White 469 vs Black 514

The two setups

White: setup #469 R N B B N K R Q

King on the f-file, rooks on a, g, queen on the h-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 469 gives White +0.21 (Morozov Balance Index, 400M nodes).

Black: setup #514 B R N Q K B N R

King on the e-file, rooks on b, h, queen on the d-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 514 gives White +0.08 (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 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 shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±9 cp.

For comparison, in symmetric play setup 469 gives White +0.21 and setup 514 gives White +0.08: 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 h4, and 3 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the evaluation stayed within ±21 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 held exactly 0.00 up to 1 600 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: -1
• Lc0 0.32.1: -3

Independent confirmations: 2 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 -2, Black +40, difference -42. 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, 10 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| 21 cp, mean 2.3 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 36.5 moves.

1. e4 b5 2. a4 b4 3. d3 g6 4. O-O Bg7 5. Nd2 c5 6. h4 h5 7. Qh2 Nd6 8. Nef3 Nh6 9. Qg3 Ng4 10. Ng5 Be5 11. Qh3 f5 12. Re1 Bd4 13. Bxg4 fxg4 14. Qg3 O-O 15. Re2 Rc8 16. Rb1 Qc7 17. Nb3 Bg7 18. Bf4 c4 19. Nd2 Qc6 20. Be5 Bh6 21. Bf4 Bg7 22. Be5 Bh6 23. Bf4

1. e4 e5 2. h4 b5 3. d3 d5 4. exd5 Nf6 5. c4 Nb6 6. Bb3 a5 7. O-O Bc5 8. Nc3 O-O 9. Nxb5 a4 10. Bd1 Nbxd5 11. Qh3 c6 12. Nc3 Nxc3 13. bxc3 Re8 14. Nc2 h6 15. Qg3 Kh8 16. Re1 Qa5 17. Bd2 Bf8 18. Rc1 a3 19. Re2 Rb2 20. d4 c5 21. dxe5 Ne4 22. Qf4 Nxd2 23. Qxf7 Rbb8 24. Rxd2 Qxc3 25. Qf4 Be7 26. Rd7 Qb2 27. Ne1 Bc6 28. Ra7 Rf8 29. Qe3 Bxh4 30. g3 Rxf2 31. Rc2 Rxc2 32. Bxc2 Bg5 33. Qd3 Qd4+ 34. Qxd4 cxd4 35. Rc7 Be8 36. c5 Kg8 37. Bb3+ Kf8 38. Kf2 h5 39. Nd3 Bd8 40. Ra7 g5 41. e6 Be7 42. Rc7 h4 43. g4 h3 44. Bd5 h2 45. Kg3 Rb1 46. Kxh2 Rd1 47. Ne5 Re1 48. Nd7+ Bxd7 49. Rxd7 Re2+ 50. Kg3 Bxc5 51. Bc4 Re4 52. Rf7+ Ke8 53. Bb5+ Kd8 54. Rd7+ Kc8

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 469 / 514 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): brnqkbnr/pppppppp/8/8/8/8/PPPPPPPP/RNBBNKRQ w AGbh - 0 1

Mirror twin (the same position mirrored): White 682 vs Black 535.