White 84 vs Black 120
White starts from setup 84 (NBBNRKRQ), Black from setup 120 (NBQRBNKR). In the encyclopedia since 2026-10-03: 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. 84, Black by position No. 120, 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 #84 N B B N R K R Q
King on the f-file, rooks on e, 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 84 gives White +0.17 (Morozov Balance Index, 400M nodes).
Black: setup #120 N B Q R B N K R
King on the g-file, rooks on d, h, queen on the c-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 120 gives White +0.40 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 62.
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 ±13 cp.
For comparison, in symmetric play setup 84 gives White +0.17 and setup 120 gives White +0.40: 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 11), ending at 0 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 0, drawn 8, Black won 2 (White scored 40.0%).
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 | +3 | 1. d4 c5 2. d5 h5 3. h4 Nb6 4. g3 e6 |
| S1 | 500 000 | 18 | 0 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. h4 Nc4 |
| S2 | 2 000 000 | 23 | -4 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. h4 Nc4 |
| S3 | 8 000 000 | 30 | -13 | 1. d4 d5 2. Nb3 Nb6 3. c3 h5 4. h4 Nc4 |
| S4 | 32 000 000 | 38 | -13 | 1. d4 d5 2. Nb3 Nb6 3. c3 h5 4. h4 Nc4 |
| S5 | 128 000 000 | 48 | 0 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. Ne3 Nc4 |
| S6 | 400 000 000 | 53 | 0 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. Ne3 Nc4 |
| S7 | 800 000 000 | 59 | 0 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. Ne3 Nc4 |
| S8 | 1 600 000 000 | 59 | 0 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. Ne3 Nc4 |
| S9 | 3 200 000 000 | 62 | 0 | 1. d4 d5 2. Nb3 h5 3. c3 Nb6 4. Ne3 Nc4 |
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: -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 +23, Black +142, difference -119. 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, 8 draws, 2 Black wins, White scored 40.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | -5 | 43 | 1. d4 d5 2. Nb3 Nb6 3. c3 Nc4 4. h4 h5 5. Ne3 Nxe3+ |
| 2 | -27 | 43 | 1. Nb3 c5 2. c3 d5 3. d4 cxd4 4. cxd4 Nb6 5. h4 h5 |
| 3 | -26 | 42 | 1. c3 c5 2. Nb3 d5 3. d4 cxd4 4. Nxd4 h5 5. Ne3 e6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 36 cp, mean 5.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | -17 | d5 | -11 |
| 2 | Nb3 | -13 | h5 | -10 |
| 3 | c3 | 0 | Nb6 | 0 |
| 4 | h4 | 0 | Nc4 | -5 |
| 5 | Ne3 | 0 | g6 | -2 |
| 6 | Nxc4 | 0 | dxc4 | 0 |
| 7 | Nc5 | 0 | b6 | 0 |
| 8 | Ne4 | +2 | c5 | 0 |
| 9 | dxc5 | +16 | b5 | +9 |
| 10 | b4 | +19 | cxb3 | +29 |
| 11 | axb3 | +36 | a5 | +18 |
| 12 | b4 | +15 | axb4 | +11 |
| 13 | cxb4 | +14 | Rd4 | +12 |
| 14 | Bb2 | +10 | Rxb4 | +8 |
| 15 | Bxh8 | +9 | Kxh8 | +11 |
| 16 | Qh3 | +7 | Qxh3 | +14 |
| 17 | gxh3 | +17 | Ne6 | +9 |
| 18 | e3 | +6 | Kg7 | +7 |
| 19 | Rc1 | +5 | Bc6 | +6 |
| 20 | Ng3 | 0 | Rb2 | +3 |
| 21 | Nxh5+ | 0 | Kh6 | 0 |
| 22 | Ng3 | 0 | b4 | 0 |
| 23 | Bd3 | 0 | Rd2 | 0 |
| 24 | Bc4 | 0 | Be5 | 0 |
| 25 | h5 | 0 | Ng5 | 0 |
| 26 | hxg6 | 0 | fxg6 | 0 |
| 27 | f4 | +3 | Nxh3 | 0 |
| 28 | Rh1 | 0 | Bxh1 | 0 |
| 29 | Nxh1 | 0 | Bc7 | 0 |
| 30 | Rb1 | 0 | g5 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 8, Black won 2 — White scored 40.0%. Average length 43.2 moves.
Sample game 1 (1/2-1/2)
1. d4 h5 2. Nb3 Nb6 3. Ne3 d5 4. c3 Nc4 5. h4 c6 6. Nxc4 dxc4 7. Nd2 c5 8. d5 Rxd5 9. g3 Qe6 10. Nxc4 Rd8 11. Qe4 Qh3+ 12. Qg2 Qe6 13. Qe4 Qh3+ 14. Qg2 Qe6
Sample game 2 (0-1)
1. d4 h5 2. c3 c5 3. dxc5 h4 4. Nb3 d6 5. cxd6 Bxd6 6. Nd4 Bd7 7. Ne3 g6 8. O-O Ne6 9. Nxe6 Bxe6 10. Rd1 Nb6 11. h3 Kg7 12. Rfe1 f6 13. Rd4 a5 14. Red1 Nc4 15. Nxc4 Bxc4 16. Kf1 a4 17. Qg1 Qe6 18. Re1 Bxa2 19. Bd3 Qd7 20. Rg4 f5 21. Rg5 Kf7 22. f4 e5 23. fxe5 Bxe5 24. Qb6 Qc6 25. Qf2 Qd6 26. Rd1 Bg3 27. Qf3 Rhe8 28. Rxg3 Qxg3 29. Qxb7+ Re7 30. Qf3 Bb3 31. Re1 Rc8 32. Qxg3 hxg3 33. Bg5 Re6 34. Ra1 Bc4 35. Bxc4 Rxc4 36. e3 Rce4 37. Bf4 Kf6 38. Ra2 g5 39. Bxg3 Rxe3 40. Bf2 Re2 41. Rxa4 Rxb2 42. Rb4 Rc2 43. Bd4+ Kg6 44. Rb8 f4 45. Ra8 Kf5 46. Ra5+ Kg6 47. Ra8 Rb2 48. c4 Rc2 49. Rg8+ Kf5 50. Rf8+ Ke4 51. Bf2 Ra6 52. Re8+ Kf5 53. g4+ Kf6 54. Bd4+ Kf7 55. Re2 Rxe2 56. Kxe2 Ke6 57. Kf3 Ra3+ 58. Ke4 Rxh3 59. c5 Rh2 60. Kd3 Rg2 61. c6 Rxg4 62. c7 Kd7 63. Bb6 Rg2 64. Ke4 Rb2 65. Ba5 Re2+ 66. Kf3 Re3+ 67. Kf2 Rg3 68. Ke2 Ra3 69. Bb6 Rb3 70. Ba5 Rb5 71. c8=Q+ Kxc8 72. Bc3 Kd7 73. Bg7 Ke6 74. Kd3 Kf5 75. Kc2 g4 76. Kd3 g3 77. Ba1 Re5 78. Bb2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 84 / 120 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): nbqrbnkr/pppppppp/8/8/8/8/PPPPPPPP/NBBNRKRQ w EGdh - 0 1
Mirror twin: White 878 vs Black 845 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 24.