White 74 vs Black 835

The two setups

White: setup #74 N N R K B B Q R

King on the d-file, rooks on c, h, queen on the g-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 74 gives White +0.25 (Morozov Balance Index, 400M nodes).

Black: setup #835 B R K N R Q N B

King on the c-file, rooks on b, e, queen on the f-file; one bishop starts in a corner; the knights start on central files. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 835 gives White +0.25 (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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.

For comparison, in symmetric play setup 74 gives White +0.25 and setup 835 gives White +0.25: 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 Nc3, and 3 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the evaluation stayed within ±26 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 1, drawn 9, Black won 0 (White scored 55.0%).

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 +62. 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: -14

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 +52, Black +114, difference -62. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 6 White wins, 153 draws, 1 Black wins, White scored 51.6%.

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| 26 cp, mean 5.4 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 51.2 moves.

1. O-O-O e5 2. Nc3 g6 3. f3 b6 4. e4 Ne6 5. Nb3 O-O-O 6. Bc4 f5 7. Qf1 Kb8 8. Kb1 Nf4 9. Bh4 Ne7 10. g3 Ne6 11. Bxe6 dxe6 12. Qc4 Bf6 13. Bxf6 Qxf6 14. a4 a5 15. Nb5 Nc6 16. d3 Qe7 17. Nd2 Bb7 18. Rde1 Nd4 19. h4 Qd7 20. Na3 Rf8 21. Rh2 Qe7 22. Nb5 Qd7 23. Na3 Qe7 24. Nb5 Qd7

1. e4 f5 2. e5 Nc6 3. f4 g5 4. d4 gxf4 5. O-O-O e6 6. g3 f3 7. Nd2 d6 8. Nxf3 dxe5 9. dxe5 O-O-O 10. Bd2 Nge7 11. Qe3 b6 12. Bb5 Ng6 13. Bc3 Rxd1+ 14. Rxd1 Rd8 15. Rxd8+ Nxd8 16. Nb3 f4 17. Ba6+ Kb8 18. gxf4 Qxf4 19. Qxf4 Nxf4 20. Nbd2 Nf7 21. b3 c5 22. Kd1 Kc7 23. a4 h6 24. Be2 Nd5 25. Bb2 Ne3+ 26. Kc1 Bc6 27. Kb1 Kd7 28. h4 Bg7 29. Kc1 Bd5 30. Kb1 Bc6 31. Kc1 Kc7 32. a5 bxa5 33. Bc3 Kb6 34. Bd3 Nd8 35. Kb1 a4 36. b4 Nd1 37. bxc5+ Kxc5 38. Bd4+ Kb4 39. Ne1 Nc3+ 40. Kb2 a3+ 41. Ka1 Nb7 42. Nb1 Nxb1 43. Kxb1 Bf8 44. c3+ Ka4 45. Bc2+ Ka5 46. Bxa7 Bd5 47. Nd3 Be4 48. Nb4 Bxc2+ 49. Nxc2 h5 50. Ka2 Be7 51. Nd4 Ka6 52. Bb8 Nd8 53. Ne2 Bxh4 54. Nf4 Kb5 55. Nxh5 Kc4 56. Kxa3 Kxc3 57. Bc7 Kd4 58. Ng7 Kd5 59. Nh5 Be7+ 60. Ka4 Ke4 61. Ng3+ Kd4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 74 / 835 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): brknrqnb/pppppppp/8/8/8/8/PPPPPPPP/NNRKBBQR w CHbe - 0 1

Mirror twin: White 885 vs Black 115 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 22.