White 61 vs Black 423
White starts from setup 61 (NNRBQKBR), Black from setup 423 (RNBQNKRB). 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. 61, Black by position No. 423, 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 #61 N N R B Q K B R
King on the f-file, rooks on c, h, queen on the e-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 61 gives White +0.49 (Morozov Balance Index, 400M nodes).
Black: setup #423 R N B Q N K R B
King on the f-file, rooks on a, g, 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 423 gives White +0.15 (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 50.
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 -17 and +30 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 61 gives White +0.49 and setup 423 gives White +0.15: 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 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 33 cp (around move 5), 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 | 14 | +30 | 1. c3 g6 2. f3 d5 3. Bf2 O-O 4. O-O b6 |
| S1 | 500 000 | 18 | +2 | 1. c3 g6 2. f3 O-O 3. Bf2 d5 4. O-O Bg7 |
| S2 | 2 000 000 | 22 | -17 | 1. c3 g6 2. f3 d5 3. Bf2 O-O 4. O-O e5 |
| S3 | 8 000 000 | 30 | -16 | 1. c4 c5 2. f3 g6 3. Nc3 b6 4. Ba4 O-O |
| S4 | 32 000 000 | 32 | -3 | 1. c4 c5 2. Nc3 b6 3. h3 g6 4. Bh2 Bb7 |
| S5 | 128 000 000 | 37 | +5 | 1. c4 c5 2. f3 g6 3. Nc3 d6 4. Be3 Bg7 |
| S6 | 400 000 000 | 42 | 0 | 1. c4 c5 2. Nc3 Nc6 3. Nc2 b6 4. d3 e6 |
| S7 | 800 000 000 | 49 | 0 | 1. c4 c5 2. Nc3 Nc6 3. f3 d6 4. Ba4 g6 |
| S8 | 1 600 000 000 | 50 | 0 | 1. c4 c5 2. Nc3 Nc6 3. Nc2 b6 4. d3 e6 |
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 | -2 |
| 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: -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 +38, Black +26, difference +12. 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 | +12 | 42 | 1. d4 |
| 2 | +11 | 42 | 1. c3 g6 2. d4 d5 3. h3 O-O 4. Bh2 Nd6 5. O-O Nd7 |
| 3 | +11 | 41 | 1. c4 c5 2. Nc3 Nc6 3. Ba4 d6 4. f3 Rb8 5. d3 g6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 33 cp, mean 7.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c3 | -18 | d5 | -22 |
| 2 | f3 | -20 | g6 | -19 |
| 3 | Bf2 | -16 | O-O | -21 |
| 4 | d4 | -22 | e5 | -21 |
| 5 | O-O | -24 | c6 | -33 |
| 6 | Nd2 | -19 | Nd6 | -13 |
| 7 | e4 | -16 | Re8 | -18 |
| 8 | Nab3 | -15 | a5 | -16 |
| 9 | a4 | -16 | Nd7 | -13 |
| 10 | Bh4 | -10 | g5 | -3 |
| 11 | Bf2 | -3 | b6 | -4 |
| 12 | Be2 | -7 | Nf8 | -10 |
| 13 | Qd1 | -10 | Bd7 | -11 |
| 14 | Qc2 | -4 | Ng6 | 0 |
| 15 | Rfe1 | 0 | h5 | 0 |
| 16 | g3 | 0 | h4 | 0 |
| 17 | Bd3 | 0 | Qf6 | -6 |
| 18 | Ra1 | -6 | Rab8 | 0 |
| 19 | exd5 | -4 | cxd5 | 0 |
| 20 | Bxg6 | +3 | Qxg6 | 0 |
| 21 | Qxg6+ | 0 | fxg6 | 0 |
| 22 | dxe5 | 0 | Bxe5 | 0 |
| 23 | gxh4 | 0 | gxh4 | 0 |
| 24 | Bxh4 | 0 | Nf5 | +6 |
| 25 | Bf2 | 0 | Bf4 | 0 |
| 26 | Nf1 | 0 | Rxe1 | +3 |
| 27 | Rxe1 | 0 | Bxa4 | 0 |
| 28 | Nd4 | +4 | Kf7 | 0 |
| 29 | Nxf5 | +2 | gxf5 | 0 |
| 30 | Bd4 | 0 | Rg8+ | 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 44.0 moves.
Sample game 1 (1/2-1/2)
1. d4 d5 2. h3 O-O 3. Bh2 g6 4. e3 Nd6 5. O-O Nd7 6. Qa5 e5 7. c3 b6 8. Qxd5 Bb7 9. Qb3 Qg5 10. Bg4 h5 11. f4 Qe7 12. Bxd7 exd4 13. cxd4 Qxd7 14. f5 gxf5 15. Bf4 Rfe8 16. Qd1 Re6 17. Nd2 Rg6 18. Nf3 Bf6 19. Kh2 Rc8 20. Rf2 Qe7 21. Rfc2 Be4 22. Rf2 Bb7 23. Rfc2 Be4 24. Rf2
Sample game 2 (1/2-1/2)
1. d4 d5 2. c3 O-O 3. f3 g6 4. Bf2 Nc6 5. Bh4 Qd6 6. e3 e5 7. O-O exd4 8. exd4 Bg7 9. Nc2 Bh6 10. Nd2 f5 11. Ne3 Be6 12. g4 Qd7 13. g5 Bg7 14. f4 Nd6 15. Bg3 Ne4 16. h4 Ne7 17. Bf2 c5 18. dxc5 Nxc5 19. Bc2 Nc6 20. Nf3 Ne4 21. Ng2 Rfe8 22. Qd1 Bf7 23. h5 Qc7 24. h6 Bf8 25. Bb3 Rad8 26. Rc2 Na5 27. Re2 Nxf2 28. Kxf2 Re4 29. Kg3 Bd6 30. Nd4 Qe7 31. Kh3 Nxb3 32. axb3 Re8 33. Ree1 a5 34. Qd2 Bc7 35. Rd1 Rd8 36. Rfe1 Be8 37. Qf2 Bc6 38. Qd2 Bb6 39. Kh2 Qd7 40. Nc2 Bc7 41. Nd4 Rde8 42. Kh3 Qd8 43. Qf2 Bd6 44. Qg3 Qb8 45. Qf2 Bd7 46. Kg3 Qd8 47. Nf3 Bc6 48. Qd2 b6 49. Qf2 b5 50. Kh3 Bxf4 51. Nxf4 Rxf4 52. Rxe8+ Qxe8 53. Rd4 Re4 54. Rxe4 dxe4 55. Qa7 Qd7 56. Qb8+ Qe8 57. Qc7 Qd7 58. Qb8+ Qe8 59. Qc7 Qd7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 61 / 423 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): rnbqnkrb/pppppppp/8/8/8/8/PPPPPPPP/NNRBQKBR w CHag - 0 1
Mirror twin: White 904 vs Black 722 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 265.