White 122 vs Black 419
White starts from setup 122 (NQRNBBKR), Black from setup 419 (BRNQNKRB). In the encyclopedia since 2026-11-01: 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. 122, Black by position No. 419, 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 #122 N Q R N B B K R
King on the g-file, rooks on c, 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 122 gives White +0.30 (Morozov Balance Index, 400M nodes).
Black: setup #419 B R N Q N K R B
King on the f-file, rooks on b, 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 419 gives White +0.14 (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 61.
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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.
For comparison, in symmetric play setup 122 gives White +0.30 and setup 419 gives White +0.14: 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 c4, and 2 first moves are within 10 cp of it.
Along the engine's main line (22 moves) the evaluation stayed within ±10 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 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 | 13 | -9 | 1. Nb3 e5 2. c4 g6 3. e3 b6 4. d4 f5 |
| S1 | 500 000 | 21 | +5 | 1. c4 g6 2. b4 b6 3. Nb3 c5 4. bxc5 bxc5 |
| S2 | 2 000 000 | 25 | +13 | 1. c4 g6 2. Nb3 e5 3. e3 b6 4. d4 exd4 |
| S3 | 8 000 000 | 31 | +11 | 1. c4 g6 2. Nb3 b6 3. d4 O-O 4. e3 e5 |
| S4 | 32 000 000 | 37 | +7 | 1. c4 g6 2. e3 b6 3. d4 c5 4. Nb3 cxd4 |
| S5 | 128 000 000 | 41 | +11 | 1. c4 g6 2. e3 b6 3. d4 c5 4. Nb3 cxd4 |
| S6 | 400 000 000 | 49 | 0 | 1. c4 g6 2. e3 e5 3. Nb3 Qe7 4. Nc3 b6 |
| S7 | 800 000 000 | 55 | 0 | 1. c4 g6 2. e3 e5 3. Nb3 Qe7 4. Nc3 b6 |
| S8 | 1 600 000 000 | 61 | 0 | 1. c4 g6 2. e3 e5 3. Nb3 Qe7 4. Nc3 b6 |
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: +5
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 +56, Black +99, difference -43. 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 | +6 | 41 | 1. c4 g6 2. e3 e5 3. Nb3 b6 4. d4 exd4 5. Nxd4 Ncd6 |
| 2 | +4 | 41 | 1. e3 f5 2. d4 b6 3. c4 e6 4. b4 g5 5. Nb3 Qf6 |
| 3 | -13 | 40 | 1. h4 g6 2. c4 b6 3. e3 e6 4. d4 Ncd6 5. f3 f5 |
Main-line play-out
22 moves, 5 000 000 nodes per half-move. Largest |evaluation| 10 cp, mean 1.8 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | +7 | g6 | -5 |
| 2 | Nb3 | 0 | b6 | -4 |
| 3 | d4 | -4 | O-O | +1 |
| 4 | e3 | 0 | e6 | -7 |
| 5 | Be2 | +3 | Ne7 | +2 |
| 6 | O-O | +5 | d6 | 0 |
| 7 | Nc3 | 0 | c5 | +1 |
| 8 | Rd1 | +6 | Nf5 | 0 |
| 9 | d5 | 0 | Nc7 | +3 |
| 10 | e4 | 0 | Nd4 | 0 |
| 11 | Bd3 | +9 | f5 | +7 |
| 12 | Nxd4 | +10 | cxd4 | +4 |
| 13 | Ne2 | 0 | fxe4 | 0 |
| 14 | Bxe4 | 0 | exd5 | 0 |
| 15 | cxd5 | 0 | Nxd5 | 0 |
| 16 | Nxd4 | 0 | Nf4 | 0 |
| 17 | Bxa8 | 0 | Rxa8 | 0 |
| 18 | Qc2 | 0 | Qg5 | 0 |
| 19 | g3 | 0 | Nh3+ | 0 |
| 20 | Kg2 | 0 | Nf4+ | 0 |
| 21 | Kg1 | 0 | Nh3+ | 0 |
| 22 | Kg2 | 0 | Nf4+ | 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 34.8 moves.
Sample game 1 (1/2-1/2)
1. h4 a5 2. c4 g6 3. Nc3 b6 4. Nb3 e6 5. e3 f5 6. d4 O-O 7. Qc2 Ncd6 8. f3 Nf6 9. c5 Nf7 10. cxb6 cxb6 11. Bg3 Rc8 12. Ba6 Rc6 13. Bb5 Rc8 14. Ba6 Rc6 15. Bb5 Nh5 16. Bh2 Rc8 17. Ba6 Rc6 18. Bb5 Rc8 19. Ba6 Rc6
Sample game 2 (1/2-1/2)
1. b4 g6 2. c4 b6 3. h4 h5 4. e3 e5 5. Nc3 O-O 6. Nc2 Nf6 7. Rh3 Ne7 8. d4 e4 9. Rd1 d5 10. b5 c6 11. bxc6 Bxc6 12. Nb4 Bd7 13. cxd5 Bg4 14. Rg3 Bxd1 15. Qxd1 Qd6 16. Qb3 Kh7 17. Nb5 Qd7 18. Nc6 Nxc6 19. dxc6 Qxc6 20. Bb4 Ng4 21. Bxf8 Rxf8 22. Nxa7 Qd7 23. Qxb6 Ra8 24. Nb5 Rc8 25. Qd6 Qf5 26. Qf4 Rc1 27. Qxf5 gxf5 28. Rxg4 hxg4 29. g3 Kg6 30. Nd6 Bg7 31. Kg2 Bf8 32. Nc4 Bb4 33. a3 Be1 34. Be2 Kf6 35. Ne5 Rc2 36. Kf1 Ba5 37. a4 Kg7 38. Bb5 Rc1+ 39. Kg2 Be1 40. Kf1 Ba5+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 122 / 419 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): brnqnkrb/pppppppp/8/8/8/8/PPPPPPPP/NQRNBBKR w CHbg - 0 1
Mirror twin: White 837 vs Black 723 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 486.