White 396 vs Black 423
White starts from setup 396 (QBRNNKBR), Black from setup 423 (RNBQNKRB). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #396 Q B R N N K B R
King on the f-file, rooks on c, h, queen on the a-file; no 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 396 gives White +0.26 (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 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 shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±15 cp.
For comparison, in symmetric play setup 396 gives White +0.26 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 h3, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±16 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 1, drawn 9, Black won 0 (White scored 55.0%).
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 | 16 | +5 | 1. c3 g6 2. d4 O-O 3. f3 Nc6 4. h4 d5 |
| S1 | 500 000 | 21 | +4 | 1. c3 g6 2. d4 O-O 3. h4 Nf6 4. f3 Nh5 |
| S2 | 2 000 000 | 23 | -2 | 1. c3 g6 2. f4 O-O 3. Bf2 b6 4. Nf3 Bb7 |
| S3 | 8 000 000 | 31 | +15 | 1. c4 g6 2. f3 Nc6 3. Bf2 d6 4. O-O e5 |
| S4 | 32 000 000 | 37 | +11 | 1. c3 g6 2. d4 d5 3. h3 e5 4. dxe5 Bxe5 |
| S5 | 128 000 000 | 42 | +4 | 1. h3 g6 2. c3 c5 3. Bh2 b6 4. a4 Nc6 |
| S6 | 400 000 000 | 44 | 0 | 1. c4 g6 2. f3 e5 3. b4 d6 4. a4 a5 |
| S7 | 800 000 000 | 52 | 0 | 1. c4 g6 2. f3 e5 3. b4 d6 4. a4 O-O |
| S8 | 1 600 000 000 | 57 | 0 | 1. c4 g6 2. f3 c6 3. d4 d5 4. cxd5 cxd5 |
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 | not checked |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair held exactly 0.00 up to 1 600 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: -1
- Lc0 0.32.1: -7
Independent confirmations: 2 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 +42, Black +26, difference +16. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 45 | 1. h3 c5 2. c3 g6 3. Bh2 O-O 4. a4 b6 5. Qa3 Bb7 |
| 2 | 0 | 44 | 1. a4 g6 2. h3 b6 3. Bh2 c5 4. c3 Nc6 5. Qa3 a5 |
| 3 | 0 | 44 | 1. a4 g6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 16 cp, mean 2.8 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | +14 | g6 | +13 |
| 2 | f3 | +1 | e5 | -16 |
| 3 | b4 | +13 | d6 | +11 |
| 4 | a4 | +3 | O-O | 0 |
| 5 | Bf2 | 0 | Be6 | +8 |
| 6 | O-O | +8 | a5 | 0 |
| 7 | b5 | +2 | c6 | +5 |
| 8 | d4 | 0 | exd4 | 0 |
| 9 | Bxd4 | -6 | Bxd4+ | -10 |
| 10 | Qxd4 | 0 | Nd7 | +2 |
| 11 | Ba2 | +3 | Qb6 | +3 |
| 12 | Nc2 | +8 | Nef6 | 0 |
| 13 | Nde3 | -3 | Rfc8 | -1 |
| 14 | bxc6 | 0 | Qxd4 | -6 |
| 15 | Nxd4 | 0 | bxc6 | -3 |
| 16 | f4 | 0 | Ng4 | 0 |
| 17 | Nxg4 | 0 | Bxg4 | -3 |
| 18 | h3 | 0 | Be6 | 0 |
| 19 | f5 | -7 | Bxf5 | 0 |
| 20 | Nxf5 | -6 | gxf5 | 0 |
| 21 | Rcd1 | 0 | Nc5 | -3 |
| 22 | Rxd6 | 0 | Nxa4 | -8 |
| 23 | Bb1 | 0 | Nc3 | 0 |
| 24 | Bxf5 | 0 | Rd8 | 0 |
| 25 | Rxd8+ | 0 | Rxd8 | 0 |
| 26 | Bd3 | 0 | a4 | 0 |
| 27 | Ra1 | 0 | Rb8 | 0 |
| 28 | Kf2 | 0 | Rb2 | 0 |
| 29 | Ke3 | 0 | c5 | 0 |
| 30 | Ra3 | 0 | Rb3 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 46.0 moves.
Sample game 1 (1/2-1/2)
1. f3 e5 2. c4 g6 3. b4 Nc6 4. Qb2 d6 5. Bf2 O-O 6. O-O Bg7 7. a4 Be6 8. d3 a6 9. a5 Nf6 10. Ba2 d5 11. cxd5 Bxd5 12. Bc4 e4 13. Qd2 Re8 14. Kh1 Be6 15. Rc2 exd3 16. Nxd3 Bf8 17. Qc3 Nd5 18. Bxd5 Qxd5 19. Nc5 Rad8 20. Ne4 Bg7 21. Nf6+ Bxf6 22. Qxf6 Qb3 23. Rc1 Qxb4 24. Nc3 Bf5 25. g4 Rd6 26. Qh4 Bd7 27. Bg3 Rd4 28. Bf2 Rd6 29. Bg3 Rd4 30. Bf2
Sample game 2 (1/2-1/2)
1. d4 O-O 2. h4 Nc6 3. d5 Ne5 4. c4 g6 5. f3 d6 6. Nd3 Nf6 7. Nxe5 Nh5 8. Bh2 Bxe5 9. Bxe5 dxe5 10. Kf2 e4 11. g4 Nf6 12. Ne3 Qd6 13. b3 Bxg4 14. Nxg4 Nxg4+ 15. fxg4 Qf4+ 16. Kg2 Qxg4+ 17. Kf1 Qf4+ 18. Kg2 Qg4+ 19. Kf1 Qf4+ 20. Kg2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 396 / 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/QBRNNKBR w CHag - 0 1
Mirror twin (the same position mirrored): White 764 vs Black 722.