White 284 vs Black 406
White starts from setup 284 (NBRKNRBQ), Black from setup 406 (RQBNNBKR). 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 #284 N B R K N R B Q
King on the d-file, rooks on c, f, queen on the h-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 284 gives White +0.19 (Morozov Balance Index, 400M nodes).
Black: setup #406 R Q B N N B K R
King on the g-file, rooks on a, h, queen on the b-file; no bishop starts in a corner; the knights start on central files. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 406 gives White +0.19 (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 ±11 cp.
For comparison, in symmetric play setup 284 gives White +0.19 and setup 406 gives White +0.19: 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 f4, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 43 cp (around move 7), 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 | -11 | 1. f4 b6 2. c3 h5 3. g3 Ba6 4. Bd3 Bxd3 |
| S1 | 500 000 | 19 | -4 | 1. f4 b6 2. c3 h5 3. e4 c5 4. O-O-O e6 |
| S2 | 2 000 000 | 23 | 0 | 1. g4 d5 2. f4 Bxg4 3. Qxd5 Nf6 4. Qd3 Qc8 |
| S3 | 8 000 000 | 30 | +1 | 1. g4 d5 2. h3 e6 3. c3 c5 4. f4 h5 |
| S4 | 32 000 000 | 33 | -5 | 1. f4 h5 2. e4 d6 3. c3 b5 4. Be3 b4 |
| S5 | 128 000 000 | 41 | 0 | 1. f4 Nf6 2. c3 d5 3. g4 Bxg4 4. f5 Bh3 |
| S6 | 400 000 000 | 50 | 0 | 1. g4 d5 2. f4 Bxg4 3. Qxd5 Nf6 4. Qg5 Bh3 |
| S7 | 800 000 000 | 52 | 0 | 1. g4 d5 2. f4 Bxg4 3. Qxd5 Nf6 4. Qg5 Bh3 |
| S8 | 1 600 000 000 | 57 | 0 | 1. g4 d5 2. f4 Bxg4 3. Qxd5 Nf6 4. Qg5 Bh3 |
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: 0
- 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 +33, Black +43, difference -10. 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 | 0 | 40 | 1. f4 Nf6 2. c3 d5 3. g4 Bxg4 4. f5 Bh3 5. Rf3 Bg4 |
| 2 | 0 | 40 | 1. g4 d5 2. f4 Bxg4 3. Qxd5 Nf6 4. Qh1 Bh3 5. Rf3 Bg4 |
| 3 | -13 | 39 | 1. c3 h5 2. f4 b5 3. Bf2 a5 4. Nf3 b4 5. O-O a4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 43 cp, mean 12.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g4 | +5 | d5 | +6 |
| 2 | h3 | +8 | e6 | +8 |
| 3 | f4 | -2 | c5 | -24 |
| 4 | c3 | -40 | Bd6 | -41 |
| 5 | e4 | -26 | dxe4 | -27 |
| 6 | Qxe4 | -30 | b6 | -30 |
| 7 | Qe2 | -43 | a5 | -35 |
| 8 | Nd3 | -29 | Ba6 | -24 |
| 9 | O-O-O | -31 | Qc7 | -35 |
| 10 | Nc2 | -31 | O-O | -25 |
| 11 | Ne3 | -32 | Nc6 | -39 |
| 12 | g5 | -31 | Ne7 | -26 |
| 13 | h4 | -21 | a4 | -20 |
| 14 | Qf3 | -7 | Bb7 | +6 |
| 15 | Qh3 | +15 | c4 | +14 |
| 16 | Ne5 | +15 | a3 | 0 |
| 17 | N3xc4 | +1 | axb2+ | 0 |
| 18 | Kxb2 | +7 | Bxe5 | 0 |
| 19 | Qd3 | 0 | Bxc3+ | 0 |
| 20 | dxc3 | 0 | Nf5 | 0 |
| 21 | Nxb6 | 0 | Rb8 | +3 |
| 22 | Qd7 | +4 | Bg2 | 0 |
| 23 | Qxc7 | 0 | Nxc7 | 0 |
| 24 | Bxf5 | 0 | exf5 | 0 |
| 25 | a4 | 0 | Bxf1 | 0 |
| 26 | Rxf1 | 0 | f6 | 0 |
| 27 | a5 | 0 | Rfd8 | 0 |
| 28 | gxf6 | 0 | gxf6 | 0 |
| 29 | Kb3 | 0 | Kf7 | 0 |
| 30 | h5 | 0 | Rd6 | 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 46.5 moves.
Sample game 1 (1/2-1/2)
1. c3 d5 2. d4 a5 3. h4 h5 4. Bh2 Qa7 5. Nd3 Bf5 6. Nb3 Ne6 7. O-O Nf6 8. Be5 Ng4 9. Nd2 f6 10. Bg3 g6 11. Rfe1 Bh6 12. Rcd1 Qb6 13. e3 c5 14. b3 a4 15. b4 cxd4 16. cxd4 Rc8 17. Nf1 Bxd3 18. Bxd3 f5 19. f3 Nf6 20. Be5 O-O 21. Bxf6 exf6 22. f4 Rfd8 23. Qh2 Bf8 24. Qg3 Kh7 25. Qf3 Rc3 26. Rd2 Kh6 27. Rb1 Ra3 28. b5 Rc8 29. Be2 Rac3 30. Bd3 Re8 31. Kh2 Qd6 32. b6 a3 33. Rb5 Rd8 34. Qd1 Rdc8 35. Qf3 Rd8 36. Qd1 Rdc8 37. Qf3
Sample game 2 (1/2-1/2)
1. c3 d5 2. d4 Nf6 3. h3 h5 4. Bh2 h4 5. Nb3 b6 6. Nf3 Rh5 7. Be5 g6 8. O-O Ba6 9. Rfe1 Qb7 10. Qh2 Ne6 11. Nbd2 c5 12. e4 cxd4 13. exd5 Qxd5 14. Nxd4 Nxd4 15. Bxd4 e5 16. Bxe5 Qxd2 17. Rcd1 Qg5 18. f4 Bc5+ 19. Kh1 Ng4 20. fxg5 Nf2+ 21. Kg1 Nxh3+ 22. Kh1 Nf2+ 23. Kg1 Nh3+ 24. Kh1 Nf2+ 25. Kg1
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 284 / 406 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): rqbnnbkr/pppppppp/8/8/8/8/PPPPPPPP/NBRKNRBQ w CFah - 0 1
Mirror twin (the same position mirrored): White 588 vs Black 742.