White 407 vs Black 755
White starts from setup 407 (RQBNNKRB), Black from setup 755 (BRKNNRQB). In the encyclopedia since 2026-09-21: 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. 407, Black by position No. 755, 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 #407 R Q B N N K R B
King on the f-file, rooks on a, g, queen on the b-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 407 gives White +0.16 (Morozov Balance Index, 400M nodes).
Black: setup #755 B R K N N R Q B
King on the c-file, rooks on b, f, queen on the g-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 755 gives White +0.19 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 66.
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 ±10 cp.
For comparison, in symmetric play setup 407 gives White +0.16 and setup 755 gives White +0.19: 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 g4, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 69 cp (around move 24), ending at -11 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 0, drawn 8, Black won 2 (White scored 40.0%).
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 | -10 | 1. g4 g6 2. c3 Nd6 3. d4 b6 4. Bxa8 Rxa8 |
| S1 | 500 000 | 19 | +1 | 1. g4 g6 2. c3 b6 3. Bxa8 Rxa8 4. d4 a5 |
| S2 | 2 000 000 | 25 | -6 | 1. g4 g6 2. c3 b6 3. Bxa8 Rxa8 4. d4 a5 |
| S3 | 8 000 000 | 37 | 0 | 1. g4 g6 2. c3 Be5 3. h3 Bh2 4. Rg2 Bf4 |
| S4 | 32 000 000 | 43 | 0 | 1. g4 g6 2. c3 Be5 3. h3 Bh2 4. Rg2 Bf4 |
| S5 | 128 000 000 | 51 | 0 | 1. g4 g6 2. c3 Be5 3. h3 Bh2 4. Rg2 Bf4 |
| S6 | 400 000 000 | 56 | 0 | 1. g4 g6 2. c3 Be5 3. h4 Bh2 4. Rg2 Bf4 |
| S7 | 800 000 000 | 60 | 0 | 1. g4 g6 2. c3 Be5 3. h4 Bh2 4. Rg2 Bf4 |
| S8 | 1 600 000 000 | 61 | 0 | 1. g4 g6 2. c3 Be5 3. h4 Bh2 4. Rg2 Bf4 |
| S9 | 3 200 000 000 | 66 | 0 | 1. g4 g6 2. c3 Be5 3. h4 Bh2 4. Rg2 Bf4 |
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 | 0 |
| 16 000 000 000 | 0 |
This pair stays within the ±5 cp corridor up to 16 000 000 000 nodes.
Swap the two setups, giving White the black back rank and Black the white one, and the evaluation jumps to +77. The same two armies dealt the other way round are no longer balanced at all: that is how precisely this pair pays for the first move.
Independent engines, run on the same position:
- Berserk 14: 0
- Lc0 0.32.1: +7
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 +42, Black +159, difference -117. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 160 games, 0 White wins, 148 draws, 12 Black wins, White scored 46.2%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 45 | 1. g4 g6 2. c3 Be5 3. h3 Bh2 4. Rg2 Bf4 5. Rg1 Bh2 |
| 2 | -10 | 44 | 1. c3 f5 2. g3 g5 3. d4 Nd6 4. a4 a5 5. h4 h6 |
| 3 | -14 | 44 | 1. g3 f5 2. a4 a5 3. c3 Nd6 4. d4 g5 5. h4 h6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 69 cp, mean 24.3 cp, final -11 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g4 | 0 | g6 | 0 |
| 2 | c3 | 0 | Be5 | 0 |
| 3 | h3 | 0 | Bh2 | 0 |
| 4 | Rg2 | 0 | Bf4 | 0 |
| 5 | Rg1 | 0 | Bh2 | 0 |
| 6 | Rg2 | 0 | Bf4 | 0 |
| 7 | Rg1 | -12 | f6 | 0 |
| 8 | Qc2 | 0 | Bh2 | 0 |
| 9 | Rg2 | 0 | Bd6 | 0 |
| 10 | d4 | 0 | b6 | 0 |
| 11 | e4 | 0 | g5 | -7 |
| 12 | f3 | -8 | h5 | -18 |
| 13 | Be3 | -20 | Qh7 | -34 |
| 14 | Nf2 | -32 | c5 | -27 |
| 15 | Ned3 | -37 | c4 | -50 |
| 16 | Nc1 | -45 | Nc7 | -49 |
| 17 | Qd2 | -42 | hxg4 | -45 |
| 18 | hxg4 | -53 | e6 | -38 |
| 19 | Ne2 | -48 | b5 | -44 |
| 20 | f4 | -46 | Bxe4 | -46 |
| 21 | Nxe4 | -44 | Qxe4 | -57 |
| 22 | Rh2 | -48 | Qg6 | -52 |
| 23 | O-O-O | -60 | Re8 | -51 |
| 24 | d5 | -54 | exd5 | -69 |
| 25 | Rh3 | -50 | Nb7 | -42 |
| 26 | f5 | -42 | Qf7 | -40 |
| 27 | Bxa7 | -27 | Ra8 | -23 |
| 28 | Bb6 | -24 | Rxa2 | -19 |
| 29 | Kb1 | -15 | Ra6 | -17 |
| 30 | Bxc7 | -12 | Bxc7 | -11 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 8, Black won 2 — White scored 40.0%. Average length 43.3 moves.
Sample game 1 (1/2-1/2)
1. g4 e6 2. a4 g6 3. a5 f5 4. c3 fxg4 5. d4 h5 6. O-O Nd6 7. Nd3 N8f7 8. Qa2 Bf6 9. e4 Ng5 10. Bxg5 Bxg5 11. Ne3 Qf7 12. Nc4 Nxc4 13. Qxc4 d6 14. Qb5 Bh4 15. e5 a6 16. Qb3 b5 17. Bxa8 Rxa8 18. exd6 cxd6 19. Rae1 O-O 20. Qxe6 Kh7 21. Qxf7+ Rxf7 22. Re6 Rd8 23. Kg2 Rf3 24. Re3 Rdf8 25. Rxf3 gxf3+ 26. Kh3 g5 27. Re1 Kg6 28. Re6+ Rf6 29. Re7 Rf7 30. Re6+ Rf6 31. Re7 Rf7 32. Re6+
Sample game 2 (1/2-1/2)
1. g4 f6 2. c4 f5 3. d4 fxg4 4. Bg5 Nf6 5. Qc2 b6 6. d5 Nf7 7. Bxf6 gxf6 8. h3 f5 9. Qxf5 Ne5 10. Qe4 Qg6 11. Qxg6 hxg6 12. hxg4 Nxc4 13. Nd3 Ne5 14. Nxe5 Bxe5 15. g5 Bh2 16. Rg4 Rf4 17. Ne3 O-O-O 18. Be4 Rxg4 19. Nxg4 Bf4 20. Rd1 Rg8 21. f3 d6 22. b4 Bxg5 23. b5 e6 24. Kg2 Rh8 25. dxe6 Bxe4 26. fxe4 Re8 27. Rd5 Bc1 28. e5 Rxe6 29. Kf3 Kd7 30. Nf6+ Ke7 31. Rd1 Ba3 32. Nd5+ Kf7 33. exd6 Bxd6 34. Rh1 g5 35. Rh7+ Kg6 36. Rd7 Kh5 37. Rh7+ Kg6 38. Rd7 Re8 39. Nxc7 Rf8+ 40. Kg2 Ba3
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 407 / 755 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): brknnrqb/pppppppp/8/8/8/8/PPPPPPPP/RQBNNKRB w AGbf - 0 1
Mirror twin: White 738 vs Black 387 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 62.