White 45 vs Black 588
White starts from setup 45 (NNQBRKBR), Black from setup 588 (QBRNKRBN). In the encyclopedia since 2026-11-01: 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. 45, Black by position No. 588, 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 #45 N N Q B R K B R
King on the f-file, rooks on e, h, queen on the c-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 45 gives White +0.31 (Morozov Balance Index, 400M nodes).
Black: setup #588 Q B R N K R B N
King on the e-file, rooks on c, f, queen on the a-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 588 gives White +0.21 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±5 centipawns of equality, 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±15 cp.
For comparison, in symmetric play setup 45 gives White +0.31 and setup 588 gives White +0.21: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.
The engine's first choice for White is d4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the largest swing was 45 cp (around move 27), ending at -41 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 | 16 | +6 | 1. f3 c5 2. Bf2 b6 3. c4 f5 4. d3 Be6 |
| S1 | 500 000 | 18 | +1 | 1. f3 c5 2. Bf2 b6 3. c4 f5 4. e3 Qc6 |
| S2 | 2 000 000 | 23 | -7 | 1. d3 f5 2. c4 c5 3. Nc3 a6 4. f3 b5 |
| S3 | 8 000 000 | 28 | -13 | 1. d4 c5 2. dxc5 Rxc5 3. Nb3 Rc8 4. c3 b5 |
| S4 | 32 000 000 | 35 | -15 | 1. d4 c5 2. dxc5 Rxc5 3. Nb3 Rc8 4. c3 f5 |
| S5 | 128 000 000 | 40 | -14 | 1. d4 c5 2. dxc5 Rxc5 3. c3 b5 4. f3 Rc8 |
| S6 | 400 000 000 | 45 | +5 | 1. d4 c5 2. dxc5 Rxc5 3. Nb3 Rc8 4. c3 b5 |
| S7 | 800 000 000 | 54 | 0 | 1. d4 c5 2. dxc5 Rxc5 3. Nb3 Rc8 4. c3 f5 |
| S8 | 1 600 000 000 | 57 | 0 | 1. d4 c5 2. dxc5 Rxc5 3. Nb3 Rc8 4. c3 f5 |
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: -5
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 +50, Black +30, difference +20. 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 | +19 | 42 | 1. d4 c5 2. dxc5 Rxc5 3. Nb3 Rc8 4. f3 f5 5. c3 b5 |
| 2 | -14 | 41 | 1. b4 a5 2. Qa3 f5 3. f3 c6 4. bxa5 Bd6 5. Bc5 Bxc5 |
| 3 | -31 | 41 | 1. c4 f5 2. d3 c5 3. Nc3 Ng6 4. f3 b6 5. Bf2 Bf7 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 45 cp, mean 24.7 cp, final -41 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +2 | c5 | -12 |
| 2 | dxc5 | -14 | Rxc5 | -23 |
| 3 | Nb3 | -18 | Rc8 | -13 |
| 4 | c3 | 0 | b5 | -12 |
| 5 | Bc2 | -8 | f5 | -4 |
| 6 | f3 | -9 | Ne6 | -13 |
| 7 | Rd1 | -7 | a6 | -7 |
| 8 | Qd2 | 0 | Qc6 | 0 |
| 9 | a4 | -7 | b4 | -5 |
| 10 | Rc1 | 0 | bxc3 | 0 |
| 11 | Nxc3 | -1 | Qb7 | 0 |
| 12 | g3 | -17 | Ng6 | -34 |
| 13 | Na5 | -43 | Qb4 | -34 |
| 14 | Nb3 | -35 | Bd6 | -30 |
| 15 | Nd5 | -27 | Qxd2 | -35 |
| 16 | Nxd2 | -31 | Nd8 | -28 |
| 17 | Nc3 | -24 | Nc6 | -31 |
| 18 | Bd3 | -34 | Nb4 | -30 |
| 19 | Bb1 | -33 | Rb8 | -33 |
| 20 | Bd4 | -38 | e5 | -41 |
| 21 | Ba7 | -35 | Rb7 | -42 |
| 22 | Bf2 | -38 | Bc7 | -32 |
| 23 | Kg2 | -43 | Ne7 | -44 |
| 24 | e4 | -39 | f4 | -28 |
| 25 | b3 | -32 | Rf6 | -33 |
| 26 | Rhd1 | -38 | Rc6 | -37 |
| 27 | Ne2 | -43 | g5 | -45 |
| 28 | Rxc6 | -37 | Nexc6 | -35 |
| 29 | h4 | -40 | h6 | -33 |
| 30 | hxg5 | -36 | hxg5 | -41 |
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 32.0 moves.
Sample game 1 (1/2-1/2)
1. f3 Ng6 2. Nb3 b6 3. h4 c5 4. h5 Ne5 5. Bf2 f5 6. Kg1 a5 7. d4 cxd4 8. Nxd4 Bxa2 9. Nc3 Be6 10. e4 f4 11. Rh4 O-O 12. Rxf4 Rxf4 13. Qxf4 Nd3 14. Qh4 Nxe1 15. Nd5 Bxd5 16. Nf5 Bd6 17. Qg5 Ne6 18. Nh6+ Kh8 19. Nf7+ Kg8 20. Nh6+ Kh8 21. Nf7+ Kg8
Sample game 2 (1/2-1/2)
1. f3 f5 2. Bf2 c5 3. c4 b6 4. e3 g5 5. d3 Qc6 6. h4 Qh6 7. Kg1 f4 8. Nb3 Ng6 9. hxg5 Qxg5 10. Nc3 fxe3 11. Bxe3 Nf4 12. Qd2 Rc6 13. Ne4 Qf5 14. d4 Rg6 15. Bxf4 Bxf4 16. Qc3 Ne6 17. Bc2 cxd4 18. Nxd4 Nxd4 19. Qxd4 Kd8 20. Re2 Bc7 21. Kf1 Be5 22. Qd3 Bxb2 23. Rh4 Be5 24. c5 Bc7 25. Qb5 Qd5 26. Qa4 Qc6 27. Qxc6 Rxc6 28. Ba4 Rg6 29. Rd2 Bc4+ 30. Kf2 Be6 31. c6 h6 32. cxd7 Bc4 33. g3 Be6 34. Bb5 Rg4 35. Rxg4 Bxg4 36. Rd3 Be6 37. a4 Rf5 38. Rd1 Rh5 39. Ke3 Rh2 40. g4 Bb3 41. Rb1 Bd5 42. Rd1 Ba8 43. g5 Bb7 44. Bc4 Bxe4 45. Kxe4 Rh4+ 46. Kd5 e6+ 47. Kxe6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 45 / 588 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): qbrnkrbn/pppppppp/8/8/8/8/PPPPPPPP/NNQBRKBR w EHcf - 0 1
Mirror twin: White 920 vs Black 284 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 205.