White 41 vs Black 825

The two setups

White: setup #41 N N Q B B R K R

King on the g-file, rooks on f, h, queen on the c-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 41 gives White +0.12 (Morozov Balance Index, 400M nodes).

Black: setup #825 R K N B B Q R N

King on the b-file, rooks on a, g, 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 825 gives White +0.22 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±1 centipawns of equality, reaching search depth 56.

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 -25 and +4 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 41 gives White +0.12 and setup 825 gives White +0.22: 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 f4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (18 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: -8

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 +48, Black +52, difference -4. 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

18 moves, 5 000 000 nodes per half-move. Largest |evaluation| 18 cp, mean 3.7 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 37.9 moves.

1. f4 e6 2. c4 f5 3. h4 h6 4. d4 g5 5. fxg5 hxg5 6. h5 Nf7 7. Nc2 g4 8. Nc3 Bg5 9. Bd2 Qh6 10. Bf4 Ne7 11. e4 O-O-O 12. exf5 Nxf5 13. Ne4 Bxf4 14. Qxf4 Qg7 15. Ng3 Nxg3 16. Qxg3 Nh6 17. Qf4 Qg5 18. Ne3 Bxh5 19. g3 c6 20. c5 Rdf8 21. Qxg5 Rxf1+ 22. Nxf1 Rxg5 23. Nd2 Nf7 24. Ne4 Rd5 25. Nf6 Rxd4 26. Bc2 Bg6 27. Bxg6 Rd1+ 28. Kg2 Rd2+ 29. Kf1 Rd1+ 30. Kg2 Rd2+ 31. Kg1 Rd1+

1. f4 g5 2. f5 e6 3. e4 d5 4. exd5 exf5 5. c4 f4 6. Nb3 a5 7. Qc2 Ng6 8. h3 a4 9. Nd4 Bf6 10. Bf2 Bd7 11. Nc3 Qg7 12. Ncb5 Nd6 13. Bg4 Nxb5 14. Nxb5 Bxb5 15. cxb5 Bd4 16. d6 Bxf2+ 17. Rxf2 cxd6 18. Kh2 Qd4 19. Rc1 Qxf2 20. Qc7+ Ka7 21. Qa5+ Kb8 22. Qc7+ Ka7 23. Qa5+ Kb8 24. Qc7+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 41 / 825 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): rknbbqrn/pppppppp/8/8/8/8/PPPPPPPP/NNQBBRKR w FHag - 0 1

Mirror twin: White 921 vs Black 137 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 195.