White 7 vs Black 850

The two setups

White: setup #7 Q N B N R K R B

King on the f-file, rooks on e, g, queen on the a-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 7 gives White +0.24 (Morozov Balance Index, 400M nodes).

Black: setup #850 B R K N R B N Q

King on the c-file, rooks on b, e, queen on the h-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 850 gives White +0.32 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±3 centipawns of equality, reaching search depth 53.

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 ±10 cp.

For comparison, in symmetric play setup 7 gives White +0.24 and setup 850 gives White +0.32: 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 e4, and 2 first moves are within 10 cp of it.

Along the engine's main line (27 moves) the evaluation stayed within ±17 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: +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 +32, Black +94, difference -62. 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

27 moves, 5 000 000 nodes per half-move. Largest |evaluation| 17 cp, mean 2.8 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 37.0 moves.

1. d4 g6 2. b3 Bg7 3. Bb2 f5 4. g3 b6 5. Bxa8 Rxa8 6. c4 e5 7. dxe5 Bxe5 8. Bxe5 Qxe5 9. Qxe5 Rxe5 10. Nd2 c6 11. e4 fxe4 12. Nxe4 Kc7 13. Kg2 Nf7 14. Re3 Nfh6 15. f4 Ree8 16. Rge1 Nf5 17. R3e2 Nd4 18. Rd2 Nf5 19. Ree2 Re7 20. h3 h6 21. Ndf2 Rae8 22. g4 Ng7 23. Ng3 a5 24. Rxe7 Nxe7 25. Re2 Ne6 26. Nd3 Rf8 27. Re4 a4 28. bxa4 Nc8 29. f5 gxf5 30. Nxf5 Nd6 31. Nxd6 Kxd6 32. Kg3 Ra8 33. h4 Ra5 34. Nb2 Ke7 35. Re3 Kf7 36. h5 Nc5 37. Re5 Ra8 38. Kh4 Kf6 39. Re3 d5 40. cxd5 cxd5 41. g5+ hxg5+ 42. Kg4 Rh8 43. Ra3 Rg8 44. a5 bxa5 45. Rxa5

1. d4 f5 2. Nd2 g6 3. b3 b5 4. g3 Bxh1 5. Rxh1 Qf6 6. e4 Bh6 7. Qc3 Bxd2 8. Bxd2 fxe4 9. Rxe4 Qf5 10. Rf4 Qh3+ 11. Kg1 Ne6 12. Rh4 Qf5 13. Ne3 Qf7 14. Nd5 Rf8 15. Rf4 Nf6 16. Rf3 Nxd5 17. Rxf7 Nxc3 18. Rxf8+ Nxf8 19. Bxc3 Rb6 20. d5 d6 21. Kg2 b4 22. Bd2 Nd7 23. Re1 Nf6 24. Rxe7 Ra6 25. Bxb4 Nxd5 26. Re8+ Kd7 27. Rb8 Rxa2 28. c4 Ne3+ 29. Kf3 Nd1 30. Be1 Nb2 31. Ke3 Nd1+ 32. Kf3 Nb2 33. Ke3 a5 34. Kd4 a4 35. bxa4 Nxa4 36. Ra8 Ra1 37. Bd2 c5+ 38. Ke3 Ra3+ 39. Kf4 Rd3 40. Rxa4 Rxd2 41. Ra7+ Kc6 42. Ke3 Rd4 43. Rxh7 Rxc4 44. Rg7 Rc3+ 45. Ke2 Rc2+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 7 / 850 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): brknrbnq/pppppppp/8/8/8/8/PPPPPPPP/QNBNRKRB w EGbe - 0 1

Mirror twin: White 946 vs Black 103 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 91.