White 40 vs Black 838
White starts from setup 40 (NBNQBRKR), Black from setup 838 (RKBNRBQN). In the encyclopedia since 2026-10-21: 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. 40, Black by position No. 838, 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 #40 N B N Q B R K R
King on the g-file, rooks on f, h, queen on the d-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 40 gives White +0.34 (Morozov Balance Index, 400M nodes).
Black: setup #838 R K B N R B Q N
King on the b-file, rooks on a, e, 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 838 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 ±2 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 -9 and +18 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 40 gives White +0.34 and setup 838 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 c3, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±21 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 1, drawn 9, Black won 0 (White scored 55.0%).
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 | -9 | 1. c4 f6 2. Qc2 g6 3. d4 e5 4. d5 a5 |
| S1 | 500 000 | 19 | +5 | 1. e4 f6 2. f3 e5 3. c3 a5 4. Bf2 Ng6 |
| S2 | 2 000 000 | 23 | +18 | 1. e4 f6 2. f3 d5 3. c3 a5 4. Bf2 e5 |
| S3 | 8 000 000 | 29 | +1 | 1. e4 e5 2. c3 a5 3. Nc2 b6 4. Ne3 Ba6 |
| S4 | 32 000 000 | 33 | -3 | 1. e4 e5 2. c3 a5 3. f4 f6 4. fxe5 fxe5 |
| S5 | 128 000 000 | 39 | 0 | 1. e4 e5 2. c3 a5 3. d4 exd4 4. cxd4 d5 |
| S6 | 400 000 000 | 43 | 0 | 1. e4 e5 2. c3 a5 3. d4 b6 4. h4 exd4 |
| S7 | 800 000 000 | 47 | -2 | 1. d4 f6 2. d5 e6 3. c4 f5 4. e4 fxe4 |
| S8 | 1 600 000 000 | 56 | 0 | 1. e4 e5 2. c3 a5 3. Nc2 f5 4. exf5 d5 |
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: +1
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 +52, Black +95, difference -43. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +7 | 42 | 1. c3 e5 2. e4 a5 3. d4 b6 4. h4 exd4 5. cxd4 Bb7 |
| 2 | 0 | 41 | 1. e4 e5 2. c3 a5 3. d4 b6 4. h4 exd4 5. cxd4 Bb7 |
| 3 | -6 | 41 | 1. d4 f6 2. d5 e6 3. c4 Ng6 4. Bc3 Ne5 5. b3 exd5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 21 cp, mean 2.7 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | +4 | a5 | +3 |
| 2 | c3 | +13 | e5 | +6 |
| 3 | Nc2 | 0 | f5 | -19 |
| 4 | exf5 | -10 | d5 | -21 |
| 5 | d4 | -21 | Bxf5 | -16 |
| 6 | dxe5 | 0 | Nhf7 | 0 |
| 7 | f4 | 0 | g5 | -5 |
| 8 | Nd3 | 0 | gxf4 | -4 |
| 9 | Nd4 | 0 | Be4 | 0 |
| 10 | Nxf4 | 0 | Bxb1 | 0 |
| 11 | Qxb1 | 0 | Nxe5 | 0 |
| 12 | Bg3 | 0 | Ndc6 | 0 |
| 13 | Qf5 | 0 | Bd6 | 0 |
| 14 | Nh5 | 0 | Nxd4 | 0 |
| 15 | cxd4 | 0 | Ng4 | -3 |
| 16 | Bxd6 | 0 | cxd6 | 0 |
| 17 | Qf7 | 0 | Ne3 | 0 |
| 18 | Qxg8 | 0 | Rxg8 | 0 |
| 19 | Rf2 | 0 | Ka7 | 0 |
| 20 | h3 | 0 | Rac8 | 0 |
| 21 | Nf6 | 0 | Rg6 | 0 |
| 22 | Nxh7 | 0 | Rh8 | 0 |
| 23 | Nf6 | 0 | Nxg2 | 0 |
| 24 | Rxg2 | 0 | Rxf6 | 0 |
| 25 | h4 | 0 | Rf4 | 0 |
| 26 | h5 | 0 | Rxd4 | -3 |
| 27 | Rh3 | 0 | Rf4 | -7 |
| 28 | Rg6 | 0 | d4 | -16 |
| 29 | h6 | -6 | Rf5 | -3 |
| 30 | Rxd6 | 0 | Rg8+ | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 45.9 moves.
Sample game 1 (1/2-1/2)
1. e4 a5 2. d4 f5 3. exf5 g6 4. c4 Ra6 5. h4 d5 6. c5 gxf5 7. f4 Rg6 8. Rh2 Nhf7 9. Nc2 Nh6 10. Ne2 Ng4 11. Rh3 e5 12. fxe5 Bh6 13. Rg3 Rf8 14. h5 Rg7 15. Bd2 f4 16. Nxf4 Rgf7 17. Rgf3 Ne6 18. Nxe6 Rxf3 19. Rxf3 Rxf3 20. Qxf3 Bxd2 21. Nf4 Qg5 22. Nxd5 Qxh5 23. Qh3 Qg6 24. Na3 Qg8 25. Qf3 Be1 26. Nf6 Qg5 27. g3 Nxf6 28. exf6 Bxg3 29. f7 Bd6+ 30. Kf1 Qc1+ 31. Kg2 Qxb2+ 32. Bc2 Bf8 33. Qe3 Qxa2 34. Qe8 Qd5+ 35. Be4 Qg5+ 36. Kf1 Qf4+ 37. Kg2 Qd2+ 38. Kf1 Qf4+ 39. Kg2 Qd2+ 40. Kf1
Sample game 2 (1/2-1/2)
1. c3 e5 2. e4 a5 3. Nc2 b6 4. Ne3 Ba6 5. Bd3 Bxd3 6. Nxd3 f6 7. Qb1 Ng6 8. f3 Ne7 9. Bf2 Ndc6 10. Rc1 Qe6 11. O-O d5 12. c4 dxc4 13. Nxc4 Ng6 14. Ne3 Kb7 15. Rc4 Nd4 16. Kh1 Qd7 17. Rfc1 Rec8 18. b4 axb4 19. Nxb4 Bxb4 20. Rxb4 Nf4 21. Nc4 Ra4 22. Bxd4 exd4 23. Rb5 Ne2 24. Qb3 Ra3 25. Qxa3 Qxb5 26. Qd3 Nf4 27. Qc2 Qd7 28. e5 fxe5 29. g3 Qd5 30. gxf4 Qxf3+ 31. Kg1 Qg4+ 32. Kh1 Qf3+ 33. Kg1 Qg4+ 34. Kh1
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 40 / 838 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): rkbnrbqn/pppppppp/8/8/8/8/PPPPPPPP/NBNQBRKR w FHae - 0 1
Mirror twin: White 925 vs Black 118 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 190.