White 31 vs Black 625
White starts from setup 31 (NQNRKRBB), Black from setup 625 (BRNBKQRN). In the encyclopedia since 2026-11-01: 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. 31, Black by position No. 625, 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 #31 N Q N R K R B B
King on the e-file, rooks on d, f, queen on the b-file; one 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 31 gives White +0.26 (Morozov Balance Index, 400M nodes).
Black: setup #625 B R N B K Q R N
King on the e-file, rooks on b, g, queen on the f-file; one 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 625 gives White +0.25 (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 -11 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 31 gives White +0.26 and setup 625 gives White +0.25: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.
The engine's first choice for White is g3; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±27 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 | +13 | 1. g3 f5 2. f4 e6 3. c4 Nf7 4. Nab3 Qe7 |
| S1 | 500 000 | 19 | +2 | 1. g3 f5 2. f4 Qf7 3. Nd3 O-O 4. c4 e6 |
| S2 | 2 000 000 | 22 | -11 | 1. g3 f5 2. f4 Qf7 3. c4 b6 4. Bxa8 Rxa8 |
| S3 | 8 000 000 | 29 | +17 | 1. g3 f5 2. c4 Qf7 3. Qc2 O-O 4. f4 b6 |
| S4 | 32 000 000 | 37 | +18 | 1. g3 f5 2. Nab3 Qf7 3. c4 O-O 4. Qc2 e6 |
| S5 | 128 000 000 | 40 | +11 | 1. g3 f5 2. Nab3 Qf7 3. c4 O-O 4. f4 Ng6 |
| S6 | 400 000 000 | 53 | 0 | 1. g3 f5 2. Nab3 Qf7 3. c4 O-O 4. f4 Ng6 |
| S7 | 800 000 000 | 58 | 0 | 1. g3 f5 2. Nab3 Qf7 3. c4 O-O 4. f4 Ng6 |
| S8 | 1 600 000 000 | 60 | 0 | 1. g3 f5 2. Nab3 Qf7 3. c4 O-O 4. f4 Ng6 |
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: +12
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 +6, Black +85, difference -79. 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 | +8 | 42 | 1. g3 f5 2. Nab3 Qf7 3. c4 O-O 4. Qc2 e6 5. f4 b6 |
| 2 | -30 | 42 | 1. g4 e5 2. c3 Ng6 3. Nc2 Qe7 4. Ne3 O-O 5. Nf5 Qe6 |
| 3 | -47 | 42 | 1. c3 b6 2. d4 f5 3. Nd3 Ng6 4. f3 Qf7 5. g3 O-O |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 27 cp, mean 7.4 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g3 | -4 | f5 | +17 |
| 2 | c4 | +18 | Qf7 | +12 |
| 3 | Nab3 | +17 | O-O | +22 |
| 4 | Qc2 | +16 | Qe8 | +18 |
| 5 | f4 | +13 | e6 | +16 |
| 6 | Bf2 | +11 | b6 | +11 |
| 7 | Bxa8 | +10 | Rxa8 | -1 |
| 8 | d4 | +4 | c6 | 0 |
| 9 | O-O | 0 | Nf7 | +5 |
| 10 | Nd2 | -1 | d5 | +1 |
| 11 | Nd3 | 0 | Ncd6 | 0 |
| 12 | c5 | -5 | Ne4 | -25 |
| 13 | Nf3 | -26 | Nh6 | -15 |
| 14 | h3 | -13 | Kh8 | -25 |
| 15 | Kg2 | -24 | Rg8 | -24 |
| 16 | Be3 | -15 | Nf7 | -27 |
| 17 | Rg1 | -22 | g5 | -18 |
| 18 | fxg5 | -7 | Nfxg5 | 0 |
| 19 | Bf4 | 0 | Bf6 | 0 |
| 20 | b4 | 0 | bxc5 | 0 |
| 21 | bxc5 | 0 | Qh5 | 0 |
| 22 | Nxg5 | 0 | Nxg5 | 0 |
| 23 | Nf2 | 0 | Nf7 | 0 |
| 24 | Qb2 | 0 | Rge8 | 0 |
| 25 | Nd3 | 0 | e5 | 0 |
| 26 | dxe5 | -2 | Rab8 | 0 |
| 27 | Qd2 | 0 | Nxe5 | 0 |
| 28 | Nxe5 | 0 | Bxe5 | 0 |
| 29 | e3 | 0 | Qg6 | 0 |
| 30 | Rgf1 | 0 | Kg8 | 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 33.4 moves.
Sample game 1 (1/2-1/2)
1. g3 e6 2. Nab3 b6 3. Bxa8 Rxa8 4. c4 f5 5. d4 Qf7 6. Nd3 O-O 7. Qc2 Ng6 8. Nd2 d6 9. f4 c5 10. O-O-O Nce7 11. Qa4 Qe8 12. Qxe8 Rxe8 13. Rde1 cxd4 14. Bxd4 e5 15. Bc3 exf4 16. Nxf4 Nxf4 17. Rxf4 d5 18. Rd4 dxc4 19. Nxc4 Nc6 20. Rd7 Re7 21. Red1 Rc8 22. Rxe7 Bxe7 23. Nd6 Rf8 24. e4 fxe4 25. Nxe4 Re8 26. Kc2 Bb4 27. a3 Bxc3 28. Nxc3 Kf7 29. Kb3 Ke6 30. Kc4 Rc8 31. Re1+ Kd7 32. Rd1+ Ke6 33. Re1+ Kd7 34. Rd1+
Sample game 2 (1/2-1/2)
1. g4 Nd6 2. f4 e6 3. c3 Ng6 4. Nd3 Bh4+ 5. Bf2 Bxf2+ 6. Rxf2 Qe7 7. f5 Nh4 8. O-O-O b6 9. Bxa8 Rxa8 10. Nf4 Qg5 11. Nc2 g6 12. fxe6 fxe6 13. Ne3 O-O 14. Rdf1 Qb5 15. Qd3 Qxd3 16. Nxd3 Rxf2 17. Rxf2 Rf8 18. Kc2 g5 19. Rxf8+ Kxf8 20. Ne5 Ke8 21. b4 Nf7 22. N3c4 Nh6 23. Ne3 Nf7 24. Nxf7 Kxf7 25. d4 Ng6 26. Kd2 e5 27. Nc2 Ke6 28. e4 d5 29. Ke3 Nf4 30. b5 Ng2+ 31. Kd3 Nf4+ 32. Ke3 dxe4 33. Kxe4 Ne2 34. d5+ Kf6 35. Kd3 Nf4+ 36. Ke4 Ne2 37. Kd3 Nf4+ 38. Ke4
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 31 / 625 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): brnbkqrn/pppppppp/8/8/8/8/PPPPPPPP/NQNRKRBB w DFbg - 0 1
Mirror twin: White 928 vs Black 235 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 171.