White 9 vs Black 850

The two setups

White: setup #9 Q N N B B R K R

King on the g-file, rooks on f, h, queen on the a-file; no 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 9 gives White +0.22 (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 is exactly 0.00 each time, reaching search depth 59.

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 -4 and +39 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 9 gives White +0.22 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.

The engine's first choice for White is d4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (30 moves) the evaluation stayed within ±9 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 4 000 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: -6
• Lc0 0.32.1: -1

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 +16, Black +94, difference -78. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.

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| 9 cp, mean 1.1 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 45.0 moves.

1. d4 g6 2. Bc3 Bg7 3. e3 b6 4. h4 Nf6 5. Nd3 h5 6. Nd2 Ne6 7. Bf3 O-O 8. Rh3 Bxf3 9. Nxf3 c5 10. Qd1 Rfc8 11. Nde5 d6 12. d5 Nd8 13. Nc4 b5 14. Na5 Ng4 15. Bxg7 Qxg7 16. Nh2 Nf6 17. Re1 c4 18. e4 Rc5 19. b4 cxb3 20. axb3 Rbc8 21. Rhe3 Qf8 22. R1e2 b4 23. Nc4 Nb7 24. Rd3 Na5 25. Nb2 Qg7 26. Na4 R5c7 27. f4 Nd7 28. Nf3 Nf6 29. Nd4 Ng4 30. Qe1 Nxb3 31. Nxb3 Rxc2 32. Rdd2 Rxd2 33. Qxd2 Qf6 34. g3 e5 35. dxe6 Qxe6 36. Qxb4 Nf6 37. Qb5 Nxe4 38. Nd2 Rc1+ 39. Kg2 Rc2 40. Nf3 Rxe2+ 41. Qxe2 a5 42. Qc2 Qf5 43. Qe2 Qe6 44. Nb6 d5 45. Qe3 Qc6 46. Qb3 Nf6 47. f5 gxf5 48. Nd4 Qc5 49. Qb2 Qe7

1. d4 g6 2. b4 Bg7 3. e3 e5 4. d5 e4 5. Bc3 Bxc3 6. Qxc3 Qe5 7. Qxe5 Rxe5 8. f4 Rxd5 9. Nc3 Rd6 10. Nxe4 Rb6 11. Nd3 Ra6 12. f5 b6 13. Ng5 Rxa2 14. Nxf7 Nxf7 15. fxg6 hxg6 16. Rxf7 O-O-O 17. h4 Nh6 18. Rf4 Nf5 19. Rh3 Ra1 20. Nf2 Ne7 21. Kh2 Rb1 22. Be2 Nd5 23. Rg4 Nxb4 24. Rxg6 Re1 25. Bb5 a6 26. Bc4 b5 27. Bf7 Re2 28. Kg1 Rxc2 29. e4 Rc1+ 30. Kh2 Rc2 31. Kg1 Nc6 32. h5 Rc1+ 33. Kh2 Rf1 34. Kg3 Ne5 35. Rxa6 Bb7 36. Rf6 Nxf7 37. Rxf7 Bxe4 38. h6 Rh8 39. h7 b4 40. Rg7 Bxh7 41. Rhxh7 Rxh7 42. Rxh7 b3 43. Rh8+ Kb7 44. Nd3 d6 45. Rh4 c5 46. Rc4 Rd1 47. Nxc5+ dxc5 48. Rxc5

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 9 / 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/QNNBBRKR w FHbe - 0 1

Mirror twin: White 953 vs Black 103 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 101.