White 231 vs Black 187
White starts from setup 231 (NRBQKNRB), Black from setup 187 (NRNKBRQB). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #231 N R B Q K N R B
King on the e-file, rooks on b, g, queen on the d-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 231 gives White +0.25 (Morozov Balance Index, 400M nodes).
Black: setup #187 N R N K B R Q B
King on the d-file, rooks on b, 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 187 gives White +0.27 (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 shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±11 cp.
For comparison, in symmetric play setup 231 gives White +0.25 and setup 187 gives White +0.27: 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 c4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±27 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. Nb3 f5 2. h4 a5 3. a4 g5 4. hxg5 b5 |
| S1 | 500 000 | 18 | -3 | 1. d3 f5 2. g3 g5 3. c4 c6 4. Nc2 Nc7 |
| S2 | 2 000 000 | 22 | +11 | 1. d3 f5 2. Nd2 g5 3. g3 Ncb6 4. c4 d5 |
| S3 | 8 000 000 | 27 | +7 | 1. d3 f5 2. a4 g5 3. c4 c6 4. g3 Nc7 |
| S4 | 32 000 000 | 32 | 0 | 1. d3 f5 2. c4 g5 3. g3 c6 4. a4 Nc7 |
| S5 | 128 000 000 | 49 | 0 | 1. d3 f5 2. c4 g5 3. g3 c6 4. Nd2 Nc7 |
| S6 | 400 000 000 | 54 | 0 | 1. d3 f5 2. c4 g5 3. g3 c6 4. Nd2 Nc7 |
| S7 | 800 000 000 | 57 | 0 | 1. d3 f5 2. c4 g5 3. g3 c6 4. Nd2 Nc7 |
| S8 | 1 600 000 000 | 56 | 0 | 1. d3 f5 2. c4 g5 3. g3 c6 4. Nd2 Nc7 |
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 | not checked |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair held exactly 0.00 up to 1 600 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: +2
- Lc0 0.32.1: +8
Independent confirmations: 2 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 +35, Black +79, difference -44. 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. c4 f5 2. d3 c6 3. g3 Nc7 4. b4 b5 5. Nd2 g5 |
| 2 | 0 | 44 | 1. d3 f5 2. c4 c6 3. g3 Nc7 4. b4 b5 5. Nd2 g5 |
| 3 | -2 | 43 | 1. a4 f5 2. d3 c6 3. g3 Nc7 4. c4 g5 5. Be3 e5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 27 cp, mean 4.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d3 | +27 | f5 | -6 |
| 2 | g3 | -13 | c6 | -11 |
| 3 | c4 | -14 | g5 | 0 |
| 4 | a4 | +4 | Nc7 | -4 |
| 5 | Nc2 | +10 | Bh5 | +7 |
| 6 | Be3 | +11 | e5 | -6 |
| 7 | h3 | -10 | f4 | -9 |
| 8 | Bc5 | -11 | d6 | -23 |
| 9 | Ba3 | -17 | Qf7 | +1 |
| 10 | Be4 | -1 | Ne6 | -3 |
| 11 | g4 | -2 | Bg6 | -7 |
| 12 | Nd2 | -7 | O-O | -8 |
| 13 | O-O | -5 | Bxe4 | -2 |
| 14 | Nxe4 | 0 | Rd8 | 0 |
| 15 | Ne1 | 0 | h6 | 0 |
| 16 | Rc1 | 0 | b6 | 0 |
| 17 | Nf3 | 0 | Bg7 | 0 |
| 18 | Nc3 | 0 | a6 | 0 |
| 19 | b4 | 0 | b5 | +7 |
| 20 | axb5 | +18 | axb5 | 0 |
| 21 | cxb5 | 0 | cxb5 | -13 |
| 22 | Bb2 | 0 | Ne7 | 0 |
| 23 | Ne4 | 0 | Rb6 | 0 |
| 24 | Ned2 | 0 | Nc6 | 0 |
| 25 | d4 | 0 | Nexd4 | 0 |
| 26 | Nxd4 | 0 | exd4 | 0 |
| 27 | Nf3 | 0 | Qd5 | 0 |
| 28 | Qd3 | 0 | Re8 | 0 |
| 29 | Rfd1 | 0 | Re4 | 0 |
| 30 | Nd2 | 0 | Re8 | 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 36.8 moves.
Sample game 1 (1/2-1/2)
1. d3 f5 2. g3 c6 3. c4 g5 4. a4 Nc7 5. Nd2 Bh5 6. b4 Qf7 7. b5 Ne6 8. bxc6 dxc6 9. a5 Nd6 10. Nab3 O-O 11. a6 Rfc8 12. Qc2 b6 13. Bb2 Bf6 14. h4 h6 15. hxg5 hxg5 16. Bg2 Qg7 17. Rh1 Be8 18. O-O-O c5 19. Bxf6 Qxf6 20. e4 Bc6 21. Rde1 Nf7 22. f4 b5 23. exf5 Qxf5 24. Be4 Qf6 25. fxg5 Nfxg5 26. Rhf1 Qg7 27. Bf5 Bd7 28. Nf3 Nxf3 29. Rxf3 Rb6 30. Re4 Rf8 31. Bxe6+ Bxe6 32. Rxf8+ Kxf8 33. Nxc5 Bh3 34. Qf2+ Ke8 35. d4 bxc4 36. Kc2 Qg6 37. Kc3 Rxa6 38. g4 Ra3+ 39. Kxc4 Ra1 40. Qf4 Qb6 41. Rxe7+ Kxe7 42. Qe4+ Kd8
Sample game 2 (1/2-1/2)
1. Nb3 f5 2. g3 c6 3. h4 Nc7 4. d3 h6 5. Be3 b6 6. Qd2 a5 7. c4 c5 8. d4 a4 9. Nc1 Qxc4 10. b3 Qb5 11. Nd3 Nd6 12. dxc5 bxc5 13. Rc1 c4 14. bxc4 Nxc4 15. Qc2 Bf7 16. Nd2 Qa5 17. O-O Nxe3 18. fxe3 g6 19. h5 Nb5 20. hxg6 Bxg6 21. Nc4 Qc7 22. Kh2 Nc3 23. Ncb2 f4 24. exf4 Qd6 25. Nc4 Bxd3 26. Qxc3 Bxc3 27. Nxd6 Bxe2 28. Rf2 Ba6 29. Rxc3 exd6 30. Rd2 Rf5 31. Bf3 Rfb5 32. Rxd6 Rb2+ 33. Kh3 Bf1+ 34. Kg4 Ke7 35. Rxh6 Rg8+ 36. Kf5 Rxg3 37. Re3+ Kd8 38. Rh8+ Kc7 39. Rc3+ Kd6 40. Rh6+ Ke7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 231 / 187 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): nrnkbrqb/pppppppp/8/8/8/8/PPPPPPPP/NRBQKNRB w BGbf - 0 1
Mirror twin (the same position mirrored): White 626 vs Black 769.
Current place in the live balance rating: 166.