White 40 vs Black 289
White starts from setup 40 (NBNQBRKR), Black from setup 289 (BQNBRKRN). In the encyclopedia since 2026-10-10: 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. 289, 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 #289 B Q N B R K R N
King on the f-file, rooks on e, g, queen on the b-file; one 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 289 gives White +0.43 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±5 centipawns of equality, 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 -7 and +24 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 289 gives White +0.43: 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 Nab3, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 32 cp (around move 9), ending at 0 cp — the position stays playable for both sides.
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 | 12 | +24 | 1. c4 O-O 2. d4 b6 3. Nab3 f5 4. h4 e6 |
| S1 | 500 000 | 15 | -4 | 1. c4 O-O 2. Nab3 b6 3. h4 f5 4. d4 e6 |
| S2 | 2 000 000 | 23 | -2 | 1. c4 O-O 2. Nab3 b6 3. d4 f5 4. h4 e5 |
| S3 | 8 000 000 | 28 | +3 | 1. c4 O-O 2. d4 b6 3. Nab3 f5 4. h4 e5 |
| S4 | 32 000 000 | 34 | +13 | 1. c4 O-O 2. Nab3 f5 3. d4 b6 4. h4 e5 |
| S5 | 128 000 000 | 38 | -7 | 1. c4 O-O 2. d4 b6 3. Nab3 f5 4. h4 e6 |
| S6 | 400 000 000 | 46 | -5 | 1. c4 O-O 2. d4 b6 3. Nab3 e6 4. h4 f5 |
| S7 | 800 000 000 | 50 | 0 | 1. c4 O-O 2. d4 b6 3. h4 c5 4. Nab3 cxd4 |
| S8 | 1 600 000 000 | 58 | 0 | 1. c4 O-O 2. d4 b6 3. h4 c5 4. dxc5 bxc5 |
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: +16
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 +142, difference -90. 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 | -10 | 42 | 1. Nab3 O-O 2. c4 f5 3. d4 b6 4. h4 e6 5. f3 Ne7 |
| 2 | -11 | 42 | 1. c4 O-O 2. d4 b6 3. Nab3 f5 4. h4 e6 5. f3 Ne7 |
| 3 | -10 | 41 | 1. d4 O-O 2. c4 b6 3. Nab3 f5 4. h4 e6 5. f3 Ne7 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 32 cp, mean 4.6 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -1 | O-O | +7 |
| 2 | d4 | 0 | b6 | +13 |
| 3 | Nab3 | +16 | f5 | 0 |
| 4 | h4 | 0 | e5 | 0 |
| 5 | dxe5 | -4 | c5 | 0 |
| 6 | Bc3 | 0 | d6 | 0 |
| 7 | e6 | +8 | Rxe6 | +12 |
| 8 | Nd2 | +11 | Ne7 | +21 |
| 9 | e4 | +32 | b5 | +28 |
| 10 | b3 | +22 | fxe4 | +15 |
| 11 | h5 | +16 | Nf5 | +16 |
| 12 | Qg4 | +15 | Qb7 | +4 |
| 13 | f3 | 0 | Qe7 | 0 |
| 14 | fxe4 | 0 | Nh6 | 0 |
| 15 | Rxf8+ | 0 | Kxf8 | 0 |
| 16 | Qh3 | 0 | N8f7 | 0 |
| 17 | Ne2 | +1 | Ng5 | +1 |
| 18 | Qg3 | +2 | b4 | 0 |
| 19 | Bb2 | 0 | Nhf7 | +4 |
| 20 | Nf4 | +5 | Rh6 | +8 |
| 21 | Nf3 | +7 | Nxf3+ | 0 |
| 22 | gxf3 | 0 | Ne5 | 0 |
| 23 | Kg2 | 0 | Qe8 | 0 |
| 24 | a3 | 0 | bxa3 | 0 |
| 25 | Bxa3 | 0 | a5 | +1 |
| 26 | Bb2 | +4 | Bb7 | 0 |
| 27 | Bc2 | 0 | Qf7 | 0 |
| 28 | Bd3 | 0 | Rf6 | 0 |
| 29 | Bc1 | 0 | Bc6 | 0 |
| 30 | Be2 | 0 | Qb7 | 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 40.3 moves.
Sample game 1 (1/2-1/2)
1. Nab3 e6 2. f3 b6 3. d4 O-O 4. c4 f5 5. h4 c5 6. dxc5 bxc5 7. Qxd7 Nb6 8. Qd3 Nf7 9. Bf2 Ne5 10. Qc2 Nbxc4 11. Nd3 Be7 12. Nbxc5 Rc8 13. Qb3 Qxb3 14. Nxb3 Nxd3 15. Bxd3 Nxb2 16. Ba6 Rc6 17. Bb5 Rc7 18. Rb1 Nc4 19. Nd4 Bd5 20. Rc1 a6 21. Bxa6 Ra8 22. Bb5 Rxa2 23. e4 Ba3 24. Re1 e5 25. exd5 exd4 26. Bxd4 Rd2 27. Bf2 Rxd5 28. Ba4 Ra5 29. Bb3 Kf8 30. Re2 Rb5 31. Ba2 Rb2 32. Rxb2 Nxb2 33. Bg3 Rc1+ 34. Kh2 Rxh1+ 35. Kxh1 g6 36. Bf4 Nd3 37. Bh6+ Ke8 38. h5 Bf8 39. Bd2 Bb4 40. Bh6 Bf8
Sample game 2 (1/2-1/2)
1. h4 b5 2. Nab3 O-O 3. d4 f5 4. f3 Nb6 5. Bf2 e5 6. dxe5 Nf7 7. e6 dxe6 8. Nc5 Nd6 9. c3 e5 10. e4 fxe4 11. fxe4 Bc6 12. Rh3 Qa8 13. Rf3 Rxf3 14. Qxf3 Bf6 15. Qh5 Nbc4 16. Qe2 a5 17. b3 Nb6 18. Bc2 Nd7 19. N1d3 Nxe4 20. Nxe4 Bxe4 21. Qg4 Nf8 22. h5 Ne6 23. Re1 Nf4 24. Nxf4 Bxc2 25. Qe2 c6 26. h6 Bg6 27. Nxg6 hxg6 28. c4 Qb7 29. Rd1 gxh6 30. Rd6 Qf7 31. cxb5 cxb5 32. Qxb5 Bg5 33. Rd7 Qf5 34. Qb7 Qf6 35. Bc5 Bf4 36. Qd5+ Qe6 37. Qb7 Qf6 38. Qd5+ Qe6 39. Qb7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 40 / 289 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): bqnbrkrn/pppppppp/8/8/8/8/PPPPPPPP/NBNQBRKR w FHeg - 0 1
Mirror twin: White 925 vs Black 379 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 189.