White 109 vs Black 28
White starts from setup 109 (QNRBNKBR), Black from setup 28 (NBQNRKBR). In the encyclopedia since 2026-10-15: 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. 109, Black by position No. 28, 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 #109 Q N R B N K B R
King on the f-file, rooks on c, h, queen on the a-file; no bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 109 gives White +0.10 (Morozov Balance Index, 400M nodes).
Black: 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).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±1 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 -28 and +29 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 109 gives White +0.10 and setup 28 gives White +0.25: 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 ±24 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 2, drawn 8, Black won 0 (White scored 60.0%).
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 | +29 | 1. c4 h5 2. h4 c5 3. b3 Nc6 4. Nc3 f6 |
| S1 | 500 000 | 16 | -2 | 1. c4 e5 2. h4 c6 3. h5 h6 4. Bc2 f6 |
| S2 | 2 000 000 | 23 | -28 | 1. c4 e5 2. h4 f6 3. b3 c6 4. h5 Ne6 |
| S3 | 8 000 000 | 28 | -8 | 1. c4 e5 2. f3 f5 3. d4 exd4 4. Bxd4 Bf7 |
| S4 | 32 000 000 | 36 | -12 | 1. c4 e5 2. f3 c6 3. c5 f5 4. e4 Be6 |
| S5 | 128 000 000 | 39 | +3 | 1. c4 e5 2. f3 c6 3. c5 h5 4. b4 Nc7 |
| S6 | 400 000 000 | 46 | 0 | 1. d4 d5 2. Nd2 Nb6 3. c4 Nxc4 4. Nxc4 dxc4 |
| S7 | 800 000 000 | 52 | +1 | 1. d4 d5 2. Nd2 Nb6 3. c4 Nxc4 4. Nxc4 dxc4 |
| S8 | 1 600 000 000 | 56 | 0 | 1. d4 d5 2. Nd2 Nb6 3. c4 Nxc4 4. Nxc4 dxc4 |
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 | +1 |
| 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: +3
- 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 +32, Black +79, difference -47. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 2 White wins, 8 draws, 0 Black wins, White scored 60.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +3 | 41 | 1. c4 |
| 2 | 0 | 41 | 1. d4 d5 2. Nd2 Nb6 3. c4 Nxc4 4. Nxc4 dxc4 5. Rxc4 f6 |
| 3 | -1 | 41 | 1. f3 e5 2. c4 c6 3. c5 f5 4. e4 Bf7 5. Be3 d5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 24 cp, mean 7.0 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -4 | e5 | -24 |
| 2 | f3 | -10 | c6 | -12 |
| 3 | c5 | -7 | f5 | -9 |
| 4 | e4 | -8 | Be6 | -10 |
| 5 | Bf2 | -10 | O-O | +1 |
| 6 | O-O | +2 | d5 | +11 |
| 7 | cxd6 | +12 | Nb6 | +5 |
| 8 | b4 | +4 | Bxd6 | 0 |
| 9 | Qb2 | +7 | Kh8 | +1 |
| 10 | a4 | +8 | Bg8 | +3 |
| 11 | d3 | +7 | Qe6 | +14 |
| 12 | Nd2 | +14 | Qh6 | +16 |
| 13 | a5 | +19 | Nc8 | +16 |
| 14 | Nc4 | +5 | Bxc4 | +5 |
| 15 | Rxc4 | +20 | Bc7 | +15 |
| 16 | Rc1 | +15 | b6 | +17 |
| 17 | axb6 | +10 | Bxb6 | +7 |
| 18 | Bb3 | +3 | Ne7 | +17 |
| 19 | Qc3 | +12 | Ne6 | +6 |
| 20 | Bxe6 | +1 | Qxe6 | +13 |
| 21 | Nc2 | +7 | Rd8 | +6 |
| 22 | Bxb6 | +11 | axb6 | +5 |
| 23 | Ne3 | 0 | fxe4 | 0 |
| 24 | dxe4 | 0 | Rd4 | +3 |
| 25 | Nc2 | 0 | Rd6 | 0 |
| 26 | Rcd1 | 0 | Rfd8 | 0 |
| 27 | Rxd6 | 0 | Rxd6 | 0 |
| 28 | Ne3 | +6 | Rd4 | 0 |
| 29 | g3 | 0 | b5 | 0 |
| 30 | Ng4 | 0 | Qd6 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 2, drawn 8, Black won 0 — White scored 60.0%. Average length 50.1 moves.
Sample game 1 (1/2-1/2)
1. c4 e5 2. a4 c5 3. Qa3 d6 4. b4 cxb4 5. Qxb4 Nc6 6. Qa3 f5 7. f3 Bf7 8. Bf2 O-O 9. Nc3 Qd8 10. d3 Nc7 11. O-O Ne6 12. Rb1 Nc5 13. e3 a6 14. d4 Nd7 15. Nd5 f4 16. e4 exd4 17. Be2 Nde5 18. Qa2 Qc8 19. Nxf4 Na5 20. Nd5 Ba7 21. h3 h6 22. Kh1 Nexc4 23. Rc1 Bxd5 24. exd5 b5 25. axb5 axb5 26. Bxc4 Bb6 27. Qb2 Nxc4 28. Qxb5 Na3 29. Qc6 Qxc6 30. dxc6 Re2 31. Nd3 Rc8 32. Nf4 Re5 33. Nd3 Re2 34. Nf4 Re5 35. Ng6 Re6 36. Nh4 d5 37. Nf5 g6 38. Bxd4 gxf5 39. Bxb6 Rexc6 40. Be3 Nc2 41. Bf4 Nd4 42. Rcd1 Ne2 43. Be5 d4 44. Rfe1 Rc1 45. Rxc1 Rxc1 46. Rxc1 Nxc1 47. Bxd4 Ne2 48. Be5 f4 49. g4 fxg3 50. f4 h5 51. Kg2 Kf7 52. f5 h4 53. Kf3 Ng1+ 54. Kg2 Ne2 55. Kf3 Nc1
Sample game 2 (1/2-1/2)
1. h4 f6 2. Bh2 d6 3. b3 e5 4. c4 Bf7 5. d4 c6 6. Nd2 e4 7. e3 O-O 8. a4 f5 9. Be2 Nb6 10. h5 d5 11. a5 Nd7 12. cxd5 Bxd5 13. Bxb8 Qxb8 14. g3 b5 15. Ng2 Ne6 16. Qc3 Rf6 17. b4 Rh6 18. Nf4 Nxf4 19. gxf4 Qd6 20. O-O-O Bf7 21. Rdg1 Nf6 22. Rg5 Nd5 23. Qc5 Qxc5+ 24. bxc5 g6 25. Kb2 Kg7 26. Nf1 Be6 27. Rh2 Nb4 28. Kc3 Na2+ 29. Kb2 Nb4 30. Rg1 Bd5 31. Kc3 Na2+ 32. Kc2 Nb4+ 33. Kc3 Na2+ 34. Kc2 Nb4+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 109 / 28 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): nbqnrkbr/pppppppp/8/8/8/8/PPPPPPPP/QNRBNKBR w CHeh - 0 1
Mirror twin: White 856 vs Black 940 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 443.