White 121 vs Black 209
White starts from setup 121 (NQRBBNKR), Black from setup 209 (BNQBRKNR). 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 #121 N Q R B B N 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 121 gives White +0.19 (Morozov Balance Index, 400M nodes).
Black: setup #209 B N Q B R K N R
King on the f-file, rooks on e, h, queen on the c-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 209 gives White +0.13 (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 53.
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 +31 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 121 gives White +0.19 and setup 209 gives White +0.13: 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 d4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±30 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 | 14 | +31 | 1. d4 Nf6 2. c4 b6 3. b4 c5 4. e3 O-O |
| S1 | 500 000 | 21 | +5 | 1. d4 b6 2. c4 c5 3. e3 e6 4. b4 cxd4 |
| S2 | 2 000 000 | 25 | +14 | 1. d4 b6 2. c4 c5 3. e3 e6 4. b4 cxd4 |
| S3 | 8 000 000 | 28 | +11 | 1. d4 b6 2. c4 c5 3. e3 e6 4. b4 Ne7 |
| S4 | 32 000 000 | 33 | +5 | 1. d4 b6 2. c4 c5 3. e3 h5 4. h4 cxd4 |
| S5 | 128 000 000 | 40 | 0 | 1. d4 b6 2. c4 c5 3. e3 Nf6 4. b4 h5 |
| S6 | 400 000 000 | 47 | 0 | 1. d4 b5 2. e3 Nf6 3. b4 h5 4. Nd2 e5 |
| S7 | 800 000 000 | 48 | 0 | 1. d4 b5 2. b4 Nf6 3. e3 O-O 4. a4 a6 |
| S8 | 1 600 000 000 | 53 | 0 | 1. d4 b6 2. c4 c5 3. e3 e6 4. b4 Ne7 |
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: +12
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 +40, Black +89, difference -49. 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 | 41 | 1. d4 b5 2. e3 Nf6 3. b4 O-O 4. a4 a6 5. Ng3 d6 |
| 2 | -19 | 41 | 1. Nb3 c5 2. d4 c4 3. Nbd2 d5 4. c3 b5 5. a4 a6 |
| 3 | -30 | 41 | 1. c4 c5 2. b4 b6 3. Ng3 Nf6 4. h4 O-O 5. d3 e6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 30 cp, mean 7.5 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +11 | b6 | +20 |
| 2 | c4 | +13 | c5 | +3 |
| 3 | e3 | +9 | cxd4 | +11 |
| 4 | exd4 | +12 | Nc6 | -13 |
| 5 | Nc2 | 0 | e6 | -2 |
| 6 | Nfe3 | +4 | Nf6 | -16 |
| 7 | b4 | -22 | Ne7 | -16 |
| 8 | b5 | -25 | h5 | -18 |
| 9 | Nb4 | -30 | Bc7 | -27 |
| 10 | h4 | -30 | Bf4 | -23 |
| 11 | Nd3 | -23 | Bxe3 | -24 |
| 12 | fxe3 | -17 | Nf5 | -16 |
| 13 | Rh3 | -7 | Ng4 | -7 |
| 14 | Qb4+ | 0 | Kg8 | 0 |
| 15 | Qd2 | 0 | Be4 | 0 |
| 16 | c5 | 0 | Qb7 | -2 |
| 17 | Nf4 | +1 | g6 | +3 |
| 18 | Ne2 | 0 | bxc5 | 0 |
| 19 | dxc5 | 0 | Bxg2 | 0 |
| 20 | c6 | 0 | dxc6 | 0 |
| 21 | Kxg2 | 0 | cxb5+ | 0 |
| 22 | Kg1 | 0 | Kh7 | 0 |
| 23 | Nd4 | 0 | Rc8 | 0 |
| 24 | Bf3 | 0 | Qb6 | -5 |
| 25 | Nxf5 | 0 | exf5 | -14 |
| 26 | Bd5 | -7 | Rc7 | -1 |
| 27 | Rxc7 | 0 | Qxc7 | -7 |
| 28 | Qc3 | 0 | Qe7 | 0 |
| 29 | Qb4 | 0 | Qd7 | -9 |
| 30 | Bb3 | 0 | Rc8 | 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 37.8 moves.
Sample game 1 (1/2-1/2)
1. d4 b6 2. c4 Nf6 3. Bc2 e6 4. e4 c5 5. d5 b5 6. b3 Na6 7. Ne3 Qb8 8. a4 bxa4 9. bxa4 Nb4 10. Bc3 Bc7 11. Qb2 O-O 12. Bxf6 gxf6 13. Qxf6 Be5 14. Qh4 f5 15. exf5 Bf6 16. Qg4+ Kh8 17. fxe6 dxe6 18. O-O Re7 19. Rcd1 exd5 20. cxd5 Bb7 21. Bb3 Bc8 22. Qg3 Be5 23. Qh4 Bf6 24. Qg3 Be5 25. Qh4 Bf6
Sample game 2 (1/2-1/2)
1. d4 Nf6 2. c4 c5 3. dxc5 Qxc5 4. b4 Qc7 5. Nb3 b6 6. Bc3 e6 7. e3 Be7 8. a3 d6 9. Bb2 Nc6 10. Nbd2 a5 11. Ng3 Ne5 12. f4 Qc6 13. e4 Ng6 14. f5 Ne5 15. O-O O-O 16. Qc2 axb4 17. axb4 exf5 18. Nxf5 Nxe4 19. b5 Qb7 20. Bf3 Nxf3+ 21. gxf3 Nxd2 22. Qxd2 f6 23. Ba3 Qd7 24. Qf4 h5 25. Rce1 Bd8 26. Bxd6 g5 27. Nh6+ Kh8 28. Rxe8 Rxe8 29. Qf5 Qg7 30. Ra1 Bxf3 31. Qxf3 Qxh6 32. Qc6 Qg6 33. c5 bxc5 34. b6 Bxb6 35. Qxb6 Qe4 36. Qb2 Qg4+ 37. Bg3 Rf8 38. Kh1 h4 39. Bd6 Qe4+ 40. Kg1 Qg4+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 121 / 209 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): bnqbrknr/pppppppp/8/8/8/8/PPPPPPPP/NQRBBNKR w CHeh - 0 1
Mirror twin (the same position mirrored): White 841 vs Black 651.