White 45 vs Black 180
White starts from setup 45 (NNQBRKBR), Black from setup 180 (NBBRNKRQ). In the encyclopedia since 2026-10-21: 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. 180, 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 #180 N B B R N K R Q
King on the f-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 180 gives White +0.12 (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 56.
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 -17 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 45 gives White +0.31 and setup 180 gives White +0.12: 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 h4, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±29 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 | 15 | +21 | 1. h4 d5 2. e4 dxe4 3. Nc3 Nf6 4. Nxe4 Nxe4 |
| S1 | 500 000 | 18 | 0 | 1. h4 d5 2. Nb3 c6 3. d3 g6 4. N1d2 Nf6 |
| S2 | 2 000 000 | 22 | -17 | 1. h4 d5 2. e4 dxe4 3. Nc3 c5 4. Nxe4 b6 |
| S3 | 8 000 000 | 29 | -8 | 1. e4 g5 2. h4 gxh4 3. Rxh4 Qf6 4. Rh1 d5 |
| S4 | 32 000 000 | 35 | 0 | 1. e4 g5 2. Nb3 c6 3. h4 gxh4 4. Rxh4 Qf6 |
| S5 | 128 000 000 | 42 | +10 | 1. h4 d5 2. e4 dxe4 3. Bh2 g5 4. hxg5 Qg7 |
| S6 | 400 000 000 | 46 | 0 | 1. h4 c6 2. e4 g6 3. Nb3 d5 4. d4 dxe4 |
| S7 | 800 000 000 | 55 | 0 | 1. h4 c6 2. e4 g6 3. c3 d5 4. exd5 cxd5 |
| S8 | 1 600 000 000 | 56 | 0 | 1. h4 c6 2. e4 g6 3. c3 d5 4. exd5 cxd5 |
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: +3
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 +70, 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 | 0 | 44 | 1. h4 c6 2. e4 g6 3. c3 d5 4. exd5 cxd5 5. d4 Qf6 |
| 2 | 0 | 44 | 1. e4 c6 2. h4 g6 3. c3 d5 4. exd5 cxd5 5. d4 Qf6 |
| 3 | -11 | 44 | 1. d4 d5 2. h4 c6 3. c3 Nf6 4. Nd2 Nb6 5. e4 dxe4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 29 cp, mean 10.7 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | -8 | g5 | -7 |
| 2 | Nb3 | -2 | c6 | -13 |
| 3 | h4 | -17 | gxh4 | -19 |
| 4 | Rxh4 | -16 | Qf6 | -18 |
| 5 | Rh1 | -11 | d5 | -23 |
| 6 | Bf3 | -25 | dxe4 | -26 |
| 7 | Rxe4 | -29 | Nd6 | -20 |
| 8 | Reh4 | -20 | Bf5 | -24 |
| 9 | d3 | -18 | O-O-O | -20 |
| 10 | Nc3 | -15 | Nb6 | -15 |
| 11 | Nc5 | -11 | Bg6 | -19 |
| 12 | N5e4 | -18 | Nxe4 | -19 |
| 13 | Nxe4 | -9 | Qe6 | -12 |
| 14 | Nc3 | -7 | f5 | -20 |
| 15 | Bh2 | -24 | Bxh2 | -23 |
| 16 | R1xh2 | -12 | Qd6 | -14 |
| 17 | a4 | -13 | Nd7 | -6 |
| 18 | a5 | -3 | Nf6 | -8 |
| 19 | Qf4 | -6 | e5 | -5 |
| 20 | Qb4 | -5 | Rge8 | -3 |
| 21 | Qxd6 | 0 | Rxd6 | -5 |
| 22 | Ra4 | -7 | e4 | -6 |
| 23 | Be2 | 0 | Kb8 | 0 |
| 24 | Rh3 | -7 | Rd7 | -6 |
| 25 | Re3 | -8 | f4 | -10 |
| 26 | Rh3 | 0 | Re5 | 0 |
| 27 | Rh4 | 0 | exd3 | 0 |
| 28 | cxd3 | 0 | f3 | +3 |
| 29 | Bxf3 | +3 | Rxd3 | +1 |
| 30 | Raf4 | 0 | Rd6 | 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 36.9 moves.
Sample game 1 (1/2-1/2)
1. e4 c6 2. h4 g6 3. Nb3 d5 4. exd5 cxd5 5. d4 Qf6 6. Qh6+ Ng7 7. Bh2 Bxh2 8. Rxh2 O-O 9. c3 Qd6 10. Kg1 f6 11. Bc2 Bf5 12. Bxf5 Nxf5 13. Qd2 Rde8 14. Na3 Nb6 15. h5 g5 16. Qc2 e6 17. Nc5 Qc6 18. Rh3 g4 19. Rh1 Kh8 20. g3 Nh6 21. Qd1 Rg8 22. Nc2 e5 23. Nd3 Nf7 24. Kg2 Qd7 25. dxe5 fxe5 26. Rh4 Nc4 27. h6 Rg5 28. Ndb4 Rd8 29. b3 Ncd6 30. Ne3 Nf5 31. Nxf5 Qxf5 32. Nc2 Rg6 33. Ne3 Qe4+ 34. Kf1 Rxh6 35. Rxg4 Qh1+ 36. Ke2 Qh2 37. Qd3 Qh5 38. Qf5 Qxf5 39. Nxf5 Rf6 40. Ne3 d4 41. cxd4 exd4 42. Nc4 d3+ 43. Kf1 Rf8
Sample game 2 (1/2-1/2)
1. h4 c6 2. e4 g6 3. Nb3 d5 4. exd5 cxd5 5. d4 Qf6 6. Qh6+ Ng7 7. Bh2 Bxh2 8. Rxh2 O-O 9. c3 Qd6 10. Kg1 f6 11. Bc2 Bf5 12. Bxf5 Nxf5 13. Qd2 Rde8 14. Na3 Nb6 15. h5 g5 16. Qc2 e6 17. Nc5 Qc6 18. Rh3 g4 19. Rh1 Kh8 20. g3 Nh6 21. Qd1 Rg8 22. Nc2 e5 23. Nd3 Nf7 24. Kg2 Qd7 25. dxe5 fxe5 26. Rh4 Nc4 27. h6 Rg5 28. Ndb4 Rd8 29. b3 Ncd6 30. Ne3 Nf5 31. Nxf5 Qxf5 32. Nc2 Rg6 33. Ne3 Qe4+ 34. Kf1 Rxh6 35. Rxg4 Qh1+ 36. Ke2 Qh2 37. Qd3 Qh5 38. Qf5 Qxf5 39. Nxf5 Rf6 40. Ne3 d4 41. cxd4 exd4 42. Nc4 d3+ 43. Kf1 Rf8
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 45 / 180 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): nbbrnkrq/pppppppp/8/8/8/8/PPPPPPPP/NNQBRKBR w EHdg - 0 1
Mirror twin: White 920 vs Black 782 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 202.