White 51 vs Black 499
White starts from setup 51 (BNNRQKRB), Black from setup 499 (BRQNKNRB). 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. 51, Black by position No. 499, 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 #51 B N N R Q K R B
King on the f-file, rooks on d, g, queen on the e-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 51 gives White +0.24 (Morozov Balance Index, 400M nodes).
Black: setup #499 B R Q N K N R B
King on the e-file, rooks on b, g, queen on the c-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 499 gives White +0.18 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation is exactly 0.00 each time, reaching search depth 60.
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 0 and +21 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 51 gives White +0.24 and setup 499 gives White +0.18: 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 d4, and 2 first moves are within 10 cp of it.
Along the engine's main line (10 moves) the evaluation stayed within ±25 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 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 | 13 | +21 | 1. d4 g5 2. O-O b6 3. d5 f5 4. g3 Nf7 |
| S1 | 500 000 | 19 | +2 | 1. d4 g5 2. g3 d6 3. b3 b6 4. O-O Bxh1 |
| S2 | 2 000 000 | 23 | +12 | 1. g3 g5 2. d4 d6 3. e3 b6 4. O-O g4 |
| S3 | 8 000 000 | 30 | +20 | 1. g3 g5 2. d4 d6 3. e3 c5 4. b3 b6 |
| S4 | 32 000 000 | 38 | 0 | 1. d4 b5 2. b4 g6 3. Nb3 d6 4. O-O Nd7 |
| S5 | 128 000 000 | 41 | 0 | 1. d4 b5 2. b4 g6 3. Nb3 d6 4. O-O Nd7 |
| S6 | 400 000 000 | 51 | 0 | 1. d4 b5 2. b4 g6 3. Nb3 d6 4. O-O Nd7 |
| S7 | 800 000 000 | 56 | 0 | 1. d4 b5 2. b4 g6 3. Nb3 d6 4. O-O Nd7 |
| S8 | 1 600 000 000 | 60 | 0 | 1. d4 b5 2. b4 g6 3. Nb3 d6 4. O-O Nd7 |
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: -2
- Lc0 0.32.1: -5
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 +81, Black +115, difference -34. 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 | 41 | 1. d4 b5 2. b4 d6 3. Nb3 Nd7 4. O-O g6 5. Nc3 c5 |
| 2 | -3 | 41 | 1. g3 c5 2. b3 b5 3. Bxa8 Rxa8 4. O-O d6 5. e4 Nd7 |
| 3 | -26 | 40 | 1. b3 b5 2. d3 d6 3. e3 g5 4. Bxh8 Rxh8 5. Ne2 Nd7 |
Main-line play-out
10 moves, 5 000 000 nodes per half-move. Largest |evaluation| 25 cp, mean 2.2 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g3 | +14 | g5 | +6 |
| 2 | d4 | 0 | d6 | +25 |
| 3 | e4 | 0 | b5 | 0 |
| 4 | Qe3 | 0 | f5 | 0 |
| 5 | Nd2 | 0 | f4 | 0 |
| 6 | Qb3 | 0 | Qh3+ | 0 |
| 7 | Bg2 | 0 | Qh5 | 0 |
| 8 | Bf3 | 0 | Qh3+ | 0 |
| 9 | Bg2 | 0 | Qh5 | 0 |
| 10 | Bf3 | 0 | Qh3+ | 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 39.3 moves.
Sample game 1 (1/2-1/2)
1. b4 d6 2. Nb3 b5 3. d4 g5 4. N1d2 Nfe6 5. e4 c5 6. d5 Bxa1 7. Rxa1 c4 8. Na5 Nf4 9. Qe3 f5 10. g3 Nh3 11. Bg2 Nxg1 12. Kxg1 a6 13. Nf3 f4 14. Qa7 Nf7 15. Nd4 Ne5 16. Nf5 Qd8 17. a4 bxa4 18. Rxa4 h5 19. Bh3 fxg3 20. hxg3 g4 21. Bg2 Rc8 22. Ra3 Qd7 23. Qd4 Qb5 24. c3 Rg6 25. Qe3 Qd7 26. Nh4 Rf6 27. Ra2 e6 28. Qd4 Kf7 29. Bf1 Qb5 30. Qa7+ Qd7 31. Qd4 Qb5 32. Qa7+ Kg8 33. Qe7 Rcf8 34. Qxd6 Qb8 35. Qxb8 Rxb8 36. Nxc4 Nxc4 37. Bxc4 Rc8 38. Bxa6 Rxc3 39. Bf1 Rf8 40. Ng6 Rd8
Sample game 2 (1/2-1/2)
1. d4 g5 2. O-O d6 3. b4 b6 4. g3 Bxh1 5. Kxh1 c5 6. Nb3 Ng6 7. e4 cxd4 8. Qe2 Ne6 9. Nxd4 Nxd4 10. Bxd4 Bxd4 11. Rxd4 Kf8 12. Na3 Ne5 13. f4 gxf4 14. gxf4 Ng4 15. c4 a6 16. Nc2 b5 17. a3 bxc4 18. Rxc4 Qb7 19. Ne3 Rc8 20. Rxc8+ Qxc8 21. Qc4 Qe6 22. Qxe6 fxe6 23. Nd1 Nf6 24. Nf2 Ke8 25. e5 Nd5 26. Ne4 Kd7 27. exd6 exd6 28. f5 Re8 29. f6 Rf8 30. Kg1 e5 31. Rd1 Nxf6 32. Rxd6+ Ke7 33. Rxf6 Rxf6 34. Nxf6 Kxf6 35. a4 Ke6 36. Kf2 Kd5 37. b5 axb5 38. axb5 Kc5 39. Kf3 Kxb5 40. Ke4 h6 41. Kxe5
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 51 / 499 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): brqnknrb/pppppppp/8/8/8/8/PPPPPPPP/BNNRQKRB w DGbg - 0 1
Mirror twin: White 899 vs Black 547 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 226.