White 63 vs Black 31

The two setups

White: setup #63 N N R Q K R B B

King on the e-file, rooks on c, f, queen on the d-file; one bishop starts in a corner; the knights start away from the centre. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 63 gives White +0.23 (Morozov Balance Index, 400M nodes).

Black: setup #31 N Q N R K R B B

King on the e-file, rooks on d, f, queen on the b-file; one bishop starts in a corner; the knights start away from the centre. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 31 gives White +0.26 (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 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±11 cp.

For comparison, in symmetric play setup 63 gives White +0.23 and setup 31 gives White +0.26: 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 c4, and 3 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the evaluation stayed within ±24 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 10, Black won 0 (White scored 50.0%).

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 +58. 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: 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 +30, Black +6, difference +24. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 0 White wins, 160 draws, 0 Black wins, White scored 50.0%.

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| 24 cp, mean 6.2 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 0, drawn 10, Black won 0 — White scored 50.0%. Average length 37.1 moves.

1. g3 c6 2. Nb3 f5 3. f4 g6 4. c3 Nc7 5. d3 e5 6. fxe5 Bxe5 7. Qc2 Bf7 8. N1d2 Nd6 9. e4 O-O 10. Nf3 Bg7 11. e5 Rde8 12. O-O-O Bxe5 13. Nxe5 Rxe5 14. c4 Qe8 15. Qc3 b6 16. Nd4 Qe7 17. Nf3 Re2 18. Rde1 Re6 19. Bd4 Re8 20. Qd2 Re2 21. Qh6 Rxe1+ 22. Rxe1 Qf8 23. Qxf8+ Kxf8 24. Be5 Ke7 25. Ng5 Bg8 26. b4 Ne6 27. Nxe6 Bxe6 28. a4 g5 29. Kd2 Nf7 30. Bd4 Rb8 31. h3 a6 32. Bf3 h6 33. Kc3 Nd6 34. Bf2 Ne8 35. h4 g4 36. Bg2 f4 37. gxf4 Ng7 38. h5 Kf7 39. Re5 d6 40. Re1 Bd7 41. f5 Nxf5 42. Rf1 g3 43. Bxg3 Rg8 44. Bh3 Rxg3 45. Bxf5 Bxf5 46. Rxf5+ Ke7 47. a5 b5 48. cxb5 cxb5

1. f4 g5 2. c3 gxf4 3. Rxf4 d5 4. e4 dxe4 5. g3 Nd6 6. Qh5 Nb6 7. Bxe4 e5 8. Rh4 Nd7 9. Bd5 O-O-O 10. O-O-O Rfe8 11. Qe2 e4 12. d4 exd3 13. Qxd3 Bf6 14. Rh5 h6 15. Be3 c6 16. Bb3 Bh7 17. Qxh7 Rxe3 18. Qxh6 Re7 19. Qf4 Ne4 20. Nd2 Qxf4 21. gxf4 Nf2 22. Rf1 Nd3+ 23. Kb1 Re2 24. Nc4 b5 25. Bd1 Rf2 26. Rxf2 Nxf2 27. Ne3 Nxd1 28. Nxd1 Nb6 29. Kc1 Nd5 30. Nb3 Nxf4 31. Rf5 Be5 32. Rxf7 Rh8 33. Na5 Rh6 34. Rxa7 Nd5 35. Ra6 Kd7 36. h3 Bf4+ 37. Kc2 Nc7 38. Rb6 Nd5 39. Ra6 Nc7 40. Rb6 Nd5

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 63 / 31 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): nqnrkrbb/pppppppp/8/8/8/8/PPPPPPPP/NNRQKRBB w CFdf - 0 1

Mirror twin: White 896 vs Black 928 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 16.