White 478 vs Black 54
White starts from setup 478 (RNNKRBBQ), Black from setup 54 (NNBRQBKR). In the encyclopedia since 2026-10-09: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #478 R N N K R B B Q
King on the d-file, rooks on a, e, queen on the h-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 478 gives White +0.35 (Morozov Balance Index, 400M nodes).
Black: setup #54 N N B R Q B K R
King on the g-file, rooks on d, 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 54 gives White +0.20 (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 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 wandered between -10 and +23 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 478 gives White +0.35 and setup 54 gives White +0.20: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.
The engine's first choice for White is e4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the largest swing was 32 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 | 12 | -10 | 1. f4 d5 2. Bxa7 Nc6 3. Bf2 h5 4. e4 dxe4 |
| S1 | 500 000 | 19 | +1 | 1. e4 d6 2. f4 c5 3. Nc3 h5 4. Be3 Nc7 |
| S2 | 2 000 000 | 26 | +23 | 1. e4 d6 2. Nc3 c5 3. g3 g6 4. Nb3 Bg7 |
| S3 | 8 000 000 | 29 | +20 | 1. e4 c5 2. Nc3 d6 3. f4 h5 4. Nb3 Nc7 |
| S4 | 32 000 000 | 33 | +12 | 1. e4 d5 2. exd5 Nb6 3. Nc3 Nxd5 4. Nxd5 Rxd5 |
| S5 | 128 000 000 | 39 | 0 | 1. e4 d6 2. f4 c5 3. Nc3 g6 4. g3 Bg7 |
| S6 | 400 000 000 | 50 | 0 | 1. e4 d6 2. Nc3 c5 3. Nb3 e5 4. O-O-O h5 |
| S7 | 800 000 000 | 50 | 0 | 1. e4 d6 2. Nc3 c5 3. Nb3 e5 4. O-O-O h5 |
| S8 | 1 600 000 000 | 55 | 0 | 1. f4 d5 2. Bxa7 Nc6 3. Bc5 h5 4. Qg1 Rh6 |
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: -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 +96, Black +133, difference -37. 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 | +18 | 39 | 1. e4 d5 2. exd5 Nb6 3. Nc3 Nxd5 4. Nd3 Nxc3+ 5. dxc3 Qa4 |
| 2 | -10 | 38 | 1. f4 d5 2. Bxa7 Nc6 3. Bc5 h5 4. h3 Rh6 5. e4 dxe4 |
| 3 | -14 | 38 | 1. f3 b6 2. e4 c5 3. Nc3 Nc7 4. h4 h5 5. Qh2 d6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 32 cp, mean 5.7 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | +26 | c5 | +15 |
| 2 | Nc3 | +22 | d6 | +26 |
| 3 | f4 | +22 | h5 | +25 |
| 4 | g3 | +23 | Nc7 | +27 |
| 5 | Qg2 | +20 | Nc6 | +32 |
| 6 | h3 | +16 | b6 | +21 |
| 7 | f5 | +13 | e6 | +4 |
| 8 | fxe6 | -1 | fxe6 | -8 |
| 9 | Nb3 | -9 | Be7 | -6 |
| 10 | O-O-O | -5 | h4 | -4 |
| 11 | g4 | -6 | O-O | -8 |
| 12 | d4 | +4 | e5 | 0 |
| 13 | Bc4+ | 0 | Kh8 | 0 |
| 14 | dxc5 | 0 | Bg5+ | 0 |
| 15 | Kb1 | 0 | dxc5 | 0 |
| 16 | Rxd8 | 0 | Qxd8 | 0 |
| 17 | Rd1 | 0 | Nd4 | 0 |
| 18 | Bh2 | 0 | Qd6 | 0 |
| 19 | a4 | 0 | a6 | 0 |
| 20 | Rf1 | 0 | Rd8 | 0 |
| 21 | Bf7 | 0 | b5 | 0 |
| 22 | Nd5 | 0 | Nxb3 | 0 |
| 23 | cxb3 | 0 | bxa4 | 0 |
| 24 | bxa4 | 0 | Rf8 | 0 |
| 25 | Nxc7 | 0 | Rxf7 | 0 |
| 26 | Rxf7 | 0 | Qd1+ | 0 |
| 27 | Ka2 | 0 | Qxa4+ | 0 |
| 28 | Kb1 | 0 | Qd1+ | 0 |
| 29 | Ka2 | 0 | Qa4+ | 0 |
| 30 | Kb1 | 0 | Qd1+ | 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 35.0 moves.
Sample game 1 (1/2-1/2)
1. e4 d6 2. g3 c5 3. Nc3 Nc6 4. f4 Nc7 5. Qg2 h5 6. h3 b6 7. N1e2 e6 8. d4 b5 9. O-O-O b4 10. Nb1 Ba6 11. dxc5 dxc5 12. Rxd8 Qxd8 13. Be3 Qc8 14. Rd1 Na5 15. Ng1 Nb5 16. Nf3 Be7 17. Ng5 c4 18. Qd2 O-O 19. Qd7 b3 20. axb3 Nxb3+ 21. cxb3 cxb3+ 22. Qxc8 Rxc8+ 23. Nc3 Nxc3 24. bxc3 Rxc3+ 25. Kb2 Rxe3 26. Bxa6 Rxg3 27. Rd3 h4 28. Nf3 Rxh3 29. Kxb3 Rg3 30. f5 exf5 31. exf5 Kh7 32. Kc4 h3 33. Bb7 Kh6 34. Bd5 a5 35. Bxf7 a4 36. Re3 a3 37. Kd4 Bf6+ 38. Ke4 Rg4+ 39. Kd3 Rg3 40. Ke4 Rg4+
Sample game 2 (1/2-1/2)
1. e4 d5 2. exd5 Nb6 3. Nc3 Nxd5 4. Nxd5 Rxd5 5. g3 Rd8 6. f4 Nc6 7. Ne2 h5 8. h3 Bf5 9. Nc3 g6 10. O-O-O Qd7 11. d4 Bg7 12. Bb5 Qd6 13. Ne4 Qb4 14. Bxc6 bxc6 15. Qg2 Rb8 16. b3 a5 17. g4 Be6 18. Nc5 Bd5 19. Qg3 Qa3+ 20. Kd2 hxg4 21. hxg4 Ra8 22. Bf2 a4 23. Nxa4 Qb4+ 24. Qc3 Qd6 25. Qg3 Qb4+ 26. Qc3 Qd6 27. Qg3
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 478 / 54 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): nnbrqbkr/pppppppp/8/8/8/8/PPPPPPPP/RNNKRBBQ w AEdh - 0 1
Mirror twin: White 676 vs Black 902 — a different position (castling squares are fixed), not evaluated by the search.