White 307 vs Black 759
White starts from setup 307 (BNQRKRNB), Black from setup 759 (RKBNNRQB). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #307 B N Q R K R N B
King on the e-file, rooks on d, f, queen on the c-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 307 gives White +0.33 (Morozov Balance Index, 400M nodes).
Black: setup #759 R K B N N R Q B
King on the b-file, rooks on a, f, queen on the g-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 759 gives White +0.13 (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 58.
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 shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.
For comparison, in symmetric play setup 307 gives White +0.33 and setup 759 gives White +0.13: 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 b4, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±23 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 9, Black won 1 (White scored 45.0%).
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 | 15 | -11 | 1. b3 g5 2. Bxh8 Qxh8 3. d4 Qg7 4. Nf3 g4 |
| S1 | 500 000 | 20 | -3 | 1. b3 a5 2. g3 Ra6 3. c4 f5 4. f4 g5 |
| S2 | 2 000 000 | 23 | +3 | 1. b3 a5 2. g3 Ra6 3. c4 f5 4. f4 g5 |
| S3 | 8 000 000 | 29 | -5 | 1. b3 a5 2. c4 Ra6 3. Nf3 f5 4. d4 f4 |
| S4 | 32 000 000 | 35 | +13 | 1. b3 a5 2. c4 f5 3. g3 g5 4. Bxh8 Qxh8 |
| S5 | 128 000 000 | 40 | 0 | 1. b4 f5 2. c4 f4 3. g3 d6 4. gxf4 Rxf4 |
| S6 | 400 000 000 | 48 | 0 | 1. b4 f5 2. c4 f4 3. g3 d6 4. gxf4 Rxf4 |
| S7 | 800 000 000 | 55 | 0 | 1. b4 f5 2. c4 f4 3. g3 d6 4. gxf4 Rxf4 |
| S8 | 1 600 000 000 | 58 | 0 | 1. b4 f5 2. c4 f4 3. g3 d6 4. gxf4 Rxf4 |
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 | not checked |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair held exactly 0.00 up to 1 600 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: 0
- Lc0 0.32.1: +4
Independent confirmations: 2 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 +75, Black +123, difference -48. 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, 9 draws, 1 Black wins, White scored 45.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +18 | 40 | 1. b4 f5 2. c4 d6 3. f4 Nf6 4. d3 h6 5. g3 g5 |
| 2 | +16 | 40 | 1. b3 a5 2. g3 Ra6 3. c4 g5 4. Bxh8 Qxh8 5. d4 Qg7 |
| 3 | 0 | 40 | 1. c4 g5 2. d4 a5 3. b3 Ra6 4. Nc3 f5 5. g3 d6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 23 cp, mean 3.5 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | b3 | -7 | a5 | -2 |
| 2 | c4 | +8 | f5 | +14 |
| 3 | g3 | +11 | g5 | +21 |
| 4 | Bxh8 | +20 | Qxh8 | +23 |
| 5 | d4 | +11 | Qg7 | +17 |
| 6 | Nh3 | +8 | h6 | +11 |
| 7 | f4 | +3 | Ra6 | +14 |
| 8 | Nc3 | +6 | Nf6 | 0 |
| 9 | Nf2 | 0 | d6 | -11 |
| 10 | Nd3 | 0 | gxf4 | 0 |
| 11 | gxf4 | +9 | h5 | +8 |
| 12 | a3 | 0 | e5 | -2 |
| 13 | dxe5 | 0 | dxe5 | 0 |
| 14 | fxe5 | 0 | Ng4 | -5 |
| 15 | Rg1 | 0 | Qe7 | 0 |
| 16 | Nd5 | 0 | Qh4+ | 0 |
| 17 | Kd2 | 0 | Nf7 | 0 |
| 18 | Qc3 | 0 | Re8 | 0 |
| 19 | Kc1 | 0 | Qxh2 | 0 |
| 20 | Nc5 | 0 | Rc6 | 0 |
| 21 | e6 | 0 | Ng5 | 0 |
| 22 | Nd7+ | 0 | Bxd7 | 0 |
| 23 | Nf6 | 0 | Bc8 | 0 |
| 24 | Nd7+ | 0 | Bxd7 | 0 |
| 25 | exd7 | 0 | Rd8 | 0 |
| 26 | Bxc6 | 0 | bxc6 | 0 |
| 27 | Rgf1 | 0 | Nf2 | 0 |
| 28 | Qxa5 | 0 | Qf4+ | 0 |
| 29 | Kb1 | 0 | Qe4+ | 0 |
| 30 | Ka1 | 0 | Nxd1 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 9, Black won 1 — White scored 45.0%. Average length 40.0 moves.
Sample game 1 (1/2-1/2)
1. b3 f6 2. d4 g5 3. c4 a5 4. g3 f5 5. Nc3 Ra6 6. Nf3 g4 7. Nh4 e6 8. d5 d6 9. e4 Bf6 10. exf5 Bg5 11. Qc2 Bxh4 12. gxh4 e5 13. f4 gxf3 14. Bxf3 b6 15. Qg2 Qf7 16. Ne4 Rg8 17. Qf2 Qxf5 18. Bh1 Qh3 19. Ng5 Qd7 20. O-O-O Ng7 21. Nxh7 Nh5 22. Be4 Nb7 23. Bc2 Nc5 24. Kb1 Qd8 25. Rg1 Rh8 26. Rg5 Qe7 27. Rxh5 Bg4 28. Rxe5 dxe5 29. Rg1 Rxh7 30. Rxg4 Rf7 31. Qg2 Ka7 32. Rg8 Qxh4 33. Bc3 Qf6 34. Rg5 Qf1+ 35. Qxf1 Rxf1+ 36. Kb2 Rf2 37. Kc1 Kb7 38. Bxe5 Ra8 39. Bg3 Rg2 40. Bf4 Rf2 41. Bg3 Rg2 42. Bf4 Rf2
Sample game 2 (1/2-1/2)
1. b3 a5 2. g3 h6 3. f4 f5 4. Nf3 a4 5. b4 Qxa2 6. Na3 Qg8 7. c4 d6 8. e3 g5 9. Bxh8 Qxh8 10. d4 Nf6 11. O-O Bd7 12. Bg2 Qg7 13. d5 Ne4 14. c5 Qc3 15. Qxc3 Nxc3 16. Rd3 Ne4 17. Rc1 c6 18. Nc4 Ra6 19. Rdd1 dxc5 20. Nfe5 Bc8 21. bxc5 gxf4 22. exf4 cxd5 23. Nb6 Re8 24. Nxd5 Nc6 25. Nxc6+ Rxc6 26. Bxe4 fxe4 27. Nb6 e5 28. Rc4 exf4 29. Rxa4 Rxc5 30. Ra8+ Kc7 31. Nd5+ Kc6 32. Nf6 Bg4 33. Rxe8 Bxd1 34. Nxe4 Rh5 35. Re6+ Kd5 36. Re7 Kc6 37. Re6+ Kc7 38. Re7+ Kc6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 307 / 759 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): rkbnnrqb/pppppppp/8/8/8/8/PPPPPPPP/BNQRKRNB w DFaf - 0 1
Mirror twin (the same position mirrored): White 355 vs Black 386.
Current place in the live balance rating: 200.