White 87 vs Black 757
White starts from setup 87 (NNBRKRQB), Black from setup 757 (RKBBNNRQ). 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. 87, Black by position No. 757, 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 #87 N N B R K R Q B
King on the e-file, rooks on d, f, queen on the g-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 87 gives White +0.25 (Morozov Balance Index, 400M nodes).
Black: setup #757 R K B B N N R Q
King on the b-file, rooks on a, g, queen on the h-file; no 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 757 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 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 -6 and +21 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 87 gives White +0.25 and setup 757 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 f4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±22 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 | -6 | 1. f4 g5 2. fxg5 d5 3. g3 c6 4. c4 dxc4 |
| S1 | 500 000 | 20 | -3 | 1. f4 h5 2. g3 g5 3. fxg5 h4 4. d3 Ne6 |
| S2 | 2 000 000 | 25 | +21 | 1. f4 g5 2. fxg5 Ne6 3. g3 Nxg5 4. d4 d6 |
| S3 | 8 000 000 | 28 | +20 | 1. g3 g5 2. d4 a5 3. f4 gxf4 4. Bxf4 Ng6 |
| S4 | 32 000 000 | 32 | +4 | 1. f4 g5 2. fxg5 Ne6 3. g3 Nxg5 4. d4 a5 |
| S5 | 128 000 000 | 40 | +1 | 1. f4 g5 2. fxg5 Ne6 3. d4 Nxg5 4. g3 a5 |
| S6 | 400 000 000 | 46 | 0 | 1. g3 g5 2. d4 e5 3. dxe5 Qxe5 4. Nc3 Ne6 |
| S7 | 800 000 000 | 49 | 0 | 1. g3 g5 2. d4 e5 3. dxe5 Qxe5 4. Nc3 Ne6 |
| S8 | 1 600 000 000 | 51 | 0 | 1. f4 g5 2. fxg5 Ne6 3. a4 a5 4. g3 Nxg5 |
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: +3
- Lc0 0.32.1: +2
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 +60, Black +67, difference -7. 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 | 44 | 1. f4 d5 2. d3 c6 3. c4 Bb6 4. Be3 g5 5. fxg5 Qxb2 |
| 2 | 0 | 44 | 1. g3 g5 2. d4 a5 3. f4 gxf4 4. Bxf4 f5 5. Be3 d6 |
| 3 | 0 | 44 | 1. d4 g5 2. g3 a5 3. f4 gxf4 4. Bxf4 h5 5. a4 f5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 22 cp, mean 3.2 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g3 | +22 | g5 | +13 |
| 2 | d4 | +9 | a5 | +11 |
| 3 | f4 | +3 | gxf4 | 0 |
| 4 | Bxf4 | 0 | f5 | -1 |
| 5 | c4 | -8 | Ng6 | -6 |
| 6 | Bd2 | -8 | d6 | -14 |
| 7 | Nc2 | -12 | e5 | +2 |
| 8 | Bd5 | -13 | Rg7 | -17 |
| 9 | Nc3 | -8 | Nf6 | -14 |
| 10 | Bh6 | -8 | Re7 | 0 |
| 11 | Bg2 | 0 | Re8 | 0 |
| 12 | Bh3 | 0 | Ng4 | 0 |
| 13 | Bxg4 | 0 | exd4 | 0 |
| 14 | Nxd4 | 0 | fxg4 | 0 |
| 15 | Ndb5 | 0 | a4 | 0 |
| 16 | Qd4 | 0 | Qxd4 | 0 |
| 17 | Rxd4 | 0 | Ne5 | 0 |
| 18 | Kd2 | 0 | Ra6 | 0 |
| 19 | b3 | 0 | d5 | 0 |
| 20 | Bf4 | 0 | Ng6 | 0 |
| 21 | cxd5 | 0 | Nxf4 | 0 |
| 22 | gxf4 | +5 | Rh6 | +7 |
| 23 | f5 | +9 | Rg8 | 0 |
| 24 | Rb4 | 0 | Bd7 | 0 |
| 25 | Nd4 | 0 | Rxh2 | 0 |
| 26 | f6 | 0 | Rf8 | +2 |
| 27 | Nc6+ | 0 | Bxc6 | 0 |
| 28 | dxc6 | 0 | Rxf6 | 0 |
| 29 | Rxf6 | 0 | Bxf6 | 0 |
| 30 | Rxb7+ | 0 | Kc8 | 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 44.2 moves.
Sample game 1 (1/2-1/2)
1. c4 a5 2. d4 e5 3. Nc2 g5 4. dxe5 f6 5. g3 fxe5 6. Nc3 Nf6 7. Be3 h5 8. O-O-O Ra6 9. a4 Ne6 10. Bd5 Ng4 11. Bd2 Nf6 12. Be3 d6 13. f3 g4 14. Na3 gxf3 15. Rxf3 Nxd5 16. cxd5 Ng5 17. Rff1 Bh3 18. Rf2 Qh7 19. Qh1 Qg6 20. b3 Nh7 21. Kb2 Nf6 22. Rf3 Ng4 23. Nc4 e4 24. Rf4 Bg5 25. Qxe4 Bxf4 26. Qxg6 Rxg6 27. gxf4 Nxe3 28. Nxe3 Rf6 29. Rd4 Rf7 30. Nc4 Ra8 31. e3 b6 32. Rd2 Rg7 33. e4 Rg2 34. Rxg2 Bxg2 35. Ne3 Bh1 36. e5 dxe5 37. fxe5 Kb7 38. e6 Rg8 39. Nf5 Bg2 40. Nh6 Re8 41. Nf7 Kc8 42. Kc1 Bxd5 43. Nxd5 Rxe6 44. Kd2 Kb8 45. Kd3 Re1 46. Nf6 Rd1+ 47. Kc4 Rf1 48. Ne5 Kb7 49. Ne4 c6 50. Nd6+ Kc7 51. Ne8+ Kc8 52. Nd6+ Kc7 53. Ne8+ Kb7 54. Nd6+
Sample game 2 (1/2-1/2)
1. f4 g5 2. fxg5 Ne6 3. h4 h6 4. gxh6 Qxh6 5. g3 c6 6. d4 Qg7 7. d5 cxd5 8. Bxd5 Bb6 9. Qg2 a5 10. h5 Nf6 11. h6 Qg6 12. Nc3 a4 13. Bc4 Qg4 14. Bxe6 fxe6 15. Bf4+ d6 16. Bxd6+ exd6 17. Rxf6 Ra5 18. h7 Rh8 19. Qf3 Qxf3 20. Rxf3 Rxh7 21. b3 Rh1+ 22. Kd2 Rxd1+ 23. Nxd1 Bd7 24. Rd3 Kc7 25. Nc3 Ra8 26. bxa4 Bxa4 27. Rf3 Bd7 28. Nb3 Rg8 29. Rf7 Rg4 30. a4 Kd8 31. Rh7 Bc6 32. Nb5 Rxg3 33. N3d4 Bd7 34. c3 e5 35. Rh8+ Ke7 36. Rh7+ Kd8 37. Rh8+ Ke7 38. Rh7+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 87 / 757 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): rkbbnnrq/pppppppp/8/8/8/8/PPPPPPPP/NNBRKRQB w DFag - 0 1
Mirror twin: White 866 vs Black 394 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 379.