White 21 vs Black 392
White starts from setup 21 (NQBBNRKR), Black from setup 392 (QBRNBNKR). 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. 21, Black by position No. 392, 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 #21 N Q B B N R K R
King on the g-file, rooks on f, h, queen on the b-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 21 gives White +0.29 (Morozov Balance Index, 400M nodes).
Black: setup #392 Q B R N B N K R
King on the g-file, rooks on c, h, queen on the a-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 392 gives White +0.31 (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 -42 and +13 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 21 gives White +0.29 and setup 392 gives White +0.31: 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 61 cp (around move 10), ending at -8 cp — the position stays playable for both sides.
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 | 12 | -42 | 1. c4 h5 2. b3 c5 3. e3 e6 4. f4 d5 |
| S1 | 500 000 | 19 | -5 | 1. e4 b5 2. c3 c5 3. h4 h5 4. d4 cxd4 |
| S2 | 2 000 000 | 24 | +13 | 1. e4 h5 2. h4 c5 3. c3 b5 4. d4 cxd4 |
| S3 | 8 000 000 | 29 | -18 | 1. e4 b5 2. c3 c5 3. d4 cxd4 4. cxd4 h5 |
| S4 | 32 000 000 | 35 | -21 | 1. h4 h5 2. d4 d5 3. c3 b6 4. Nf3 c5 |
| S5 | 128 000 000 | 39 | -3 | 1. e4 b5 2. c3 c5 3. Nf3 d5 4. exd5 Qxd5 |
| S6 | 400 000 000 | 51 | 0 | 1. e4 b5 2. c3 c5 3. Nf3 d5 4. exd5 Qxd5 |
| S7 | 800 000 000 | 55 | 0 | 1. e4 b5 2. c3 c5 3. Nf3 d5 4. exd5 Qxd5 |
| S8 | 1 600 000 000 | 55 | 0 | 1. e4 b5 2. c3 c5 3. Nf3 d5 4. exd5 Qxd5 |
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: +1
- Lc0 0.32.1: -9
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 +33, Black +61, difference -28. 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 | -4 | 42 | 1. e4 b5 2. c3 c5 3. Nf3 d5 4. exd5 Qxd5 5. d4 cxd4 |
| 2 | -16 | 42 | 1. h4 h5 2. c3 c5 3. d4 b6 4. Nf3 d5 5. Bc2 cxd4 |
| 3 | -17 | 42 | 1. d4 d5 2. h4 h5 3. c3 b6 4. Nf3 c5 5. Bc2 cxd4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 61 cp, mean 35.5 cp, final -8 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | -12 | b5 | -21 |
| 2 | c3 | -24 | c5 | -23 |
| 3 | d4 | -30 | cxd4 | -32 |
| 4 | cxd4 | -40 | f6 | -42 |
| 5 | f4 | -45 | a5 | -44 |
| 6 | Nf3 | -40 | e6 | -38 |
| 7 | Re1 | -47 | Ng6 | -50 |
| 8 | f5 | -42 | Ne7 | -46 |
| 9 | O-O | -40 | O-O | -49 |
| 10 | Bd2 | -41 | exf5 | -61 |
| 11 | exf5 | -48 | Bd6 | -53 |
| 12 | Qd3 | -54 | Ndc6 | -48 |
| 13 | Qxb5 | -40 | Rb8 | -45 |
| 14 | Bb3+ | -49 | Kh8 | -48 |
| 15 | Qd3 | -43 | Nb4 | -51 |
| 16 | Qe4 | -43 | Nbd5 | -49 |
| 17 | a4 | -44 | Bf7 | -31 |
| 18 | Qg4 | -39 | Rfe8 | -28 |
| 19 | Nh4 | -31 | Bb4 | -33 |
| 20 | Bxb4 | -31 | Rxb4 | -53 |
| 21 | Qg3 | -39 | Qb7 | -47 |
| 22 | Rf3 | -25 | Rxd4 | -40 |
| 23 | Nc2 | -32 | Rd2 | -28 |
| 24 | Na3 | -31 | Qb6+ | -28 |
| 25 | Kh1 | -26 | Rxb2 | -29 |
| 26 | Nc4 | -29 | Nxf5 | -32 |
| 27 | Nxf5 | -29 | Rxe1+ | -31 |
| 28 | Qxe1 | -13 | Qb4 | -5 |
| 29 | Qd1 | -16 | Nc3 | -9 |
| 30 | Rxc3 | -8 | Qxc3 | -8 |
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 47.5 moves.
Sample game 1 (1-0)
1. e4 h5 2. c3 d5 3. exd5 c6 4. dxc6 h4 5. h3 Bxc6 6. d4 b5 7. Bf3 b4 8. cxb4 Ng6 9. Nb3 e5 10. Bxc6 Qxc6 11. Nd3 exd4 12. Nxd4 Qd6 13. Nb5 Qc6 14. Nc3 Ne6 15. Be3 O-O 16. Rd1 Rfe8 17. Ne1 Be5 18. Nd3 Bb8 19. Ne1 Be5 20. Nf3 Nef4 21. b5 Qa8 22. Rd2 Bxc3 23. bxc3 Re5 24. Qf1 Rf5 25. c4 Nxg2 26. Qxg2 Rxf3 27. Rd5 Rf6 28. Rd4 Qb8 29. Rg4 Qd6 30. O-O Re8 31. c5 Qd3 32. Bd4 Rf3 33. c6 Rxh3 34. Be3 Rhxe3 35. fxe3 Rxe3 36. Qf2 Ne5 37. c7 Qc3 38. c8=Q+ Qxc8 39. Rxg7+ Kxg7 40. Qxe3 Qe6 41. a4 Qd5 42. Rf4 Qd1+ 43. Kg2 Qd5+ 44. Kg1 Kf8 45. Qe4 Qd1+ 46. Rf1 Qd6 47. Kh1 Qc5 48. Rg1 Ng6 49. Qd3 Qc7 50. Rd1 Kg7 51. Qd4+ Kh7 52. Qd5 Ne5 53. Qe4+ Ng6 54. Qd5 Ne5 55. a5 Qc3 56. Qe4+ Kg7 57. Rf1 Kf8 58. Qa8+ Kg7 59. Qg2+ Ng6 60. b6 axb6 61. axb6 Qb4 62. b7 h3 63. Qf3 f5 64. Qd5 h2 65. Rxf5 Qe1+ 66. Kxh2 Qh4+ 67. Kg2 Qg4+ 68. Kf1 Qb4 69. Rf7+ Kh6 70. b8=Q Qxb8 71. Qh1+
Sample game 2 (1/2-1/2)
1. h4 d5 2. c3 h5 3. d4 b6 4. Nf3 c5 5. Bc2 cxd4 6. cxd4 Qb7 7. Bd3 Nh7 8. Be3 Ne6 9. Rc1 Rxc1+ 10. Qxc1 O-O 11. Nc2 Bd7 12. O-O g6 13. Bd2 Nf6 14. Bb4 Re8 15. Ne5 Bxe5 16. dxe5 Ng4 17. Bc3 Qb8 18. f3 Nxe5 19. Qh6 Rc8 20. Nd4 Ng7 21. Ba6 Re8 22. Bd3 Rc8 23. Ba6 Re8 24. Bd3
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 21 / 392 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): qbrnbnkr/pppppppp/8/8/8/8/PPPPPPPP/NQBBNRKR w FHch - 0 1
Mirror twin: White 938 vs Black 765 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 135.