White 76 vs Black 692

The two setups

White: setup #76 N B N R K Q B R

King on the e-file, rooks on d, h, queen on the f-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 76 gives White +0.29 (Morozov Balance Index, 400M nodes).

Black: setup #692 R B B Q K N N R

King on the e-file, rooks on a, h, queen on the d-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 692 gives White +0.15 (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 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 -20 and +7 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 76 gives White +0.29 and setup 692 gives White +0.15: 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 e4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (24 moves) the evaluation stayed within ±18 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: 0
• Lc0 0.32.1: 0

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 +39, Black +53, difference -14. 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

24 moves, 5 000 000 nodes per half-move. Largest |evaluation| 18 cp, mean 1.9 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 43.6 moves.

1. c3 d5 2. d4 c6 3. f3 Nf6 4. e4 dxe4 5. fxe4 e5 6. dxe5 N6d7 7. Nab3 Qh4+ 8. g3 Qh5 9. Qf5 Qh6 10. Bd4 Bc7 11. Qf4 Qe6 12. Nd3 Ng6 13. Qf2 Ndxe5 14. Nf4 Qf6 15. h3 O-O 16. Nd2 b6 17. Nc4 Qg5 18. Nxe5 Nxe5 19. O-O-O Ba6 20. Bc2 Rad8 21. Kb1 Rfe8 22. b3 Qe7 23. Rhe1 h6 24. Rd2 Rd7 25. Red1 Red8 26. Kb2 Bc8 27. a4 Bb7 28. Ka2 c5 29. Be3 Rxd2 30. Rxd2 Rxd2 31. Qxd2 Nf3 32. Qe2 Ng5 33. Nd5 Bxd5 34. exd5 g6 35. Qd3 Nxh3 36. Bxh6 Qe5 37. b4 cxb4 38. cxb4 Qxg3 39. Qxg3 Bxg3 40. Kb3 Bf4 41. Bxf4 Nxf4 42. Kc4 Kf8 43. d6 Ke8 44. Kb5 Kd7 45. Ka6 Kxd6 46. Kxa7 Kc7 47. Bb3 Nd3 48. Bxf7 g5 49. a5 bxa5 50. bxa5 Nf4 51. Ka6 g4 52. Bc4 g3 53. Bf1 Kc6

1. d4 d5 2. c3 Ng6 3. f3 c6 4. Nd3 Nf6 5. g4 e5 6. h4 e4 7. h5 Nf4 8. Ne5 Nd7 9. Nxd7 Bxd7 10. Be3 exf3 11. Qxf3 Ne6 12. Bf5 O-O 13. O-O-O f6 14. Nb3 Qe7 15. Bc2 Bc7 16. Bd2 Rae8 17. Qd3 f5 18. Rdf1 Ng5 19. gxf5 Ne4 20. f6 Rxf6 21. Rxf6 Qxf6 22. Nc5 Bg4 23. Nxe4 dxe4 24. Qc4+ Be6 25. Qc5 Bd5 26. Bb3 Bxb3 27. axb3 h6 28. Be3 Bb6 29. Qc4+ Kh7 30. b4 Qf5 31. Kd2 Re7 32. Qb3 Bd8 33. Qd1 Rf7 34. Qg1 b6 35. Qg3 Bg5 36. Bxg5 hxg5 37. Rg1 Kh6 38. Kc2 Rf6 39. Qb8 Kh7 40. Qg3 Kh6 41. Qb8 Kh7 42. Qg3

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 76 / 692 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): rbbqknnr/pppppppp/8/8/8/8/PPPPPPPP/NBNRKQBR w DHah - 0 1

Mirror twin: White 892 vs Black 462 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 335.