White 56 vs Black 37
White starts from setup 56 (NBNRBQKR), Black from setup 37 (NNBBQRKR). In the encyclopedia since 2026-10-09: 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. 56, Black by position No. 37, 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 #56 N B N R B Q K R
King on the g-file, rooks on d, h, queen on the f-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 56 gives White +0.44 (Morozov Balance Index, 400M nodes).
Black: setup #37 N N B B Q R K R
King on the g-file, rooks on f, h, queen on the e-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 37 gives White +0.25 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±2 centipawns of equality, reaching search depth 55.
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 ±15 cp.
For comparison, in symmetric play setup 56 gives White +0.44 and setup 37 gives White +0.25: 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 (30 moves) the evaluation stayed within ±13 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 | 14 | +15 | 1. d4 d5 2. f3 h5 3. Qf2 e5 4. O-O exd4 |
| S1 | 500 000 | 18 | +2 | 1. d4 d5 2. c3 h5 3. e4 dxe4 4. Bxe4 e5 |
| S2 | 2 000 000 | 25 | -12 | 1. d4 d5 2. e3 Nb6 3. Qe2 e5 4. dxe5 Qxe5 |
| S3 | 8 000 000 | 29 | +1 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 |
| S4 | 32 000 000 | 38 | +6 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 |
| S5 | 128 000 000 | 44 | +5 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 |
| S6 | 400 000 000 | 49 | +2 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 |
| S7 | 800 000 000 | 51 | 0 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 |
| S8 | 1 600 000 000 | 55 | 0 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 |
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: +8
- Lc0 0.32.1: +3
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 +104, Black +65, difference +39. 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 | +6 | 43 | 1. d4 d5 2. c3 Nb6 3. e4 dxe4 4. Bxe4 e5 5. Qe2 exd4 |
| 2 | 0 | 43 | 1. e4 e5 2. d4 exd4 3. Ne2 d6 4. Nxd4 Qxe4 5. c4 Qe5 |
| 3 | -11 | 43 | 1. Nab3 e5 2. e4 d6 3. Qe2 Nc6 4. c4 Nd4 5. Nxd4 exd4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 13 cp, mean 3.0 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | 0 | d5 | +3 |
| 2 | c3 | +9 | Nb6 | 0 |
| 3 | e4 | +1 | dxe4 | +5 |
| 4 | Bxe4 | +2 | e5 | +10 |
| 5 | Qe2 | +9 | exd4 | +11 |
| 6 | cxd4 | +10 | Qe7 | +10 |
| 7 | Nc2 | +10 | Re8 | +13 |
| 8 | Bf3 | +4 | Qxe2 | +4 |
| 9 | Nxe2 | +8 | N8d7 | +5 |
| 10 | Ne3 | +3 | c6 | +6 |
| 11 | Nc3 | +11 | Nf6 | +3 |
| 12 | h3 | 0 | Be6 | 0 |
| 13 | O-O | 0 | h5 | 0 |
| 14 | d5 | 0 | Nbxd5 | 0 |
| 15 | Ncxd5 | +7 | cxd5 | 0 |
| 16 | Bc3 | +5 | Ne4 | -5 |
| 17 | Nxd5 | 0 | Nxc3 | 0 |
| 18 | Nxc3 | 0 | Ba5 | 0 |
| 19 | Nb5 | -2 | Bxa2 | -3 |
| 20 | Ra1 | +7 | Re5 | -4 |
| 21 | Nxa7 | 0 | Bc4 | 0 |
| 22 | Rfb1 | 0 | Kh7 | 0 |
| 23 | Bxb7 | 0 | Bb6 | 0 |
| 24 | Nc8 | 0 | Bc5 | 0 |
| 25 | b4 | 0 | Bd4 | 0 |
| 26 | Ra5 | 0 | Rd8 | 0 |
| 27 | Rc1 | -5 | Bb3 | -5 |
| 28 | Rxe5 | -3 | Bxe5 | 0 |
| 29 | b5 | 0 | g6 | 0 |
| 30 | Bf3 | 0 | Bf4 | 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 38.5 moves.
Sample game 1 (1/2-1/2)
1. d4 d5 2. e3 e5 3. dxe5 Nb6 4. Nab3 Nc6 5. Nd3 Nxe5 6. Qe2 f5 7. Bb4 Be7 8. c3 Nxd3 9. Bxd3 Bxb4 10. cxb4 f4 11. exf4 Qxe2 12. Bxe2 Rxf4 13. Nd4 O-O 14. f3 c6 15. g3 R4f7 16. h4 Re8 17. Kf2 g6 18. Rhe1 Nd7 19. Bf1 Ne5 20. Kg2 Kf8 21. g4 h6 22. g5 hxg5 23. hxg5 Rfe7 24. Kg3 Kg7 25. Bd3 Bd7 26. Bc2 Nf7 27. Rxe7 Rxe7 28. f4 Nd6 29. Kf3 a6 30. a3 b6 31. Rc1 Nc4 32. Kf2 Nxb2 33. Nf3 Nc4 34. Bd3 Nb2 35. Bb1 Nc4 36. Bd3 Nb2 37. Bb1 Nc4
Sample game 2 (1/2-1/2)
1. d4 d5 2. e3 e5 3. dxe5 Nb6 4. Nab3 Nc6 5. Nd3 Nxe5 6. Qe2 f5 7. Bb4 Be7 8. c3 Nxd3 9. Bxd3 Bxb4 10. cxb4 f4 11. exf4 Qxe2 12. Bxe2 Rxf4 13. Nd4 O-O 14. f3 c6 15. g3 R4f7 16. h4 Re8 17. Kf2 g6 18. Rhe1 Nd7 19. Bf1 Ne5 20. Kg2 Kf8 21. g4 h6 22. g5 hxg5 23. hxg5 Rfe7 24. Kg3 Kg7 25. Bd3 Bd7 26. Bc2 Nf7 27. Rxe7 Rxe7 28. f4 Nd6 29. Kf3 a6 30. a3 b6 31. Rc1 Nc4 32. Kf2 Nxb2 33. Nf3 Nc4 34. Bd3 Nb2 35. Bb1 Nc4 36. Bd3 Nb2 37. Bb1 Nc4
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 56 / 37 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): nnbbqrkr/pppppppp/8/8/8/8/PPPPPPPP/NBNRBQKR w DHfh - 0 1
Mirror twin: White 909 vs Black 922 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 234.