White 28 vs Black 132
White starts from setup 28 (NBQNRKBR), Black from setup 132 (NBBRQNKR). 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. 28, Black by position No. 132, 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 #28 N B Q N 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 28 gives White +0.25 (Morozov Balance Index, 400M nodes).
Black: setup #132 N B B R Q N K R
King on the g-file, rooks on d, h, queen on the e-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 132 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 never left ±4 centipawns of equality, 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 -7 and +18 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 28 gives White +0.25 and setup 132 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 f3, and 3 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 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 | 17 | -1 | 1. h4 h5 2. Bh2 e5 3. c4 d6 4. Nb3 Qe7 |
| S1 | 500 000 | 21 | -3 | 1. h4 h5 2. Bh2 e5 3. c4 c6 4. Nb3 Qe7 |
| S2 | 2 000 000 | 23 | +18 | 1. h4 h5 2. d4 c6 3. Nb3 d5 4. c3 Nb6 |
| S3 | 8 000 000 | 28 | +12 | 1. Nb3 d5 2. d4 Nb6 3. c3 h5 4. h4 c6 |
| S4 | 32 000 000 | 35 | -7 | 1. Nb3 d5 2. d4 Nb6 3. c3 c6 4. h4 h5 |
| S5 | 128 000 000 | 41 | +8 | 1. d4 d5 2. Nb3 c6 3. c3 Nb6 4. f3 f5 |
| S6 | 400 000 000 | 45 | +4 | 1. d4 d5 2. c3 c5 3. f3 cxd4 4. cxd4 h5 |
| S7 | 800 000 000 | 52 | 0 | 1. d4 d5 2. c3 Nb6 3. h4 f6 4. Bh2 e5 |
| S8 | 1 600 000 000 | 56 | 0 | 1. d4 d5 2. c3 Nb6 3. h4 f6 4. Bh2 e5 |
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: -9
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 +79, Black +172, difference -93. 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 | 46 | 1. f3 d5 2. d4 c6 3. c3 f6 4. h4 e5 5. Nf2 Ne6 |
| 2 | 0 | 46 | 1. d4 d5 2. c3 c5 3. f3 cxd4 4. cxd4 h5 5. Be3 Nb6 |
| 3 | -1 | 46 | 1. Nb3 d5 2. d4 Nb6 3. f3 c6 4. c3 f6 5. h4 e5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 29 cp, mean 4.2 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | h4 | +29 | d5 | -23 |
| 2 | d4 | +9 | c6 | +9 |
| 3 | c3 | +3 | Nb6 | +3 |
| 4 | Nb3 | +4 | h5 | +11 |
| 5 | f3 | +4 | Nc4 | +4 |
| 6 | Nd2 | +4 | Bf4 | +8 |
| 7 | e3 | +2 | Bg3 | 0 |
| 8 | Bf2 | +4 | Nxd2+ | 0 |
| 9 | Qxd2 | 0 | Bc7 | 0 |
| 10 | Bg1 | +10 | Rh6 | +4 |
| 11 | Nf2 | -4 | c5 | +8 |
| 12 | Nd3 | +9 | c4 | +6 |
| 13 | Nf4 | -1 | b5 | -7 |
| 14 | Bh2 | 0 | e5 | -14 |
| 15 | Ne2 | +4 | f6 | 0 |
| 16 | Ng3 | 0 | Ng6 | 0 |
| 17 | Nf5 | 0 | Bxf5 | 0 |
| 18 | Bxf5 | 0 | Nxh4 | -13 |
| 19 | Bc2 | -17 | Ng6 | -12 |
| 20 | O-O-O | -6 | Qf7 | 0 |
| 21 | Kb1 | -3 | Bb6 | 0 |
| 22 | Rdf1 | -7 | h4 | +7 |
| 23 | g4 | +6 | h3 | 0 |
| 24 | a3 | 0 | O-O-O | 0 |
| 25 | e4 | 0 | exd4 | 0 |
| 26 | cxd4 | 0 | Ne7 | 0 |
| 27 | a4 | 0 | Nc6 | 0 |
| 28 | exd5 | 0 | Rxd5 | 0 |
| 29 | axb5 | 0 | Rxb5 | 0 |
| 30 | Ba4 | 0 | Qg6+ | 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 50.0 moves.
Sample game 1 (1/2-1/2)
1. f3 c6 2. h4 Nb6 3. h5 d5 4. d4 h6 5. c3 Nh7 6. Nb3 O-O 7. Nf2 f5 8. Nd3 Bd6 9. Nf4 Nc4 10. Bh2 Nf6 11. Kg1 Bxf4 12. Bxf4 Nxh5 13. Bc7 Rd7 14. Be5 Rd6 15. Nc5 Nxe5 16. dxe5 Rd8 17. Kf2 b6 18. Nb3 f4 19. Nd4 Ng3 20. Rh4 c5 21. Qc2 Nf5 22. Rxf4 cxd4 23. g4 dxc3 24. Rg1 e6 25. gxf5 exf5 26. Qxc3 Qe7 27. Qd4 Rde8 28. Qxd5+ Kh8 29. Rg6 Be6 30. Qd3 Rd8 31. Rd4 Rxd4 32. Qxd4 Kh7 33. Rg1 Kg8 34. Qd6 Qxd6 35. exd6 Rd8 36. Rd1 Kf7 37. f4 Kf6 38. Kg3 g5 39. a3 h5 40. fxg5+ Kxg5 41. Rd4 Kf6 42. Rh4 Kg5 43. Rd4 Kf6 44. Rh4 Rxd6 45. Rxh5 Rd2 46. Bd3 Ke5 47. Rh7 a5 48. Re7 Kd6 49. Rh7 Rxb2 50. Kf4 Bd5 51. Ke3 Kc5 52. Bxf5 Rb3+ 53. Bd3 Rxa3 54. Rh5 Kd6 55. Rh6+ Kc5 56. Rh5
Sample game 2 (1/2-1/2)
1. Nb3 d5 2. d4 c6 3. c3 Nb6 4. h4 Nfd7 5. h5 O-O 6. Ne3 Nf6 7. f3 e5 8. dxe5 Bxe5 9. Nf5 Bxf5 10. Bxf5 Nc4 11. Bf2 Qe7 12. Bd3 Rfe8 13. g4 Qc7 14. Nd4 Bf4 15. e3 Bg3 16. g5 Bxf2 17. Kxf2 Nd7 18. Qc2 Nf8 19. f4 Nd6 20. h6 g6 21. c4 dxc4 22. Bxc4 Ne4+ 23. Kg2 c5 24. Nf3 Qd7 25. Kg1 b5 26. Bf1 c4 27. Bg2 a6 28. Ne5 Rxe5 29. fxe5 Nxg5 30. Rh4 Nfe6 31. Qf2 Qe7 32. Rd4 Nxd4 33. exd4 Qf8 34. d5 Qxh6 35. e6 fxe6 36. dxe6 Re8 37. Qe3 Qh4 38. e7 Qg4 39. Kh2 Qh4+ 40. Kg1 Qg4 41. Kf2 h5 42. Bd5+ Kh7 43. Bc6 Nh3+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 28 / 132 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): nbbrqnkr/pppppppp/8/8/8/8/PPPPPPPP/NBQNRKBR w EHdh - 0 1
Mirror twin: White 940 vs Black 830 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 157.