White 4 vs Black 837
White starts from setup 4 (QBBNNRKR), Black from setup 837 (RKBBNRQN). 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. 4, Black by position No. 837, 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 #4 Q B B N N R K R
King on the g-file, rooks on f, h, queen on the a-file; no 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 4 gives White +0.38 (Morozov Balance Index, 400M nodes).
Black: setup #837 R K B B N R Q N
King on the b-file, rooks on a, f, queen on the g-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 837 gives White +0.26 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±1 centipawns of equality, reaching search depth 55.
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 -24 and 0 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 4 gives White +0.38 and setup 837 gives White +0.26: 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 (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 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 | -18 | 1. h4 e5 2. b3 d6 3. c4 f5 4. d4 Nf7 |
| S1 | 500 000 | 21 | -1 | 1. d4 f5 2. h4 d6 3. b3 Nf7 4. c4 e5 |
| S2 | 2 000 000 | 25 | -24 | 1. h4 e5 2. b3 d6 3. d4 e4 4. f3 exf3 |
| S3 | 8 000 000 | 31 | -15 | 1. h4 f5 2. d4 a5 3. b3 d6 4. c4 Nf6 |
| S4 | 32 000 000 | 34 | -7 | 1. h4 e5 2. b3 d6 3. c4 f5 4. d4 e4 |
| S5 | 128 000 000 | 41 | 0 | 1. h4 e5 2. b3 d6 3. d4 e4 4. c4 f5 |
| S6 | 400 000 000 | 53 | 0 | 1. h4 f5 2. d4 a5 3. b3 d6 4. c4 Nf6 |
| S7 | 800 000 000 | 53 | -1 | 1. h4 f5 2. d4 a5 3. b3 d6 4. c4 Nf6 |
| S8 | 1 600 000 000 | 55 | 0 | 1. h4 f5 2. d4 a5 3. b3 d6 4. c4 Nf6 |
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 | -1 |
| 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: +1
- Lc0 0.32.1: -6
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 +79, Black +70, 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 | -6 | 42 | 1. d4 |
| 2 | -7 | 42 | 1. h4 f5 2. a4 a5 3. d4 h6 4. b3 g5 5. c4 d6 |
| 3 | -18 | 41 | 1. a4 a5 2. h4 e5 3. d4 Ng6 4. dxe5 Nxe5 5. Ba2 Nf6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 26 cp, mean 3.7 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | h4 | -10 | f5 | -15 |
| 2 | d4 | -9 | a5 | -13 |
| 3 | Nd3 | -13 | Nf7 | -7 |
| 4 | a4 | -21 | e6 | -24 |
| 5 | c4 | -12 | d6 | -26 |
| 6 | b4 | -15 | axb4 | -20 |
| 7 | Nxb4 | -11 | Bd7 | 0 |
| 8 | Qb2 | -9 | Bf6 | -8 |
| 9 | Bg5 | -7 | Nxg5 | 0 |
| 10 | hxg5 | 0 | Bxg5 | 0 |
| 11 | c5 | 0 | dxc5 | 0 |
| 12 | dxc5 | 0 | Bf6 | 0 |
| 13 | Qd2 | 0 | Bxa4 | 0 |
| 14 | Rh3 | 0 | c6 | 0 |
| 15 | Nc3 | 0 | Nc7 | 0 |
| 16 | Nxa4 | 0 | Rxa4 | 0 |
| 17 | Nxc6+ | 0 | bxc6 | 0 |
| 18 | Rb3+ | 0 | Kc8 | 0 |
| 19 | Qd6 | 0 | Rd8 | 0 |
| 20 | Qxc6 | 0 | Rdd4 | 0 |
| 21 | Rb7 | 0 | Qd8 | 0 |
| 22 | Qb6 | 0 | Na6 | 0 |
| 23 | Qc6+ | 0 | Nc7 | 0 |
| 24 | Qb6 | 0 | Ra8 | 0 |
| 25 | Bc2 | 0 | Be5 | 0 |
| 26 | Bb3 | 0 | Qf6 | 0 |
| 27 | e3 | 0 | Rd2 | 0 |
| 28 | Qc6 | 0 | Ra3 | 0 |
| 29 | Qb6 | 0 | Qh4 | 0 |
| 30 | f4 | 0 | Qg3 | 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 41.5 moves.
Sample game 1 (1/2-1/2)
1. h4 f5 2. d4 Nf7 3. b4 a5 4. b5 a4 5. a3 Ned6 6. Ba2 Nxb5 7. c4 Na7 8. c5 e6 9. d5 Bf6 10. Bb2 exd5 11. Bxd5 d6 12. Nd3 dxc5 13. Bxf6 gxf6 14. Nc3 c6 15. Ba2 Qg4 16. Nxc5 Qd4 17. N5xa4 Nb5 18. Rd1 Qe5 19. Rh3 Nxc3 20. Nxc3 Rxa3 21. Qb2 Qa5 22. Bxf7 Rxf7 23. Rg3 Rc7 24. Rc1 b5 25. e4 fxe4 26. Nxe4 Rxg3 27. fxg3 Re7 28. Nxf6 Re1+ 29. Kh2 Rxc1 30. Qxc1 Qb6 31. Nxh7 b4 32. Ng5 b3 33. Qb2 Qe3 34. Qf6 Bb7 35. Nf3 Ka7 36. Nd4 Kb6 37. Nf5 Qe2 38. Nd4 Qe3 39. Nxb3 Qxb3 40. h5 Ka5
Sample game 2 (1/2-1/2)
1. h4 e5 2. b4 d6 3. a4 a5 4. b5 f5 5. d4 Ng6 6. h5 Nf4 7. Bxf4 exf4 8. Ba2 Be6 9. Bxe6 Qxe6 10. Qb2 Qc4 11. e3 fxe3 12. Nxe3 Qf7 13. Nf3 f4 14. Nd1 Nf6 15. Nc3 Nd7 16. Qb3 Nb6 17. Qxf7 Rxf7 18. h6 g6 19. O-O-O Ka7 20. Kd2 g5 21. Kd3 Be7 22. Nh2 c5 23. bxc6 bxc6 24. Rde1 Rc8 25. Re6 d5 26. Nf3 Nc4 27. Rb1 Rc7 28. Ne2 g4 29. Ne5 Nxe5+ 30. dxe5 f3 31. Nd4 fxg2 32. Nxc6+ Rxc6 33. Rxc6 Rf3+ 34. Ke2 Bh4 35. Rc7+ Ka6 36. Rc6+ Ka7 37. Rg1 Rxf2+ 38. Kd3 Kb7 39. Rd6 Rf3+ 40. Ke2 Rf2+ 41. Kd3
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 4 / 837 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): rkbbnrqn/pppppppp/8/8/8/8/PPPPPPPP/QBBNNRKR w FHaf - 0 1
Mirror twin: White 958 vs Black 122 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 79.