White 167 vs Black 543
White starts from setup 167 (NRBNKQRB), Black from setup 543 (RNKQNRBB). In the encyclopedia since 2026-10-15: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #167 N R B N K Q R B
King on the e-file, rooks on b, g, queen on the f-file; one 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 167 gives White +0.21 (Morozov Balance Index, 400M nodes).
Black: setup #543 R N K Q N R B B
King on the c-file, rooks on a, f, queen on the d-file; one 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 543 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 57.
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 -19 and 0 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 167 gives White +0.21 and setup 543 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 b3, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 43 cp (around move 3), ending at +14 cp — the position stays playable for both sides.
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 | -19 | 1. g4 f5 2. b3 g6 3. c4 Nd6 4. Nc2 |
| S1 | 500 000 | 18 | -2 | 1. d3 f5 2. c4 d5 3. cxd5 Qxd5 4. g4 Qxa2 |
| S2 | 2 000 000 | 23 | -14 | 1. d3 f5 2. c4 a5 3. Nc3 Nc6 4. g3 e5 |
| S3 | 8 000 000 | 27 | -17 | 1. c4 f5 2. b3 g6 3. d3 d5 4. g3 c6 |
| S4 | 32 000 000 | 35 | -10 | 1. g3 f5 2. b3 Nc6 3. c4 g5 4. Nc2 Nd6 |
| S5 | 128 000 000 | 40 | 0 | 1. g3 f5 2. b3 Nc6 3. c4 e5 4. Nc2 g5 |
| S6 | 400 000 000 | 48 | 0 | 1. g3 f5 2. b3 Nc6 3. c4 g5 4. Nc2 e5 |
| S7 | 800 000 000 | 53 | 0 | 1. g3 f5 2. b3 Nc6 3. c4 g5 4. Nc2 Nd6 |
| S8 | 1 600 000 000 | 57 | 0 | 1. g3 f5 2. b3 Nc6 3. c4 g5 4. Nc2 e5 |
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: -6
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 +36, Black +95, difference -59. 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 | +15 | 43 | 1. b3 f5 2. g3 g5 3. f4 gxf4 4. gxf4 c6 5. Bb2 Bxb2 |
| 2 | +10 | 43 | 1. g3 f5 2. b3 g5 3. f4 gxf4 4. gxf4 c6 5. Bb2 Bxb2 |
| 3 | 0 | 42 | 1. c4 f5 2. b3 g5 3. g3 d5 4. d3 c6 5. a4 dxc4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 43 cp, mean 20.4 cp, final +14 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d3 | -16 | f5 | -22 |
| 2 | b3 | -22 | c6 | -20 |
| 3 | Bd2 | -35 | g5 | -43 |
| 4 | c4 | -24 | d5 | -15 |
| 5 | g3 | -8 | e5 | -4 |
| 6 | Nc2 | -4 | dxc4 | -3 |
| 7 | dxc4 | +7 | Na6 | 0 |
| 8 | e4 | 0 | Be6 | +1 |
| 9 | Qe2 | +8 | f4 | 0 |
| 10 | Nb2 | -10 | g4 | 0 |
| 11 | f3 | 0 | Qf6 | 0 |
| 12 | Nd3 | +24 | O-O-O | +27 |
| 13 | Bc3 | +28 | Qg5 | +24 |
| 14 | O-O-O | +23 | fxg3+ | +30 |
| 15 | Bd2 | +31 | Qh5 | +35 |
| 16 | Rxg3 | +35 | gxf3 | +36 |
| 17 | Bxf3 | +32 | Rxf3 | +27 |
| 18 | Qxf3 | +26 | Qxf3 | +30 |
| 19 | Rxf3 | +31 | Bg4 | +22 |
| 20 | Re3 | +30 | Bxd1 | +20 |
| 21 | Kxd1 | +34 | Bg7 | +18 |
| 22 | Nce1 | +26 | Nf6 | +23 |
| 23 | Re2 | +27 | Nd7 | +30 |
| 24 | Rg2 | +22 | Bf6 | +16 |
| 25 | Ke2 | +27 | Nac5 | +25 |
| 26 | Nf2 | +23 | Ne6 | +24 |
| 27 | Be3 | +27 | a5 | +23 |
| 28 | Nf3 | +27 | Re8 | +21 |
| 29 | Rg4 | +23 | b6 | +16 |
| 30 | Nd3 | +25 | Nd4+ | +14 |
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 43.2 moves.
Sample game 1 (1/2-1/2)
1. c4 f5 2. d3 Nc6 3. Nc3 Nd6 4. g3 e5 5. Qg2 g5 6. O-O Be6 7. Rd1 e4 8. c5 Nf7 9. Nc2 exd3 10. Rxd3 f4 11. Nd4 Bxd4 12. Rxd4 Qf6 13. Ra4 Bf5 14. Ra1 Bc2 15. Rc4 Nfe5 16. Ne4 Bxe4 17. Rxe4 Ng6 18. Rb1 Qf7 19. Ra4 Qf5 20. Qe4 fxg3 21. Qxf5 gxh2+ 22. Kxh2 Rxf5 23. Be3 Nf4 24. Kg3 Nh5+ 25. Kg4 Ng7 26. Kh3 Ne6 27. Kg4 Rf6 28. Bxc6 bxc6 29. f3 h6 30. Rd1 Kd8 31. Rh1 Ke7 32. Kg3 a6 33. Kf2 Kf7 34. Bd4 Rg6 35. b3 Re8 36. Be3 Nf8 37. Bc1 Rge6 38. e3 Kg6 39. Rxa6 Rf6 40. Ra4 h5 41. Rc4 Ne6 42. Kg3 Ng7 43. Rg1 Ne6 44. a4 h4+ 45. Kg4 Rf5 46. b4 Rd5 47. a5 Rd3 48. Re4 Rb8 49. a6 Ra8 50. f4 gxf4 51. exf4 Kf7 52. a7 Rxa7 53. f5 Ng7 54. Bg5 Ra4 55. Bxh4 Rd5 56. Rf1 Rd3 57. Re7+
Sample game 2 (1/2-1/2)
1. b3 f5 2. Bb2 Nc6 3. c4 e5 4. g3 Nf6 5. Nc3 Qe8 6. Nc2 g6 7. O-O-O a5 8. d3 Nb4 9. Kb1 Nxc2 10. Kxc2 e4 11. Qe1 d5 12. Nb5 Qe7 13. Ba3 Qf7 14. Qc3 Bg7 15. cxd5 Rd8 16. dxe4 Nxd5 17. Qf3 fxe4 18. Qxf7 Bxf7 19. Bb2 Bxb2 20. Kxb2 c6 21. Nc3 Nxc3 22. Rxd8+ Kxd8 23. Kxc3 Bd5 24. Kd4 a4 25. Bxe4 axb3 26. Bxd5 bxa2 27. Bxc6 a1=R 28. Rxa1 Rxa1 29. Bxb7 Re1 30. Ke3 g5 31. f4 gxf4+ 32. gxf4 Ke7 33. Be4 h6 34. Kf2 Ra1 35. Bf3 Ra4 36. Kg3 Ke6 37. h4 Ra3 38. h5 Re3 39. Kf2 Ra3 40. e4 Rb3 41. Kg2 Re3 42. Kg3 Rc3 43. Kg4 Rc4 44. e5 Rc7 45. Be2 Kd5 46. Bd3 Rg7+ 47. Kf3 Ra7 48. Bc2 Rc7 49. Bb1 Rc3+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 167 / 543 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): rnkqnrbb/pppppppp/8/8/8/8/PPPPPPPP/NRBNKQRB w BGaf - 0 1
Mirror twin: White 786 vs Black 512 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 467.