White 86 vs Black 55
White starts from setup 86 (NNBRKBRQ), Black from setup 55 (NNBRQKRB). In the encyclopedia since 2026-10-09: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
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 #55 N N B R Q K R B
King on the f-file, rooks on d, g, queen on the e-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 55 gives White +0.31 (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 60.
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 -35 and +15 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 55 gives White +0.31: 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 d4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 50 cp (around move 10), ending at 0 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 0, drawn 9, Black won 1 (White scored 45.0%).
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 | 13 | +15 | 1. g4 O-O 2. d3 Nb6 3. h4 d5 4. Nb3 a5 |
| S1 | 500 000 | 16 | +2 | 1. g4 d5 2. h4 Nb6 3. Nb3 Nc6 4. d4 e5 |
| S2 | 2 000 000 | 21 | -35 | 1. g4 d5 2. d3 c5 3. Bg2 Nc7 4. Nb3 b6 |
| S3 | 8 000 000 | 28 | -23 | 1. g4 Nb6 2. c3 c5 3. b3 O-O 4. Nc2 g6 |
| S4 | 32 000 000 | 33 | -7 | 1. d4 d5 2. g4 Nb6 3. c3 O-O 4. Nc2 e5 |
| S5 | 128 000 000 | 43 | 0 | 1. d4 d5 2. g4 e5 3. Bg5 Rd6 4. Nb3 Nc6 |
| S6 | 400 000 000 | 54 | 0 | 1. d4 d5 2. g4 e5 3. Bg5 Rd6 4. Nb3 Nc6 |
| S7 | 800 000 000 | 55 | 0 | 1. d4 d5 2. g4 e5 3. Bg5 Rd6 4. Nb3 Nc6 |
| S8 | 1 600 000 000 | 60 | 0 | 1. d4 d5 2. g4 e5 3. Bg5 Rd6 4. Nb3 Nc6 |
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: -2
- Lc0 0.32.1: -11
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 +92, difference -32. 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, 9 draws, 1 Black wins, White scored 45.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 47 | 1. d4 d5 2. g3 Nb6 3. Bg2 c6 4. Nb3 f5 5. Nc5 g6 |
| 2 | 0 | 47 | 1. g3 d5 2. d4 Nb6 3. Bg2 c6 4. Nb3 f5 5. Nc5 g6 |
| 3 | 0 | 47 | 1. g4 d5 2. d4 e5 3. Bg5 Rd6 4. Nb3 Nc6 5. Nc3 Nb6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 50 cp, mean 14.4 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g4 | -24 | d5 | -10 |
| 2 | d4 | 0 | Nb6 | 0 |
| 3 | c3 | -6 | O-O | +13 |
| 4 | Bf4 | +37 | Na6 | +22 |
| 5 | e3 | +32 | Qa4 | +34 |
| 6 | a3 | +45 | g6 | +44 |
| 7 | Bh6 | +43 | Bg7 | +45 |
| 8 | Bxg7 | +40 | Kxg7 | +39 |
| 9 | h4 | +38 | c5 | +48 |
| 10 | Qh2 | +41 | f6 | +50 |
| 11 | f4 | +43 | e5 | +25 |
| 12 | fxe5 | +26 | Rde8 | +21 |
| 13 | Nc2 | +14 | fxe5 | +8 |
| 14 | O-O-O | +6 | Qc6 | +6 |
| 15 | h5 | +12 | g5 | +6 |
| 16 | Bxa6 | +3 | bxa6 | +8 |
| 17 | dxc5 | +9 | Qxc5 | +1 |
| 18 | h6+ | +7 | Kh8 | +7 |
| 19 | Nd2 | +9 | Nd7 | +7 |
| 20 | e4 | +2 | d4 | 0 |
| 21 | Rg3 | 0 | Qd6 | +12 |
| 22 | Qg1 | +16 | Qxh6 | +3 |
| 23 | cxd4 | 0 | exd4 | 0 |
| 24 | Nxd4 | 0 | Ne5 | 0 |
| 25 | Nf5 | +5 | Qb6 | 0 |
| 26 | Rc3 | 0 | Qxg1 | 0 |
| 27 | Rxg1 | 0 | Be6 | 0 |
| 28 | Rgg3 | 0 | a5 | 0 |
| 29 | Nf3 | 0 | Nxf3 | 0 |
| 30 | Rgxf3 | 0 | Bxf5 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 9, Black won 1 — White scored 45.0%. Average length 34.6 moves.
Sample game 1 (1/2-1/2)
1. h4 d5 2. g3 Nb6 3. Bg2 g6 4. O-O e5 5. d3 O-O 6. Be3 Qe6 7. Nb3 c6 8. h5 N8d7 9. N1d2 f5 10. Nf3 Rde8 11. Bc1 e4 12. Ng5 Qf6 13. hxg6 Qxg6 14. Nh3 Na4 15. Nf4 Qf7 16. c3 Ne5 17. Nh5 Re7 18. Nd4 Nc5 19. Bg5 Rd7 20. dxe4 dxe4 21. f3 exf3 22. Bxf3 Qxa2 23. Bh6 Re8 24. Qh4 Ng6 25. Qg5 Ne6 26. Qxf5 Nxd4 27. cxd4 Rf7 28. Qc2 Be6 29. Rd2 Qa5 30. Qc3 Qxc3 31. bxc3 a5 32. Ra1 Ra8 33. Nf4 Bc4 34. Rb2 Ra6 35. Ra4 Bb5 36. Ra1 Bc4 37. Ra4 Bb5 38. Ra3 Bc4
Sample game 2 (1/2-1/2)
1. d4 Nb6 2. h4 Nc6 3. d5 Ne5 4. e4 d6 5. Be2 e6 6. dxe6 Qxe6 7. Nb3 Nc6 8. g4 Re8 9. Nc3 O-O 10. f3 a5 11. Nb5 a4 12. Nxc7 Qe7 13. Nxe8 axb3 14. Nxd6 bxa2 15. Bg5 a1=Q 16. Bxe7 Qa5+ 17. c3 Nxe7 18. Qh2 g6 19. h5 g5 20. Nf5 Nc6 21. Nh6+ Kg7 22. Nf5+ Kg8 23. Nh6+ Kg7 24. Nf5+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 86 / 55 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): nnbrqkrb/pppppppp/8/8/8/8/PPPPPPPP/NNBRKBRQ w DGdg - 0 1
Mirror twin: White 870 vs Black 898 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 275.