White 275 vs Black 403

The two setups

White: setup #275 B N R K N R Q B

King on the d-file, rooks on c, f, queen on the g-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 275 gives White +0.19 (Morozov Balance Index, 400M nodes).

Black: setup #403 B R Q N N K R B

King on the f-file, rooks on b, g, queen on the c-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 403 gives White +0.16 (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 -3 and +16 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 275 gives White +0.19 and setup 403 gives White +0.16: 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 b3, and 3 first moves are within 10 cp of it.

Along the engine's main line (20 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 +50. 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: 0
• Lc0 0.32.1: -2

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 +160, Black +143, difference +17. 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

20 moves, 5 000 000 nodes per half-move. Largest |evaluation| 24 cp, mean 7.0 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 38.9 moves.

1. g4 g6 2. c4 b6 3. Bxa8 Rxa8 4. Nc3 Qa6 5. d3 c6 6. Qg2 Rc8 7. b4 b5 8. cxb5 cxb5 9. f4 g5 10. f5 Be5 11. e3 Nc6 12. Nc2 Nf6 13. a3 Bxc3 14. Bxc3 d6 15. Kd2 Kg7 16. h4 h6 17. hxg5 hxg5 18. Rh1 Ne5 19. Bb2 Qb6 20. Nd4 Rxc1 21. Bxc1 Nexg4 22. Bb2 Kf8 23. Rc1 Kg7 24. Rg1 Rh8 25. Qf3 Rh4 26. Ne2 Kh6 27. Bxf6 Nxf6 28. Qa8 Nh7 29. Qe8 d5 30. Rc1 Kg7 31. Rc6 Nf6 32. Qa8 Rh8 33. Rxb6 Rxa8 34. Rxb5 g4 35. Ra5 Kh6 36. Rc5 Rd8 37. Rc7 Rd7 38. Rc8 Kg5 39. Nd4 g3 40. Ke2 g2 41. Nf3+ Kxf5 42. Nh4+ Ke6 43. Nxg2 Rd6 44. Ne1 Kd7 45. Rf8 Ra6 46. Nc2 Rc6 47. Kd2 Rc8 48. Rxc8 Kxc8 49. Nd4 Kc7 50. Nf5 Ng8 51. a4 e6 52. Nd4 Nh6 53. Nf3 Kd6 54. Nd4 Kc7

1. b3 b5 2. f4 d6 3. f5 g5 4. Bxh8 Rxh8 5. g3 Bxh1 6. Qxh1 Nf6 7. h4 gxh4 8. Qxh4 Rg8 9. Nc3 h5 10. e4 Qb7 11. Ng2 b4 12. Nd5 Nxd5 13. exd5 Qxd5 14. Ne3 Qe5 15. Rf4 Qf6 16. Qxf6 exf6 17. Ke2 Rxg3 18. Rh1 Rg5 19. Rfh4 c6 20. Rxh5 Rxh5 21. Rxh5 d5 22. Rh4 Rb5 23. c3 bxc3 24. dxc3 Ra5 25. a4 Nb7 26. Nc2 Nd6 27. Nb4 Rc5 28. Kd3 Ne4 29. Na2 Ke7 30. Rh8 Nf2+ 31. Ke2 Ne4 32. Kd3 Nf2+ 33. Ke2 Ng4 34. Kf3 Ne5+ 35. Ke3 Ng4+ 36. Kf4 Ne5 37. Ra8 Ra5 38. Nb4 Kd6 39. Ke3 Nd7 40. Rd8 Kc7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 275 / 403 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): brqnnkrb/pppppppp/8/8/8/8/PPPPPPPP/BNRKNRQB w CFbg - 0 1

Mirror twin: White 579 vs Black 739 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 52.