White 40 vs Black 903
White starts from setup 40 (NBNQBRKR), Black from setup 903 (RKBQRNNB). In the encyclopedia since 2026-11-01: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
How to play with different setups
White sets up the pieces by position No. 40, Black by position No. 903, mirrored on their own side; the pawns stand as usual.
Moves as usual: White starts; everything else follows the Chess960 rules.
The two setups
White: setup #40 N B N Q B R K R
King on the g-file, rooks on f, h, queen on the d-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 40 gives White +0.34 (Morozov Balance Index, 400M nodes).
Black: setup #903 R K B Q R N N B
King on the b-file, rooks on a, e, queen on the d-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 903 gives White +0.40 (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 57.
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 +4 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 40 gives White +0.34 and setup 903 gives White +0.40: 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 d4, and 2 first moves are within 10 cp of it.
Along the engine's main line (14 moves) the evaluation stayed within ±21 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.
| Stage | Nodes | Depth | Eval, cp | Main line |
|---|---|---|---|---|
| S0 | 100 000 | 15 | +2 | 1. d4 e5 2. d5 e4 3. f3 exf3 4. Rxf3 |
| S1 | 500 000 | 21 | -4 | 1. d4 g6 2. e4 f5 3. c4 fxe4 4. Bxe4 Nf6 |
| S2 | 2 000 000 | 21 | -6 | 1. d4 g6 2. c4 e5 3. d5 e4 4. Nab3 a5 |
| S3 | 8 000 000 | 26 | +4 | 1. d4 e5 2. d5 e4 3. f3 f5 4. c4 g6 |
| S4 | 32 000 000 | 34 | -20 | 1. d4 d5 2. Nab3 g6 3. f4 Nd7 4. c3 a5 |
| S5 | 128 000 000 | 38 | -12 | 1. d4 d5 2. c3 g6 3. f4 a5 4. Nd3 Nf6 |
| S6 | 400 000 000 | 52 | 0 | 1. d4 d5 2. c3 g6 3. f4 a5 4. Nd3 Nf6 |
| S7 | 800 000 000 | 55 | 0 | 1. d4 d5 2. c3 g6 3. f4 a5 4. Nd3 Nf6 |
| S8 | 1 600 000 000 | 57 | 0 | 1. d4 d5 2. c3 g6 3. f4 a5 4. Nd3 Nf6 |
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.
| Nodes | Eval, cp |
|---|---|
| 4 000 000 000 | 0 |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
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: +12
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 +103, difference -51. 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.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | -9 | 41 | 1. d4 d5 2. c3 a5 3. f4 f6 4. Bg3 g6 5. e4 dxe4 |
| 2 | -13 | 41 | 1. c3 d6 2. d4 f5 3. e4 g6 4. f3 Nf6 5. Bh4 fxe4 |
| 3 | -30 | 41 | 1. f3 g6 2. d4 d5 3. Bf2 e5 4. dxe5 Bxe5 5. c3 f5 |
Main-line play-out
14 moves, 5 000 000 nodes per half-move. Largest |evaluation| 21 cp, mean 6.1 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +4 | d5 | -2 |
| 2 | c3 | -11 | g6 | -12 |
| 3 | f4 | -21 | a5 | -16 |
| 4 | Nd3 | 0 | Nd7 | 0 |
| 5 | Nc2 | +8 | e6 | +14 |
| 6 | Ne3 | +14 | Ne7 | -1 |
| 7 | h4 | +14 | Nf6 | +14 |
| 8 | Ne5 | +17 | Rf8 | +15 |
| 9 | Bd3 | -6 | Nf5 | -9 |
| 10 | Rh3 | 0 | Ne4 | 0 |
| 11 | Qb3 | 0 | Qe8 | 0 |
| 12 | Bb5 | 0 | Qd8 | 0 |
| 13 | Bd3 | 0 | Qe8 | 0 |
| 14 | Bb5 | 0 | Qe7 | 0 |
| 15 | Bd3 | 0 |
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 38.8 moves.
Sample game 1 (1/2-1/2)
1. c3 a5 2. e4 g5 3. h4 d5 4. hxg5 dxe4 5. Bxe4 e5 6. f3 Ne7 7. Bf2 Ne6 8. Be3 Ng6 9. Qa4 Ngf4 10. Nd3 Rg8 11. Bxf4 exf4 12. Bxh7 Bd7 13. Qc4 Rxg5 14. O-O-O Bb5 15. Qe4 Bc6 16. Qc4 Bb5 17. Qe4 Bc6 18. Qc4
Sample game 2 (1/2-1/2)
1. f3 e5 2. c3 d6 3. e4 g6 4. Bf2 f5 5. Re1 Nf6 6. O-O fxe4 7. Bxe4 Nxe4 8. fxe4 Ne6 9. Nc2 a5 10. Ne3 Nf4 11. c4 Be6 12. Nd5 h5 13. d3 Qg5 14. Qf3 c6 15. h4 Qh6 16. Nb6 Ra6 17. c5 g5 18. Be3 Bg4 19. Qf2 dxc5 20. Bxc5 gxh4 21. Kh1 Qg6 22. Nc4 b5 23. Nd6 Rd8 24. Nf5 h3 25. g3 Ng2 26. Bb6 Rc8 27. Re2 Bf6 28. Nd6 Bxe2 29. Nxe2 Rf8 30. Ba7+ Ka8 31. Bb6 Kb8 32. Ba7+ Ka8 33. Bb6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 40 / 903 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): rkbqrnnb/pppppppp/8/8/8/8/PPPPPPPP/NBNQBRKR w FHae - 0 1
Mirror twin: White 925 vs Black 50 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 191.