White 76 vs Black 140
White starts from setup 76 (NBNRKQBR), Black from setup 140 (NBRQNKBR). 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. 76, Black by position No. 140, 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 #76 N B N R K Q B R
King on the e-file, rooks on d, h, queen on the f-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 76 gives White +0.29 (Morozov Balance Index, 400M nodes).
Black: setup #140 N B R Q N K B R
King on the f-file, rooks on c, h, queen on the d-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 140 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 never left ±2 centipawns of equality, reaching search depth 59.
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 -18 and +9 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 76 gives White +0.29 and setup 140 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.
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 36 cp (around move 2), ending at 0 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 | 11 | -3 | 1. f4 c5 2. Ncb3 c4 3. Nd4 f6 4. c3 Bf7 |
| S1 | 500 000 | 18 | +1 | 1. f4 c5 2. Ncb3 c4 3. Nd4 f6 4. c3 Nb6 |
| S2 | 2 000 000 | 26 | 0 | 1. f4 c5 2. Ncb3 c4 3. Nd4 f6 4. c3 Bf7 |
| S3 | 8 000 000 | 30 | -18 | 1. f4 c5 2. Ncb3 c4 3. Nd4 f6 4. c3 Nb6 |
| S4 | 32 000 000 | 36 | +3 | 1. d4 Nb6 2. c3 Nc4 3. Nd3 f5 4. O-O-O c6 |
| S5 | 128 000 000 | 41 | +9 | 1. d4 Nb6 2. c3 Nc4 3. Nd3 f5 4. f3 Bf7 |
| S6 | 400 000 000 | 48 | +2 | 1. d4 Nb6 2. c3 Nc4 3. Nd3 f5 4. f3 Bf7 |
| S7 | 800 000 000 | 53 | 0 | 1. d4 Nb6 2. c3 Nc4 3. Nd3 f5 4. f3 Bf7 |
| S8 | 1 600 000 000 | 59 | 0 | 1. d4 Nb6 2. c3 Nc4 3. Nd3 f5 4. f3 Bf7 |
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: +4
- Lc0 0.32.1: +16
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 +39, Black +47, difference -8. 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 | 42 | 1. d4 Nb6 2. c3 Nc4 3. Nd3 f5 4. f3 Bf7 5. e4 fxe4 |
| 2 | -13 | 42 | 1. c3 c5 2. f4 f6 3. Nd3 b6 4. Qf3 Nac7 5. e4 Be6 |
| 3 | -14 | 42 | 1. f4 c5 2. c3 f6 3. d4 cxd4 4. Bxd4 Bf7 5. Qf2 Nd6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 36 cp, mean 6.6 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f4 | -16 | c5 | -20 |
| 2 | Ncb3 | -20 | c4 | -36 |
| 3 | Nd4 | -20 | f6 | -27 |
| 4 | c3 | -14 | Qc7 | -28 |
| 5 | g3 | -15 | Nb6 | -12 |
| 6 | Qf3 | -16 | Bd5 | -8 |
| 7 | e4 | -5 | Bf7 | -26 |
| 8 | Be3 | +2 | Na4 | +4 |
| 9 | b3 | -3 | Nb2 | -8 |
| 10 | Rc1 | 0 | Nd3+ | -2 |
| 11 | Bxd3 | -6 | cxd3 | -12 |
| 12 | O-O | -14 | O-O | -15 |
| 13 | c4 | -10 | b6 | -12 |
| 14 | Nf5 | -17 | Qd8 | -10 |
| 15 | Rc3 | -12 | e6 | -4 |
| 16 | Nh4 | 0 | g5 | 0 |
| 17 | Ng2 | 0 | Ng7 | 0 |
| 18 | Rxd3 | 0 | d5 | 0 |
| 19 | cxd5 | 0 | exd5 | 0 |
| 20 | fxg5 | 0 | fxg5 | 0 |
| 21 | Rc3 | 0 | Bd6 | 0 |
| 22 | Qg4 | 0 | Rxc3 | 0 |
| 23 | dxc3 | 0 | Bg6 | 0 |
| 24 | Rxf8+ | 0 | Bxf8 | 0 |
| 25 | Bxg5 | 0 | Qc7 | 0 |
| 26 | Bf6 | 0 | Bxe4 | 0 |
| 27 | Nf4 | 0 | Qc5+ | 0 |
| 28 | Bd4 | 0 | Qa3 | 0 |
| 29 | Bxg7 | 0 | Bxg7 | 0 |
| 30 | Qe6+ | 0 | Kf8 | 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 42.1 moves.
Sample game 1 (1/2-1/2)
1. Ncb3 Nb6 2. f3 f6 3. O-O-O e5 4. e4 Qe7 5. Bc5 d6 6. Bxb6 axb6 7. d4 c5 8. d5 c4 9. Nd2 c3 10. bxc3 Ba7 11. c4 Qd7 12. c3 b5 13. cxb5 Rxc3+ 14. Nc2 f5 15. Kb2 Rc8 16. Qd3 Nf6 17. a4 fxe4 18. Nxe4 Nxe4 19. Qxe4 Qc7 20. Ka2 Bf7 21. Na1 Bd4 22. Rc1 Qxc1 23. Rxc1 Rxc1 24. Qf5 g6 25. Qf6 O-O 26. Qxd6 Rc4 27. Nc2 Rc5 28. Nxd4 Rxd5 29. Qa3 exd4 30. Kb2 Rc8 31. Bc2 Rdd8 32. h4 Rc3 33. Qb4 Rdc8 34. Bd1 Rd3 35. Bc2 Rdc3 36. Bd1 R8c4 37. Qd6 Rd3 38. Qb8+ Kg7 39. Qe5+ Kf8 40. Qh8+ Ke7
Sample game 2 (1/2-1/2)
1. c3 c5 2. e4 f6 3. f3 Nb6 4. d4 cxd4 5. Bxd4 Bf7 6. Nd3 Qc7 7. Qe2 Nc4 8. Nb3 O-O 9. Bf2 a5 10. Nd4 Ned6 11. e5 Nxe5 12. Nxe5 fxe5 13. Qxe5 Nc4 14. Qxc7 Rxc7 15. b3 Na3 16. c4 Nxb1 17. Rxb1 d5 18. cxd5 Bxd5 19. Rd1 Rd7 20. O-O Rfd8 21. Nf5 Be6 22. Rxd7 Rxd7 23. Ng3 Rc7 24. Ne2 Kf7 25. Nd4 Rc3 26. Nxe6 Kxe6 27. Re1+ Kd5 28. Rxe7 Bd6 29. Re2 Rc1+ 30. Re1 Rc2 31. Rd1+ Ke6 32. Re1+ Kd5 33. a4 Rb2 34. Rd1+ Kc6 35. Bd4 Rxb3 36. Bxg7 Bc5+ 37. Kf1 b6 38. Ke2 Rb4 39. Ra1 Rb3 40. h4 b5 41. axb5+ Kxb5 42. h5 a4 43. h6 Re3+ 44. Kd2 Re6 45. g4 a3 46. g5 Be3+ 47. Kd1 Bxg5 48. Rxa3 Re3 49. Rxe3 Bxe3 50. Ke2 Bc1 51. Kd3 Kc6 52. Ke4 Kd6 53. Kf5 Ke7 54. Bf6+ Kf7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 76 / 140 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): nbrqnkbr/pppppppp/8/8/8/8/PPPPPPPP/NBNRKQBR w DHch - 0 1
Mirror twin: White 892 vs Black 828 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 333.