White 48 vs Black 902
White starts from setup 48 (BBNNRQKR), Black from setup 902 (RKBQRBNN). In the encyclopedia since 2026-10-10: 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. 48, Black by position No. 902, 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 #48 B B N N R Q K R
King on the g-file, rooks on e, h, 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 48 gives White +0.23 (Morozov Balance Index, 400M nodes).
Black: setup #902 R K B Q R B N N
King on the b-file, rooks on a, e, queen on the d-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 902 gives White +0.62 (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 59.
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 ±14 cp.
For comparison, in symmetric play setup 48 gives White +0.23 and setup 902 gives White +0.62: 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 c4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 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 | 14 | -14 | 1. c4 e5 2. Bxh7 Bb4 3. Nc3 Bxc3 4. bxc3 d6 |
| S1 | 500 000 | 18 | -5 | 1. c4 e5 2. Bxh7 Bb4 3. Nc3 Bxc3 4. bxc3 d6 |
| S2 | 2 000 000 | 25 | 0 | 1. c4 e5 2. Bxh7 Bb4 3. Nc3 Bxc3 4. bxc3 a5 |
| S3 | 8 000 000 | 29 | -11 | 1. c4 e5 2. Bxh7 Nh6 3. Bc2 d5 4. cxd5 Qxd5 |
| S4 | 32 000 000 | 35 | -11 | 1. c4 a5 2. b3 e5 3. Bxh7 Nf6 4. Bf5 g6 |
| S5 | 128 000 000 | 41 | -1 | 1. c4 e5 2. Bxh7 Nf6 3. Bf5 d5 4. Bxc8 Qxc8 |
| S6 | 400 000 000 | 45 | 0 | 1. c4 a5 2. b3 e5 3. Bxh7 Nh6 4. Bc2 d5 |
| S7 | 800 000 000 | 50 | 0 | 1. c4 e5 2. Bxh7 Nf6 3. Bf5 d5 4. Bxc8 Qxc8 |
| S8 | 1 600 000 000 | 59 | 0 | 1. d4 e5 2. dxe5 Ng6 3. Nd3 f6 4. exf6 Nxf6 |
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: +9
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 +133, Black +94, difference +39. 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. c4 e5 2. b3 Ng6 3. h4 Nxh4 4. Bxh7 Bb4 5. Bc3 a5 |
| 2 | 0 | 46 | 1. d4 e5 2. dxe5 Ng6 3. Nd3 f6 4. exf6 Nxf6 5. f3 a5 |
| 3 | 0 | 46 | 1. b3 e5 2. c4 Ng6 3. h4 Nxh4 4. Bxh7 Bb4 5. Bc3 a5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 25 cp, mean 7.7 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -13 | e5 | -18 |
| 2 | Bxh7 | -4 | Nf6 | +6 |
| 3 | Bf5 | +4 | d5 | 0 |
| 4 | Bxc8 | +2 | Qxc8 | 0 |
| 5 | b3 | -20 | Qd7 | -20 |
| 6 | cxd5 | -14 | Nxd5 | -25 |
| 7 | e4 | -14 | Nf4 | -20 |
| 8 | h4 | -12 | Qxd2 | -16 |
| 9 | Ne3 | -24 | f6 | -18 |
| 10 | g3 | -17 | Ne6 | -12 |
| 11 | Kg2 | -13 | Nf7 | -13 |
| 12 | Rd1 | -16 | Qb4 | -13 |
| 13 | f3 | -17 | a5 | -15 |
| 14 | Nd5 | -8 | Qc5 | -15 |
| 15 | Qe2 | -16 | Qa7 | -19 |
| 16 | Nd3 | -15 | O-O-O | -11 |
| 17 | h5 | -7 | c6 | -10 |
| 18 | Ne3 | -12 | a4 | 0 |
| 19 | Ng4 | 0 | Nd4 | 0 |
| 20 | Bxd4 | 0 | Rxd4 | 0 |
| 21 | Ne3 | 0 | Red8 | 0 |
| 22 | Nf5 | 0 | R4d7 | 0 |
| 23 | Nf2 | 0 | Ng5 | 0 |
| 24 | Rxd7 | 0 | Rxd7 | 0 |
| 25 | Rd1 | 0 | axb3 | 0 |
| 26 | axb3 | 0 | Rxd1 | 0 |
| 27 | Qxd1 | 0 | Qa2 | 0 |
| 28 | Nd6+ | 0 | Kc7 | 0 |
| 29 | Ne8+ | 0 | Kc8 | 0 |
| 30 | Nd6+ | 0 | Kb8 | 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 34.5 moves.
Sample game 1 (1/2-1/2)
1. c4 Nh6 2. e4 e5 3. b3 Ng6 4. Nd3 d6 5. Qe2 a5 6. O-O Be7 7. Ne3 Bg5 8. Bc3 f5 9. exf5 Nxf5 10. Qh5 Rf8 11. g3 Nh6 12. Qe2 b6 13. f3 Bb7 14. Nd5 c6 15. Ne3 Qd7 16. Nf2 Ka7 17. Be4 d5 18. Bxg6 hxg6 19. Bxe5 Ba6 20. f4 Bf6 21. d4 Nf5 22. Qb2 Nxe3 23. Rxe3 g5 24. Bxf6 gxf6 25. fxg5 dxc4 26. Rfe1 Rae8 27. g6 Rxe3 28. Rxe3 Re8 29. Ng4 Rxe3 30. Nxe3 Qe8 31. Nxc4 Qxg6 32. Qe2 Qb1+ 33. Kf2 Qf5+ 34. Kg1 Qb1+ 35. Kg2 c5 36. dxc5 Bb7+ 37. Kf2 Qf5+ 38. Ke3 Qxc5+ 39. Kd3 Qg1 40. Kd2 Qb1 41. Qd3 Qxa2+ 42. Qc2 Qa1 43. Qd3 Qa2+ 44. Qc2 Qa1 45. Qc3 Qa2+
Sample game 2 (1/2-1/2)
1. c4 a5 2. Nc3 Ng6 3. h4 e5 4. h5 N6e7 5. b3 Nf6 6. Nd3 d6 7. f3 g6 8. hxg6 fxg6 9. Qf2 Ra6 10. Bc2 h5 11. b4 Ra8 12. b5 b6 13. e4 g5 14. O-O-O Ng6 15. g3 Be7 16. Rdg1 Rg8 17. Qe3 Be6 18. Nd5 Kb7 19. Nxf6 Bxf6 20. Rxh5 Bxc4 21. a4 g4 22. fxg4 Rc8 23. Nf2 c6 24. bxc6+ Rxc6 25. Kb1 Rg7 26. Rf5 Nf8 27. Bb3 Bg5 28. Qf3 Ne6 29. Rc1 Qc7 30. Bb2 Bxb3 31. Rxc6 Ba2+ 32. Kxa2 Qxc6 33. Rf7+ Rxf7 34. Qxf7+ Nc7 35. Qb3 Bxd2 36. Ba3 Bg5 37. Nd3 Bf6 38. Kb1 Qxe4 39. Bxd6 Nd5 40. g5 Bxg5 41. Qc2 Qxa4 42. Qxa4 Nc3+ 43. Kc2 Nxa4 44. Nxe5 Be3 45. Be7 Nc5 46. g4 Ne6 47. Nf3 Kc6 48. g5 b5 49. g6 Bh6 50. Bf6 Kd5 51. Kc3 Kc5 52. Be7+ Kd5
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 48 / 902 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): rkbqrbnn/pppppppp/8/8/8/8/PPPPPPPP/BBNNRQKR w EHae - 0 1
Mirror twin: White 911 vs Black 54 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 222.