White 8 vs Black 513
White starts from setup 8 (QBNNBRKR), Black from setup 513 (BRNBQKNR). In the encyclopedia since 2026-10-10: 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. 8, Black by position No. 513, 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 #8 Q B N N B 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 8 gives White +0.38 (Morozov Balance Index, 400M nodes).
Black: setup #513 B R N B Q K N R
King on the f-file, rooks on b, h, queen on the e-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 513 gives White +0.15 (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 51.
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 -22 and +34 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 8 gives White +0.38 and setup 513 gives White +0.15: 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 3 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 | 13 | +34 | 1. f3 b5 2. a4 b4 3. b3 c5 4. c4 Nf6 |
| S1 | 500 000 | 17 | +3 | 1. f3 c5 2. Bf2 b6 3. e4 Nh6 4. Re1 e6 |
| S2 | 2 000 000 | 21 | -6 | 1. f3 b5 2. a4 bxa4 3. Qxa4 c5 4. Bf2 d6 |
| S3 | 8 000 000 | 28 | -22 | 1. f3 f5 2. c4 e6 3. d4 Nf6 4. Nd3 O-O |
| S4 | 32 000 000 | 31 | -18 | 1. d4 f5 2. f3 Nf6 3. c4 e6 4. Nd3 O-O |
| S5 | 128 000 000 | 39 | +3 | 1. d4 c5 2. dxc5 b6 3. b3 bxc5 4. c4 d6 |
| S6 | 400 000 000 | 44 | 0 | 1. d4 e6 2. f3 f5 3. c4 Nf6 4. Rf2 O-O |
| S7 | 800 000 000 | 51 | 0 | 1. d4 d5 2. b3 b6 3. c4 dxc4 4. bxc4 e6 |
| S8 | 1 600 000 000 | 51 | 0 | 1. d4 d5 2. b3 b6 3. c4 dxc4 4. bxc4 e6 |
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: +13
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 +30, Black +94, difference -64. 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 | -15 | 39 | 1. d4 e6 2. c4 f5 3. f3 Nf6 4. Rf2 O-O 5. O-O Ne7 |
| 2 | -18 | 39 | 1. c4 |
| 3 | -18 | 39 | 1. f3 e6 2. c4 f5 3. d4 Nf6 4. Rf2 O-O 5. O-O Ne7 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 26 cp, mean 8.7 cp, final +11 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f3 | -23 | e6 | -21 |
| 2 | d4 | -4 | f5 | +1 |
| 3 | Nd3 | +1 | b6 | +13 |
| 4 | a4 | +15 | Nf6 | +22 |
| 5 | b4 | +19 | O-O | +6 |
| 6 | c4 | +20 | Ne7 | +16 |
| 7 | Rf2 | +12 | d6 | 0 |
| 8 | O-O | +1 | c5 | 0 |
| 9 | e3 | 0 | Ng6 | 0 |
| 10 | Qa2 | +4 | Nh5 | +6 |
| 11 | Nc3 | +1 | Rc8 | +5 |
| 12 | bxc5 | 0 | bxc5 | +5 |
| 13 | a5 | -5 | Bg5 | -3 |
| 14 | Bd2 | +4 | Bh4 | +11 |
| 15 | Re2 | +10 | Bf6 | +16 |
| 16 | Nb5 | 0 | Qd7 | -7 |
| 17 | a6 | -9 | cxd4 | -13 |
| 18 | Nxd4 | -16 | f4 | -16 |
| 19 | Rfe1 | -10 | Kh8 | -3 |
| 20 | Bb4 | 0 | fxe3 | 0 |
| 21 | Nb5 | 0 | Bh4 | 0 |
| 22 | Rxe3 | 0 | Bxe1 | 0 |
| 23 | Rxe1 | 0 | Bxf3 | 0 |
| 24 | Bxd6 | +26 | Rf5 | +12 |
| 25 | gxf3 | +25 | Nh4 | +20 |
| 26 | Re3 | +8 | e5 | +9 |
| 27 | Nxe5 | +18 | Rg5+ | +14 |
| 28 | Kf1 | +7 | Qh3+ | +8 |
| 29 | Ke1 | +15 | Rg1+ | +12 |
| 30 | Kd2 | +16 | Qf1 | +11 |
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 46.6 moves.
Sample game 1 (1/2-1/2)
1. d4 f5 2. Nd3 Nf6 3. f3 O-O 4. b4 e6 5. a4 b6 6. c4 d6 7. b5 Nh5 8. e3 c5 9. bxc6 Bxc6 10. Nc3 Bf6 11. Qa3 a5 12. Qa2 Ne7 13. Bg3 f4 14. Nxf4 Nxf4 15. Bxf4 Bxd4 16. exd4 Rxf4 17. Qd2 e5 18. dxe5 dxe5 19. Re1 Rd4 20. Qg5 Ng6 21. h4 Qd8 22. Qe3 Rxh4 23. Rxh4 Qxh4 24. Be4 Rc8 25. Rd1 Nf4 26. Bxc6 Rxc6 27. Qxe5 Re6 28. Qb8+ Kf7 29. Ne4 Ne2+ 30. Kf1 Nc3 31. Rd7+ Kg6 32. Nf2 Ne2 33. g4 Qf6 34. Qa8 Qa1+ 35. Rd1 Qf6 36. Qd5 h6 37. Rd2 Nf4 38. Qb5 Re5 39. c5 bxc5 40. Qb1+ Kf7
Sample game 2 (1/2-1/2)
1. c4 c5 2. a4 Nh6 3. f3 O-O 4. Bg3 d6 5. e3 e5 6. d4 cxd4 7. exd4 Ne7 8. Ne2 a6 9. Ndc3 Nhf5 10. Bf2 Nxd4 11. Nxd4 exd4 12. Bxd4 Qc6 13. Qa2 Rc8 14. Bf2 Bb6 15. Qa3 Rfd8 16. Re1 Kf8 17. b3 Bxf2+ 18. Kxf2 b6 19. h4 h6 20. Re3 Qc5 21. Qxc5 dxc5 22. a5 bxa5 23. Rhe1 Nc6 24. Na4 Nd4 25. Rd1 Ne6 26. Rxd8+ Rxd8 27. Bf5 Rd2+ 28. Ke1 Rxg2 29. Bxe6 fxe6 30. Nxc5 Rc2 31. f4 Kf7 32. Rxe6 a4 33. Rxa6 axb3 34. Nxb3 Bh1 35. Na5 Rh2 36. Ra7+ Ke6 37. Rxg7 Rc2 38. Kd1 Be4 39. Ra7 Kf5 40. Rf7+ Ke6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 8 / 513 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): brnbqknr/pppppppp/8/8/8/8/PPPPPPPP/QBNNBRKR w FHbh - 0 1
Mirror twin: White 957 vs Black 539 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 95.