White 9 vs Black 772
White starts from setup 9 (QNNBBRKR), Black from setup 772 (QBBRKNRN). In the encyclopedia since 2026-10-10: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #9 Q N N B B R K R
King on the g-file, rooks on f, 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 9 gives White +0.22 (Morozov Balance Index, 400M nodes).
Black: setup #772 Q B B R K N R N
King on the e-file, rooks on d, g, queen on the a-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 772 gives White +0.32 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±3 centipawns of equality, reaching search depth 51.
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 -27 and +16 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 9 gives White +0.22 and setup 772 gives White +0.32: 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 c4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the largest swing was 40 cp (around move 6), ending at 0 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 3, drawn 7, Black won 0 (White scored 65.0%).
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 | +16 | 1. c4 c5 2. h4 b6 3. e3 Bb7 4. f3 f5 |
| S1 | 500 000 | 20 | +3 | 1. h4 c5 2. b4 c4 3. e3 b6 4. f4 Bb7 |
| S2 | 2 000 000 | 22 | -13 | 1. f4 d5 2. e3 f6 3. h4 Nf7 4. c4 dxc4 |
| S3 | 8 000 000 | 24 | -9 | 1. h4 c5 2. f4 d5 3. b4 b6 4. bxc5 bxc5 |
| S4 | 32 000 000 | 32 | -27 | 1. h4 d5 2. b4 b6 3. d4 f6 4. Nd2 Ne6 |
| S5 | 128 000 000 | 42 | 0 | 1. c4 g5 2. f3 Nhg6 3. Nc3 c5 4. e3 b6 |
| S6 | 400 000 000 | 45 | 0 | 1. c4 g5 2. f3 Nhg6 3. Nc3 c5 4. e3 b6 |
| S7 | 800 000 000 | 47 | 0 | 1. c4 g5 2. f3 b5 3. cxb5 g4 4. Nc3 Bb7 |
| S8 | 1 600 000 000 | 51 | -3 | 1. c4 g5 2. f3 b5 3. cxb5 g4 4. Nc3 Bb7 |
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: +8
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 +16, Black +111, difference -95. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 3 White wins, 7 draws, 0 Black wins, White scored 65.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 39 | 1. c4 c5 2. Nc3 g5 3. f3 Nhg6 4. e3 h5 5. h4 gxh4 |
| 2 | -29 | 39 | 1. b4 d5 2. d4 b6 3. e3 Nd7 4. Nd3 c6 5. f4 O-O |
| 3 | -36 | 38 | 1. h4 d5 2. b4 f6 3. d4 Nf7 4. Nd2 Ne6 5. e3 b6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 40 cp, mean 17.5 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | h4 | -9 | c5 | -28 |
| 2 | b4 | -29 | cxb4 | -28 |
| 3 | Qb2 | -21 | Ne6 | -22 |
| 4 | e3 | -22 | b5 | -29 |
| 5 | Qxb4 | -31 | a6 | -31 |
| 6 | d4 | -38 | Bb7 | -40 |
| 7 | f3 | -33 | f5 | -30 |
| 8 | c3 | -36 | O-O | -27 |
| 9 | Nd2 | -29 | Nc7 | -33 |
| 10 | Nd3 | -33 | Nd5 | -25 |
| 11 | Qb3 | -32 | Nf7 | -26 |
| 12 | Bf2 | -24 | Nf6 | -30 |
| 13 | c4 | -29 | Rc8 | -29 |
| 14 | Nc5 | -25 | Bc6 | -21 |
| 15 | Bc2 | -19 | e6 | -21 |
| 16 | Bd3 | -27 | Nd6 | -25 |
| 17 | Rc1 | -24 | Nb7 | -22 |
| 18 | Nxb7 | -21 | Qxb7 | -17 |
| 19 | a4 | -17 | bxc4 | -14 |
| 20 | Qxb7 | -11 | Bxb7 | -14 |
| 21 | Rxc4 | -8 | Bd5 | -7 |
| 22 | Rxc8 | -1 | Rxc8 | 0 |
| 23 | O-O | -2 | a5 | 0 |
| 24 | Rb1 | -5 | Bd6 | -5 |
| 25 | e4 | 0 | Rc3 | 0 |
| 26 | exd5 | 0 | Rxd3 | 0 |
| 27 | Nc4 | 0 | Bb4 | 0 |
| 28 | dxe6 | 0 | dxe6 | 0 |
| 29 | Ne5 | 0 | Ra3 | 0 |
| 30 | Rc1 | 0 | h6 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 3, drawn 7, Black won 0 — White scored 65.0%. Average length 45.8 moves.
Sample game 1 (1/2-1/2)
1. c4 c5 2. Nc3 g5 3. Nd3 Ne6 4. f3 b5 5. Nxb5 d5 6. b4 dxc4 7. Nxc5 Ng6 8. Nxe6 Bxe6 9. Nd4 Qd5 10. e3 h5 11. Bc2 Be5 12. Nxe6 Qxe6 13. Qb1 h4 14. Rf2 Bc7 15. O-O Ne5 16. Bh7 Rg7 17. Bf5 Qb6 18. Qb2 e6 19. Bc2 f5 20. Qc3 O-O-O 21. Kh1 Rdg8 22. e4 Nd3 23. Qxc4 Nxe1 24. Bb3 Kb8 25. Re2 g4 26. fxg4 fxe4 27. Rfxe1 Qd6 28. g3 Rxg4 29. Qxe6 Qf8 30. Qc6 Qf3+ 31. Rg2 h3 32. Qb5+ Bb6 33. Qe5+ Bc7 34. Qb5+ Bb6 35. Qe5+ Bc7
Sample game 2 (1/2-1/2)
1. b4 g5 2. c4 b6 3. Nc3 h5 4. e3 Bb7 5. f3 g4 6. Nd5 Nfg6 7. e4 gxf3 8. Rxf3 c6 9. Ne3 d5 10. cxd5 cxd5 11. Ne2 Ne5 12. Rg3 Nhg6 13. O-O dxe4 14. Nd4 Bc8 15. Rg5 Qb7 16. a4 Bg4 17. Bxg4 hxg4 18. Bg3 Qd7 19. Ndf5 f6 20. Qa2 e6 21. Nxg4 Rf8 22. Nd6+ Qxd6 23. Rxg6 Qd4+ 24. Bf2 Qd6 25. Bg3 Qd4+ 26. Bf2 Qd6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 9 / 772 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): qbbrknrn/pppppppp/8/8/8/8/PPPPPPPP/QNNBBRKR w FHdg - 0 1
Mirror twin: White 953 vs Black 190 — a different position (castling squares are fixed), not evaluated by the search.