Kg3 Ke6 42. Kf4 Bd7 43. Bd8 Kd5 44. Bb6 Be8 45. Bc7 Kd4 46. Bb6+ Kd3 47. Bc7 Ke2 48. Bd8 Kf2 49. Bf6 Bc6 50. Bd8

1. c4 b6 2. d4 g5 3. Nc3 f5 4. e3 e6 5. Nc2 Nf6 6. d5 Nd6 7. dxe6 c5 8. b4 dxe6 9. Nb5 Ne4 10. bxc5 bxc5 11. f3 a6 12. fxe4 axb5 13. cxb5 Bb2 14. Rb1 Be5 15. exf5 O-O-O 16. Qc1 Qxf5 17. Nb4 g4 18. Bd3 Ne4 19. Qa3 Bb7 20. Nc6 Rge8 21. Bh4 Rxd3 22. Qxd3 g3 23. Rf1 Nf2 24. Qxf5 exf5 25. Nxe5 Nh3+ 26. gxh3 g2 27. Nc6 gxf1=R+ 28. Kxf1 Rxe3 29. Kf2 Ra3 30. Rc1 f4 31. Rxc5 Rxa2+ 32. Kf3 Rxh2 33. Kxf4 Rxh3 34. Bf6 Rh1 35. Na5+ Kb8 36. Be5+ Ka7 37. Bd4 Kb8 38. b6 Rh4+ 39. Ke3 Re4+ 40. Kd3 Re6 41. Be5+ Ka8 42. Bc7 h6 43. Rf5 Be4+ 44. Kd4 Rxb6 45. Rf8+ Ka7 46. Bxb6+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 58 / 547 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): brnknqrb/pppppppp/8/8/8/8/PPPPPPPP/NNRQBBKR w CHbg - 0 1

Mirror twin: White 901 vs Black 499 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 13.