White 86 vs Black 735
White starts from setup 86 (NNBRKBRQ), Black from setup 735 (RKNQNRBB). In the encyclopedia since 2026-10-15: 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. 86, Black by position No. 735, 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 #86 N N B R K B R Q
King on the e-file, rooks on d, g, queen on the h-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 86 gives White +0.34 (Morozov Balance Index, 400M nodes).
Black: setup #735 R K N Q N R B B
King on the b-file, rooks on a, f, 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 735 gives White +0.37 (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 -25 and +7 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 86 gives White +0.34 and setup 735 gives White +0.37: 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 d3, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 47 cp (around move 7), ending at 0 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 | 15 | -15 | 1. c4 f5 2. d3 g6 3. g3 c6 4. Bg2 e5 |
| S1 | 500 000 | 18 | +4 | 1. c4 f5 2. d3 g6 3. g3 c6 4. Bg2 a5 |
| S2 | 2 000 000 | 22 | 0 | 1. c4 f5 2. d3 c6 3. g3 g5 4. Nc3 e5 |
| S3 | 8 000 000 | 26 | -25 | 1. c4 f5 2. d3 e5 3. g3 g5 4. Bg2 c6 |
| S4 | 32 000 000 | 31 | +7 | 1. d3 f5 2. c4 e5 3. h4 c6 4. g3 g6 |
| S5 | 128 000 000 | 37 | +2 | 1. c4 f5 2. d3 e5 3. h4 d5 4. g4 f4 |
| S6 | 400 000 000 | 45 | 0 | 1. c4 f5 2. d3 e5 3. Nc3 g5 4. Nc2 e4 |
| S7 | 800 000 000 | 52 | 0 | 1. c4 f5 2. d3 e5 3. Nc3 g5 4. Nc2 e4 |
| S8 | 1 600 000 000 | 57 | 0 | 1. c4 f5 2. d3 e5 3. Nc3 g5 4. Nc2 e4 |
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: +1
- Lc0 0.32.1: -10
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 +81, difference -21. 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 | -11 | 38 | 1. d3 f5 2. c4 e5 3. Nc3 g5 4. Nc2 c6 5. g4 f4 |
| 2 | -17 | 37 | 1. c4 f5 2. d3 e5 3. Nc3 g5 4. Nc2 a5 5. g3 Ng7 |
| 3 | -26 | 37 | 1. g4 g6 2. d4 Ned6 3. Bh6 Re8 4. e4 e5 5. d5 f5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 47 cp, mean 9.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -33 | f5 | -23 |
| 2 | d3 | -10 | e5 | +9 |
| 3 | h4 | +28 | d5 | -6 |
| 4 | g4 | -1 | fxg4 | -10 |
| 5 | Rxg4 | -12 | g6 | -22 |
| 6 | Bh6 | -19 | Nf6 | -30 |
| 7 | Bxf8 | -20 | Nxg4 | -47 |
| 8 | Bc5 | -40 | b6 | -31 |
| 9 | Ba3 | -22 | a5 | -26 |
| 10 | Nc2 | -16 | d4 | -12 |
| 11 | Nd2 | -5 | c5 | 0 |
| 12 | Ne4 | 0 | Ra7 | 0 |
| 13 | b3 | 0 | Be6 | 0 |
| 14 | Bc1 | 0 | Bf5 | 0 |
| 15 | Bg2 | 0 | Bxe4 | 0 |
| 16 | Bxe4 | +9 | Rf7 | +2 |
| 17 | Bf3 | +8 | h5 | 0 |
| 18 | Bg5 | 0 | Qd7 | +3 |
| 19 | Qg1 | +5 | Nd6 | +12 |
| 20 | Bd5 | +14 | Rf8 | +12 |
| 21 | f3 | +14 | Nf6 | +8 |
| 22 | Bh6 | +12 | Bg7 | +10 |
| 23 | Qxg6 | +9 | Bxh6 | +5 |
| 24 | Qxh6 | +3 | Qe7 | +5 |
| 25 | Qg5 | +2 | Nxd5 | +3 |
| 26 | cxd5 | 0 | Qxg5 | 0 |
| 27 | hxg5 | 0 | Rg8 | 0 |
| 28 | Kf2 | 0 | Rxg5 | 0 |
| 29 | e4 | 0 | dxe3+ | +3 |
| 30 | Nxe3 | 0 | Kc7 | 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 39.0 moves.
Sample game 1 (1/2-1/2)
1. c4 f5 2. d3 c6 3. g3 g5 4. Bxg5 Bxb2 5. Nd2 Qa5 6. Bh3 Qxa2 7. O-O Nc7 8. Bh6 Rf6 9. Bg5 Ne6 10. Bxf6 Bxf6 11. Nab3 Nd6 12. Qf3 Ng5 13. Qh5 a5 14. e4 Nxh3+ 15. Qxh3 a4 16. Nc5 Kc7 17. exf5 Qb2 18. Nce4 a3 19. Nxf6 Qxf6 20. g4 a2 21. Qg3 Kc8 22. Ra1 b5 23. Qf4 Ra4 24. Rfe1 bxc4 25. dxc4 Qb2 26. h3 Nxc4 27. Nxc4 Rxc4 28. Qe5 Rc2 29. f6 exf6 30. Qa5 Be6 31. Rad1 Qb3 32. Re3 Rc3 33. Qa8+ Kc7 34. Qa7+ Kd8 35. Qa5+ Kc8 36. Qa8+ Kc7 37. Qa7+ Kd8 38. Qa5+
Sample game 2 (1/2-1/2)
1. c4 f5 2. d3 a5 3. g3 c6 4. Bg2 e5 5. h4 g6 6. O-O Nc7 7. Nc3 Ne6 8. Nc2 Bg7 9. b3 Bf7 10. e3 g5 11. hxg5 Qxg5 12. e4 f4 13. d4 a4 14. b4 Bh5 15. f3 Nd6 16. d5 cxd5 17. cxd5 Nc7 18. Qh2 fxg3 19. Bxg5 gxh2+ 20. Kxh2 Ncb5 21. Nxb5 Nxb5 22. Ne3 Bf6 23. Bh6 Rg8 24. Nf5 Bg6 25. Bh3 Bxf5 26. Bxf5 d6 27. Rg1 Ka7 28. Be6 Rxg1 29. Rxg1 Nd4 30. Kh3 Nxf3 31. Rg2 Nd4 32. a3 Bd8 33. Bd7 Be7 34. Rf2 Rg8 35. Rf7 Bg5 36. Bxg5 Rxg5 37. Bxa4 Kb6 38. Kh4 Rg8 39. Rf6 Kc7 40. Rf7+ Kb6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 86 / 735 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): rknqnrbb/pppppppp/8/8/8/8/PPPPPPPP/NNBRKBRQ w DGaf - 0 1
Mirror twin: White 870 vs Black 416 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 372.