White 446 vs Black 422
White starts from setup 446 (RNNQKBBR), Black from setup 422 (RNBQNBKR). 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 #446 R N N Q K B B R
King on the e-file, rooks on a, h, queen on the d-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 446 gives White +0.22 (Morozov Balance Index, 400M nodes).
Black: setup #422 R N B Q N B K R
King on the g-file, rooks on a, h, queen on the d-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 422 gives White +0.16 (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 60.
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 wandered between 0 and +17 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 446 gives White +0.22 and setup 422 gives White +0.16: 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 (28 moves) the largest swing was 40 cp (around move 12), ending at 0 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 0, drawn 9, Black won 1 (White scored 45.0%).
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 | 0 | 1. d4 b6 2. h3 e6 3. Bh2 Bd6 4. Bxd6 Nxd6 |
| S1 | 500 000 | 22 | +2 | 1. e4 d5 2. exd5 Nf6 3. d4 h5 4. f3 Nxd5 |
| S2 | 2 000 000 | 25 | +2 | 1. e4 d5 2. exd5 Nf6 3. d4 Nxd5 4. h3 Nc6 |
| S3 | 8 000 000 | 28 | +7 | 1. d4 d5 2. f3 h5 3. Nc3 b6 4. e4 e6 |
| S4 | 32 000 000 | 33 | +17 | 1. e4 d5 2. e5 c5 3. f4 d4 4. Nb3 e6 |
| S5 | 128 000 000 | 40 | +4 | 1. d4 d5 2. f3 g6 3. Nc3 Bg7 4. Nd3 Nc6 |
| S6 | 400 000 000 | 50 | 0 | 1. e4 e5 2. Nc3 Nf6 3. Nd3 Nc6 4. f4 exf4 |
| S7 | 800 000 000 | 55 | 0 | 1. e4 e5 2. Nc3 Nf6 3. Nd3 Nc6 4. f4 exf4 |
| S8 | 1 600 000 000 | 60 | 0 | 1. e4 e5 2. Nc3 Nf6 3. Nd3 Nc6 4. f4 exf4 |
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: -3
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 +24, Black +36, 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, 9 draws, 1 Black wins, White scored 45.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +2 | 45 | 1. d4 |
| 2 | 0 | 45 | 1. e4 e5 2. Nc3 Nf6 3. Nd3 Nc6 4. f4 exf4 5. Qf3 d5 |
| 3 | 0 | 44 | 1. Nc3 e5 2. e4 Nf6 3. Nd3 Nc6 4. f4 exf4 5. Qf3 d5 |
Main-line play-out
28 moves, 5 000 000 nodes per half-move. Largest |evaluation| 40 cp, mean 10.6 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +13 | d5 | +15 |
| 2 | f3 | +15 | h5 | +16 |
| 3 | Nc3 | +21 | e6 | +11 |
| 4 | e4 | +11 | b6 | +15 |
| 5 | Bf2 | +19 | Bb7 | +16 |
| 6 | e5 | +8 | c5 | +15 |
| 7 | Nb3 | +5 | Nc6 | +9 |
| 8 | f4 | +7 | g5 | 0 |
| 9 | g3 | -8 | Ng7 | -7 |
| 10 | Rg1 | -14 | g4 | -31 |
| 11 | h3 | -27 | cxd4 | -23 |
| 12 | Bxd4 | -21 | Nxd4 | -40 |
| 13 | Nxd4 | -29 | Bc5 | -33 |
| 14 | Nce2 | -26 | Ba6 | -24 |
| 15 | Qd2 | -22 | Qc7 | -20 |
| 16 | c3 | -27 | Nf5 | -19 |
| 17 | Nxf5 | -14 | Bxg1 | -10 |
| 18 | Nxg1 | 0 | Bxf1 | 0 |
| 19 | Nd6 | 0 | Bc4 | 0 |
| 20 | f5 | 0 | exf5 | 0 |
| 21 | Qg5+ | 0 | Kf8 | 0 |
| 22 | Qf6 | 0 | Rh7 | 0 |
| 23 | Qxf5 | 0 | Rg7 | 0 |
| 24 | Qxh5 | 0 | Qc5 | 0 |
| 25 | Qh8+ | 0 | Ke7 | 0 |
| 26 | Qh4+ | 0 | Kf8 | 0 |
| 27 | Qh8+ | 0 | Ke7 | 0 |
| 28 | Qh4+ | 0 | Kf8 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 9, Black won 1 — White scored 45.0%. Average length 43.7 moves.
Sample game 1 (1/2-1/2)
1. f3 e6 2. d4 Be7 3. Bf2 O-O 4. e4 d5 5. Be2 Nd7 6. Nc3 dxe4 7. fxe4 e5 8. dxe5 Nxe5 9. Qxd8 Bxd8 10. Nd3 Nxd3+ 11. cxd3 Nf6 12. h3 c6 13. O-O-O Re8 14. Rhf1 h6 15. b3 Bd7 16. Kb2 Ba5 17. Bd4 Bd8 18. Bg1 Nh7 19. a3 Ng5 20. Bf2 Bc7 21. h4 Nh7 22. g4 a5 23. Na4 Be6 24. Rg1 Rad8 25. g5 hxg5 26. hxg5 Nf8 27. Bf3 g6 28. d4 Bc8 29. Nc3 Bb6 30. Be3 Ne6 31. Bg4 Kg7 32. Rgf1 Ba7 33. Bxe6 Bxe6 34. Rh1 Rh8 35. Rxh8 Rxh8 36. Bf4 Rh4 37. Be5+ Kf8 38. b4 Rh5 39. Bf4 Bg4 40. Rd2 axb4
Sample game 2 (1/2-1/2)
1. d4 d5 2. Nc3 Nc6 3. f3 h5 4. Nd3 e6 5. h4 Nd6 6. e4 dxe4 7. fxe4 b5 8. a3 a6 9. Qf3 Nc4 10. O-O-O e5 11. Nxe5 N4xe5 12. dxe5 Qe8 13. Nd5 Bg4 14. Qg3 Rc8 15. Be2 Nxe5 16. Bd4 Rh6 17. Rhe1 Nc4 18. Bxc4 bxc4 19. Rd2 c6 20. Ne3 Qxe4 21. Nxc4 Qf5 22. Bc3 Re6 23. Ne5 Bc5 24. b4 Bb6 25. Nxg4 hxg4 26. Rxe6 Qxe6 27. Rd3 Bc7 28. Qf2 Rd8 29. Qd2 Rxd3 30. Qxd3 Be5 31. Bd2 Bf6 32. Qxa6 Qe4 33. Qc8+ Kh7 34. Qd7 Qxg2 35. Qf5+ Kg8 36. Qc8+ Kh7 37. Qf5+ Kh8 38. Qc8+ Kh7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 446 / 422 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): rnbqnbkr/pppppppp/8/8/8/8/PPPPPPPP/RNNQKBBR w AHah - 0 1
Mirror twin (the same position mirrored): White 708 vs Black 726.