White 140 vs Black 488

The two setups

White: setup #140 N B R Q N K B R

King on the f-file, rooks on c, h, queen on the d-file; no 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 140 gives White +0.12 (Morozov Balance Index, 400M nodes).

Black: setup #488 Q B R N B K N 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 488 gives White +0.38 (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 59.

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 ±15 cp.

For comparison, in symmetric play setup 140 gives White +0.12 and setup 488 gives White +0.38: 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 (30 moves) the evaluation stayed within ±25 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.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: +10

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 +47, Black +65, difference -18. 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| 25 cp, mean 9.3 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 42.2 moves.

1. c4 c5 2. f3 b6 3. d4 cxd4 4. Bxd4 h5 5. Nb3 Nc6 6. Bc3 Nf6 7. Nd3 d6 8. O-O Ne5 9. Nd2 Qb7 10. e3 a6 11. Re1 b5 12. cxb5 Nxd3 13. Bxd3 axb5 14. Ne4 Nd5 15. Qb3 Nxc3 16. Nxc3 Ba7 17. Bxb5 Bc5 18. Ba4 Qxb3 19. Bxb3 e6 20. Kf2 Ra8 21. Ne4 Bb4 22. Red1 d5 23. Nc5 Ra5 24. Nd3 Bd6 25. h4 O-O 26. f4 Bb5 27. Rd2 Rb8 28. Ne5 Bb4 29. Rd4 Bd6 30. Rd2 Bb4 31. Rdc2 Raa8 32. g3 Be7 33. Rd2 Bb4 34. Rd4 Bd6 35. Rd2 Bb4 36. Rd4 Bd6 37. Rc2 Rb6 38. e4 Bxe5 39. fxe5 Bc4 40. Bxc4 dxc4 41. a3 c3 42. bxc3 Rxa3 43. Ke3 Kh7 44. Rc1 Rb5 45. Rd7 Kg6 46. Kd4 f6 47. exf6 gxf6 48. Rd6 Kf7 49. Rd7+ Kg6 50. Rc7 Ra4+ 51. Kd3 Rb6 52. Rc4 Ra5 53. Rc8 Rd6+ 54. Kc4 Rda6 55. Re1 Ra4+ 56. Kc5 Kf7 57. Rc7+ Kg6 58. Re3 R4a5+ 59. Kd4 Rd6+ 60. Kc4 Rb6 61. Rc8 Rba6 62. Re1 Ra4+ 63. Kc5 Kf7 64. Rc7+ Kg6

1. c4 Nf6 2. d4 c5 3. dxc5 Rxc5 4. f3 Rc8 5. Nd3 h5 6. Nb3 h4 7. Bf2 Ne6 8. Qe1 h3 9. g3 d6 10. O-O a6 11. Nd4 Nxd4 12. Bxd4 b5 13. cxb5 Rxc1 14. Qxc1 axb5 15. Qc8 Qa4 16. e3 Ba7 17. b3 Qa3 18. Qa8 Bc5 19. Qxa3 Bxa3 20. e4 Nd7 21. Be3 Nb8 22. Bc1 Bxc1 23. Rxc1 Nc6 24. Ne1 Bd7 25. Bd3 b4 26. Rc2 Rh5 27. g4 Ra5 28. Kf2 Nd4 29. Rd2 e5 30. Kg3 Be6 31. Kxh3 g5 32. Kg3 Rc5 33. Be2 Rc3 34. Kf2 Bc8 35. Ng2 Ke7 36. h4 gxh4 37. Nxh4 Kf6 38. Ng2 Be6 39. Bd1 Bc8 40. Nf4 Bb7 41. Nd3 Nc6 42. Nb2 Nd4 43. Nd3 Nc6 44. Ne1 Nd4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 140 / 488 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): qbrnbknr/pppppppp/8/8/8/8/PPPPPPPP/NBRQNKBR w CHch - 0 1

Mirror twin: White 828 vs Black 573 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 30.