White 84 vs Black 653
White starts from setup 84 (NBBNRKRQ), Black from setup 653 (RNKBRQBN). 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. 84, Black by position No. 653, 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 #653 R N K B R Q B N
King on the c-file, rooks on a, e, queen on the f-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 653 gives White +0.22 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±3 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 -4 and +33 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 84 gives White +0.17 and setup 653 gives White +0.22: 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 e4, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±26 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 | 13 | +33 | 1. g4 Nc6 2. c3 a5 3. d4 e6 4. Ne3 f6 |
| S1 | 500 000 | 18 | -4 | 1. e4 e5 2. O-O g6 3. g3 c6 4. c3 f5 |
| S2 | 2 000 000 | 22 | +9 | 1. e4 e5 2. Ne3 Bg5 3. O-O Bxe3 4. fxe3 f6 |
| S3 | 8 000 000 | 27 | +15 | 1. e4 e5 2. O-O g6 3. h4 f5 4. f4 exf4 |
| S4 | 32 000 000 | 33 | +7 | 1. e4 e5 2. Ne3 Bg5 3. O-O f6 4. d3 Bxe3 |
| S5 | 128 000 000 | 42 | 0 | 1. e4 e5 2. O-O g6 3. h4 f5 4. f4 exf4 |
| S6 | 400 000 000 | 49 | -3 | 1. e4 e5 2. O-O g6 3. h4 f5 4. f4 exf4 |
| S7 | 800 000 000 | 52 | 0 | 1. e4 e5 2. Ne3 f6 3. O-O Na6 4. c3 c6 |
| S8 | 1 600 000 000 | 56 | 0 | 1. e4 e5 2. Ne3 Bg5 3. c3 Bxe3 4. Rxe3 Nc6 |
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: -15
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 +99, difference -76. 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 | 0 | 40 | 1. e4 f5 2. exf5 Qxf5 3. O-O Nc6 4. Ne3 Qg6 5. h4 Nd4 |
| 2 | -9 | 40 | 1. d4 f5 2. Nb3 e5 3. dxe5 Rxe5 4. c3 g6 5. O-O Nc6 |
| 3 | -22 | 40 | 1. c3 f5 2. d4 e5 3. dxe5 Rxe5 4. Nb3 Nc6 5. g3 Bd5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 26 cp, mean 2.0 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | +7 | e5 | +10 |
| 2 | O-O | -2 | g6 | +13 |
| 3 | h4 | 0 | f5 | -26 |
| 4 | f4 | -12 | exf4 | -11 |
| 5 | d4 | 0 | Qf6 | +6 |
| 6 | exf5 | -3 | Qxd4+ | 0 |
| 7 | Nf2 | +1 | Rxe1 | -8 |
| 8 | Rxe1 | -1 | gxf5 | 0 |
| 9 | c3 | 0 | Qg7 | 0 |
| 10 | h5 | 0 | Nc6 | -4 |
| 11 | Bxf5 | 0 | Be7 | 0 |
| 12 | Qh3 | 0 | O-O-O | 0 |
| 13 | Bxf4 | 0 | Nf7 | 0 |
| 14 | Qg4 | 0 | Qxg4 | 0 |
| 15 | Bxg4 | 0 | Rf8 | 0 |
| 16 | Nb3 | 0 | Kd8 | 0 |
| 17 | Nd3 | +2 | d6 | 0 |
| 18 | Bf3 | 0 | Bf6 | 0 |
| 19 | Nd2 | 0 | Ng5 | 0 |
| 20 | Bg4 | +5 | Ne7 | 0 |
| 21 | Rf1 | 0 | Ke8 | +7 |
| 22 | Re1 | 0 | Kd8 | 0 |
| 23 | Ne4 | 0 | Nxe4 | 0 |
| 24 | Rxe4 | 0 | Bd5 | 0 |
| 25 | Ra4 | 0 | a6 | 0 |
| 26 | Bh6 | 0 | Rg8 | 0 |
| 27 | Rf4 | 0 | Nc6 | 0 |
| 28 | Bf3 | 0 | Bxf3 | 0 |
| 29 | Rxf3 | 0 | Ke7 | 0 |
| 30 | Kh2 | 0 | Ne5 | 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 48.0 moves.
Sample game 1 (1/2-1/2)
1. g4 f6 2. b3 Nc6 3. c4 e5 4. h4 Be7 5. Be4 Nf7 6. Nc3 Nd6 7. Bd5 Bxd5 8. Nxd5 a5 9. Nc2 f5 10. Ba3 Ne4 11. Nxe7+ Nxe7 12. Rd1 Ra6 13. gxf5 Qxf5 14. Qf3 Rf6 15. Bxe7 Rxe7 16. Qxf5 Rxf5 17. f3 Rf4 18. Ne3 Ref7 19. Ng2 R4f6 20. Ne3 Rf4 21. d3 Nc5 22. Rh1 e4 23. Nd5 Rg4 24. Ne3 Rgf4 25. Nd5 Rg4 26. Ne3
Sample game 2 (1/2-1/2)
1. e4 e5 2. Ne3 Bg5 3. O-O Bxe3 4. Rxe3 Nc6 5. c3 Ng6 6. h4 O-O-O 7. Qh2 f6 8. h5 Nf4 9. d4 Bc4 10. d5 Bxf1 11. Kxf1 Qf7 12. g3 Nxd5 13. exd5 Qxd5 14. Qh4 g5 15. Qe4 Qd1+ 16. Re1 Qxh5 17. Qxh7 Rh8 18. Qxh5 Rxh5 19. Be4 g4 20. b4 Ne7 21. Bg2 Ng6 22. Nc2 f5 23. Ne3 b5 24. Bd2 Rf8 25. Ke2 Rh2 26. Kf1 Rh7 27. Ke2 c6 28. Ra1 d5 29. a4 bxa4 30. Rxa4 e4 31. Bf1 f4 32. Nxg4 fxg3 33. fxg3 Rf3 34. Ra6 Kb7 35. b5 Rxg3 36. Be3 Rh1 37. Rxa7+ Kb8 38. b6 Rxg4 39. Bc5 Nf4+ 40. Kd2 Rh2+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 84 / 653 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): rnkbrqbn/pppppppp/8/8/8/8/PPPPPPPP/NBBNRKRQ w EGae - 0 1
Mirror twin: White 878 vs Black 216 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 362.