White 81 vs Black 651
White starts from setup 81 (BNNBRKRQ), Black from setup 651 (RNKRBQNB). In the encyclopedia since 2026-10-09: 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. 81, Black by position No. 651, 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 #81 B N N B R K R Q
King on the f-file, rooks on e, g, queen on the h-file; one 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 81 gives White +0.35 (Morozov Balance Index, 400M nodes).
Black: setup #651 R N K R B Q N B
King on the c-file, rooks on a, d, queen on the f-file; one bishop starts in a corner; the knights start on central files. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 651 gives White +0.28 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±5 centipawns of equality, reaching search depth 51.
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 ±12 cp.
For comparison, in symmetric play setup 81 gives White +0.35 and setup 651 gives White +0.28: 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 b3; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±17 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 1, drawn 8, Black won 1 (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 | 14 | -12 | 1. b4 e5 2. Bxe5 Qxb4 3. Nb3 a5 4. O-O a4 |
| S1 | 500 000 | 20 | +4 | 1. b3 Nc6 2. g4 e5 3. Nd3 d6 4. f4 g6 |
| S2 | 2 000 000 | 24 | +9 | 1. b3 Nc6 2. e4 e5 3. O-O d6 4. f4 Bd7 |
| S3 | 8 000 000 | 31 | +11 | 1. b3 Nc6 2. O-O d6 3. f4 e5 4. e4 Bd7 |
| S4 | 32 000 000 | 35 | +8 | 1. b3 d6 2. O-O e5 3. e4 Bd7 4. f4 g6 |
| S5 | 128 000 000 | 41 | +5 | 1. b3 d6 2. O-O e5 3. f4 Nc6 4. e4 exf4 |
| S6 | 400 000 000 | 46 | -5 | 1. b3 d6 2. O-O e5 3. f4 Nc6 4. e4 exf4 |
| S7 | 800 000 000 | 51 | 0 | 1. b3 d6 2. O-O e5 3. f4 Nc6 4. e4 exf4 |
| S8 | 1 600 000 000 | 51 | 0 | 1. b3 d6 2. O-O e5 3. f4 Nc6 4. e4 exf4 |
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: -9
- Lc0 0.32.1: 0
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 +56, Black +63, difference -7. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 1 White wins, 8 draws, 1 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. b3 d6 2. e4 e5 3. O-O Nc6 4. f4 exf4 5. Nd3 Bd7 |
| 2 | -18 | 42 | 1. e3 |
| 3 | -20 | 42 | 1. d4 g6 2. e3 e5 3. b3 exd4 4. exd4 Nc6 5. c3 f5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 17 cp, mean 3.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | b3 | +12 | Nc6 | +17 |
| 2 | e4 | +17 | e5 | +11 |
| 3 | O-O | +11 | d6 | +12 |
| 4 | f4 | +16 | exf4 | 0 |
| 5 | Nd3 | +10 | Bd7 | +10 |
| 6 | Nxf4 | +4 | Nge7 | +5 |
| 7 | g4 | +11 | g6 | +7 |
| 8 | Bxh8 | +1 | Qxh8 | 0 |
| 9 | Qg2 | 0 | Rf8 | 0 |
| 10 | Nc3 | 0 | O-O-O | +10 |
| 11 | Ncd5 | +10 | a6 | +12 |
| 12 | Qg3 | +4 | Kb8 | 0 |
| 13 | h3 | +16 | Nxd5 | +11 |
| 14 | exd5 | +12 | Na7 | +8 |
| 15 | Qc3 | +2 | Qxc3 | -1 |
| 16 | dxc3 | -1 | Nc8 | 0 |
| 17 | c4 | 0 | b5 | 0 |
| 18 | cxb5 | 0 | axb5 | 0 |
| 19 | Nd3 | -1 | h5 | 0 |
| 20 | Kg2 | 0 | hxg4 | 0 |
| 21 | hxg4 | -1 | Rde8 | 0 |
| 22 | Rxe8 | 0 | Bxe8 | 0 |
| 23 | Nf4 | 0 | Rh8 | 0 |
| 24 | Kg3 | 0 | Nb6 | 0 |
| 25 | Bf3 | 0 | Kb7 | 0 |
| 26 | a3 | 0 | Nd7 | 0 |
| 27 | Nd3 | 0 | Rf8 | 0 |
| 28 | Rh1 | 0 | f6 | 0 |
| 29 | Rh7 | 0 | Rf7 | 0 |
| 30 | Rh8 | 0 | Re7 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 1, drawn 8, Black won 1 — White scored 50.0%. Average length 43.2 moves.
Sample game 1 (1-0)
1. b3 Nc6 2. e4 d6 3. g4 e5 4. f4 Nge7 5. Nd3 a5 6. Qf3 Nb4 7. O-O Nxd3 8. cxd3 g6 9. Bb2 Ra6 10. fxe5 dxe5 11. Ba3 Re6 12. Qh3 Qg7 13. Nc3 f5 14. Kh1 Kb8 15. b4 axb4 16. Bxb4 Nc6 17. Bc5 Nd4 18. Nd5 Bd7 19. Bf3 Nxf3 20. Qxf3 f4 21. Rb1 Bc6 22. Rfc1 Qd7 23. Nb4 Bf6 24. Rc3 h5 25. Qd1 Kc8 26. g5 Bxg5 27. a4 f3 28. a5 Ba4 29. Qe1 Kb8 30. a6 b6 31. Nd5 Bb5 32. a7+ Kb7 33. Be3 f2 34. Qxf2 Bxe3 35. Qxe3 Rc6 36. Rcb3 Kxa7 37. Rxb5 Rf8 38. Ra5+ Kb7 39. Ra3 Qg4 40. Rba1 Rf7 41. Ra8 Rc1+ 42. Rxc1 Kxa8 43. Nxc7+ Kb7 44. Nd5 Qf3+ 45. Qxf3 Rxf3 46. Rb1 Kc8 47. Rxb6 Rxd3 48. Rd6 Kb7 49. Rd7+ Kb8 50. Nb6 Rf3 51. Kg2 Rb3 52. Nc4 g5 53. Nxe5 Kc8 54. Rd5 g4 55. Ng6 Rb6 56. Nh4 Rb1 57. Rxh5 Re1 58. d3 Re3 59. Rd5 Rh3 60. Nf5 Kb7 61. Ng3 Rh8 62. Nh1 g3 63. hxg3 Rc8 64. Nf2 Kb6 65. g4 Rc2 66. Kg3 Rc1 67. g5 Rg1+ 68. Kh2 Ra1 69. Ng4 Rf1 70. Kg3 Kb7 71. g6 Rh1 72. Kf4 Rh8
Sample game 2 (1/2-1/2)
1. b3 d6 2. O-O e5 3. f4 g6 4. Nd3 Nc6 5. g3 Bd7 6. Qg2 Re8 7. b4 a6 8. fxe5 Bxe5 9. Bc3 Qh6 10. Rxf7 Bxc3 11. Nxc3 Qxd2 12. Nd5 Ne5 13. Nxe5 Qxe1+ 14. Rf1 Qd2 15. Nxd7 Kxd7 16. Nb6+ cxb6 17. Qxb7+ Ke6 18. Qe4+ Kd7 19. Qb7+ Ke6 20. Qe4+ Kd7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 81 / 651 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): rnkrbqnb/pppppppp/8/8/8/8/PPPPPPPP/BNNBRKRQ w EGad - 0 1
Mirror twin: White 875 vs Black 209 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 353.