White 502 vs Black 423
White starts from setup 502 (RQBNKBNR), Black from setup 423 (RNBQNKRB). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #502 R Q B N K B N R
King on the e-file, rooks on a, h, queen on the b-file; no 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 502 gives White +0.21 (Morozov Balance Index, 400M nodes).
Black: setup #423 R N B Q N K R B
King on the f-file, rooks on a, g, queen on the d-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 423 gives White +0.15 (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 58.
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 shallow rungs wandered between -8 and +25 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 502 gives White +0.21 and setup 423 gives White +0.15: 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 c3, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±22 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 | 16 | +25 | 1. c3 g6 2. d4 d5 3. Nf3 c5 4. dxc5 Nd7 |
| S1 | 500 000 | 17 | +3 | 1. c3 g6 2. d4 d5 3. Nf3 Bf5 4. Bh6+ Bg7 |
| S2 | 2 000 000 | 22 | -3 | 1. c3 g6 2. e4 c5 3. Nf3 Nc7 4. d4 cxd4 |
| S3 | 8 000 000 | 29 | -8 | 1. c3 g6 2. d4 d5 3. Nf3 Bg7 4. e4 dxe4 |
| S4 | 32 000 000 | 37 | -3 | 1. c3 g6 2. d4 d5 3. e4 dxe4 4. Qxe4 O-O |
| S5 | 128 000 000 | 44 | 0 | 1. d4 d5 2. Nf3 Nd6 3. h4 Nc6 4. Ne3 g6 |
| S6 | 400 000 000 | 53 | 0 | 1. d4 d5 2. Nf3 Nd6 3. h4 Nc6 4. Ne3 g6 |
| S7 | 800 000 000 | 58 | 0 | 1. d4 d5 2. Nf3 Nd6 3. h4 Nc6 4. Ne3 g6 |
| S8 | 1 600 000 000 | 58 | 0 | 1. d4 d5 2. Nf3 Nd6 3. h4 Nc6 4. Ne3 g6 |
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 | not checked |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair held exactly 0.00 up to 1 600 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: -2
- Lc0 0.32.1: -7
Independent confirmations: 2 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 +17, Black +26, difference -9. 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 | 47 | 1. c3 g6 2. d4 d5 3. Nf3 Bf5 4. Bh6+ Bg7 5. Qc1 Nd7 |
| 2 | 0 | 47 | 1. d4 d5 2. c3 g6 3. Nf3 Bf5 4. Bh6+ Bg7 5. Qc1 Nd7 |
| 3 | -8 | 47 | 1. Nf3 c5 2. c3 g6 3. d4 cxd4 4. cxd4 d5 5. Bh6+ Bg7 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 22 cp, mean 5.2 cp, final -5 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c3 | -2 | g6 | +2 |
| 2 | d4 | +8 | d5 | -7 |
| 3 | e4 | -10 | dxe4 | -7 |
| 4 | Qxe4 | 0 | O-O | 0 |
| 5 | Nf3 | 0 | Nd6 | -1 |
| 6 | Qc2 | -9 | Re8 | -13 |
| 7 | Bg5 | -9 | Bf5 | 0 |
| 8 | Bd3 | 0 | Bxd3 | -8 |
| 9 | Qxd3 | -10 | Nd7 | -8 |
| 10 | Ne3 | -4 | c5 | -11 |
| 11 | O-O | -8 | cxd4 | -5 |
| 12 | cxd4 | -5 | Nf8 | -7 |
| 13 | Bf4 | 0 | Ne6 | 0 |
| 14 | Be5 | 0 | Qb6 | -5 |
| 15 | Rfd1 | -3 | Rad8 | 0 |
| 16 | g3 | -5 | Bxe5 | -5 |
| 17 | Nxe5 | -3 | Ng7 | -11 |
| 18 | N5c4 | -14 | Nxc4 | -22 |
| 19 | Qxc4 | -22 | Rd6 | -10 |
| 20 | d5 | -4 | Rd7 | 0 |
| 21 | Rac1 | 0 | Qxb2 | -4 |
| 22 | Rb1 | -3 | Qa3 | -9 |
| 23 | d6 | 0 | Rxd6 | -6 |
| 24 | Rxd6 | 0 | Qxd6 | -5 |
| 25 | Rxb7 | 0 | a5 | -5 |
| 26 | Rb5 | 0 | Ra8 | -8 |
| 27 | Qe4 | -3 | Ra7 | -4 |
| 28 | Qc4 | -5 | Ne8 | -3 |
| 29 | Qc8 | 0 | Kf8 | -11 |
| 30 | Rb8 | -4 | Qd7 | -5 |
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 36.0 moves.
Sample game 1 (1/2-1/2)
1. d4 d5 2. Nf3 Nf6 3. g3 O-O 4. Bg2 g6 5. O-O a5 6. Bh6 Re8 7. Ne3 Ng4 8. Nxg4 Bxg4 9. c3 Nd7 10. e4 Bxf3 11. Bxf3 e5 12. exd5 exd4 13. cxd4 Qf6 14. Be4 Qxd4 15. Bg2 Re2 16. Qc1 Be5 17. Rb1 Qd3 18. Qd1 Qxd1 19. Rfxd1 Bd6 20. Bd2 Nf6 21. Bf1 Re7 22. Be1 Ne4 23. Rbc1 f5 24. f3 Nf6 25. a4 Kf7 26. Bc4 Nd7 27. Bb5 Nf6 28. Kg2 g5 29. Bd3 f4 30. Bd2 b6 31. Bc4 Rg8 32. Re1 Rxe1 33. Rxe1 Re8 34. gxf4 Rxe1 35. Bxe1 gxf4 36. Kh3 h6 37. b3 Nd7 38. Bd2 Kg6 39. Bd3+ Kg5 40. Be1 Ne5 41. Be4 Nf7 42. Bc2 Bb4 43. Bh4+ Kh5 44. Bf6 Bc5
Sample game 2 (1/2-1/2)
1. d4 d5 2. c3 Nf6 3. Nf3 O-O 4. g3 g6 5. a4 Bg7 6. Bg2 a5 7. O-O b6 8. b4 axb4 9. cxb4 Ne4 10. Bf4 Be6 11. Qc1 c5 12. bxc5 Nc6 13. Bh6 bxc5 14. Bxg7 Kxg7 15. dxc5 Qa5 16. Ra3 Qxc5 17. Qxc5 Nxc5 18. Nc3 d4 19. Nb5 Rxa4 20. Rxa4 Nxa4 21. Nfxd4 Nxd4 22. Nxd4 Rc8 23. f4 Rc4 24. Nxe6+ fxe6 25. Ra1 Nc3 26. Kf2 Rc5 27. e4 e5 28. fxe5 Rxe5 29. Ke3 Kf6 30. h4 Nb5 31. Bf1 Nd6 32. Bd3 Nf5+ 33. Kf4 Nd4 34. Ke3 Nf5+ 35. Kf3 Nd6 36. g4 g5 37. h5 Rc5 38. e5+ Rxe5 39. Bxh7 Nf7 40. Ra6+ e6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 502 / 423 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): rnbqnkrb/pppppppp/8/8/8/8/PPPPPPPP/RQBNKBNR w AHag - 0 1
Mirror twin (the same position mirrored): White 550 vs Black 722.