White 123 vs Black 131

The two setups

White: setup #123 N Q R N B K R B

King on the f-file, rooks on c, g, 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 123 gives White +0.25 (Morozov Balance Index, 400M nodes).

Black: setup #131 B N R Q N K R B

King on the f-file, rooks on c, g, 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 131 gives White 0.00 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±2 centipawns of equality, 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 wandered between -16 and +3 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 123 gives White +0.25 and setup 131 gives White 0.00: 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 ±13 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 4 000 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: +8
• Lc0 0.32.1: +13

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 +43, Black +77, difference -34. 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| 13 cp, mean 1.6 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 39.6 moves.

1. b4 O-O 2. g3 g6 3. c4 Nc6 4. d3 e5 5. Bc3 d6 6. Nb3 Nd4 7. e3 Nxb3 8. Qxb3 b6 9. Bxa8 Rxa8 10. O-O Qd7 11. e4 Ng7 12. Ne3 Ne6 13. Rce1 Rae8 14. f4 exf4 15. Bxh8 Kxh8 16. Qc3+ f6 17. gxf4 Qg7 18. b5 a6 19. Kh1 axb5 20. f5 gxf5 21. Rxf5 b4 22. Qxb4 Rg8 23. Qb2 Nc5 24. Qe2 Re5 25. Qf1 Nd7 26. Qe2 Rxf5 27. Nxf5 Qg5 28. d4 Nf8 29. Qf2 Ne6 30. Rg1 Qh5 31. h4 Rxg1+ 32. Kxg1 Qd1+ 33. Kh2 Qg4 34. Qg2 Qf4+ 35. Kh1 Qc1+ 36. Kh2 Qf4+ 37. Kh3 c5 38. dxc5 Qe5 39. Qf3 Nf4+ 40. Kg3 Nd3+

1. b4 O-O 2. g3 e5 3. c4 Nc6 4. d3 g6 5. Bc3 d6 6. Nb3 b6 7. Qb2 Qd7 8. O-O Bg7 9. Ne3 Bh6 10. Rce1 Ne7 11. Bxa8 Rxa8 12. Ng2 Ng7 13. d4 exd4 14. Nxd4 c5 15. Nc2 d5 16. bxc5 bxc5 17. cxd5 Nxd5 18. Rd1 Rab8 19. Qa3 Qc6 20. Bd2 Bxd2 21. Rxd2 Ne6 22. Rfd1 Rfd8 23. f3 Rd7 24. Kf2 Rbd8 25. Nge3 Nxe3 26. Qxe3 Rxd2 27. Rxd2 Rxd2 28. Qxd2 h5 29. Qa5 a6 30. Ne3 h4 31. Qc3 hxg3+ 32. hxg3 Nd4 33. Qc4 Kf8 34. Qd5 Qxd5 35. Nxd5 Ke8 36. e4 Kd7 37. Ke3 Kc6 38. f4 Kb5 39. Nc7+ Kb6 40. Ne8 Kc6 41. Kd3 f5 42. e5 Ne6 43. Nd6 g5 44. fxg5 Nxg5 45. Nxf5 Kd5 46. Ne3+ Kxe5 47. Kc4 Ne4 48. g4 Kf4 49. Nd5+ Kxg4 50. Nc7 a5 51. Na6 Kf5 52. Nxc5 Nxc5 53. Kxc5 Ke4 54. Kb5 Kd5 55. Kxa5 Kc5 56. a3 Kc4 57. Ka4 Kc5 58. Ka5

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 123 / 131 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): bnrqnkrb/pppppppp/8/8/8/8/PPPPPPPP/NQRNBKRB w CGcg - 0 1

Mirror twin: White 833 vs Black 819 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 490.