White 517 vs Black 316
White starts from setup 517 (RNBBQKNR), Black from setup 316 (NBQRKRBN). In the encyclopedia since 2026-10-21: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #517 R N B B Q K N R
King on the f-file, rooks on a, h, queen on the e-file; no 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 517 gives White +0.14 (Morozov Balance Index, 400M nodes).
Black: setup #316 N B Q R K R B N
King on the e-file, rooks on d, f, queen on the c-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 316 gives White +0.56 (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 57.
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 -25 and +11 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 517 gives White +0.14 and setup 316 gives White +0.56: 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 e4, and 3 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 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 | 15 | -25 | 1. d3 f6 2. Nh3 d5 3. O-O c5 4. e4 dxe4 |
| S1 | 500 000 | 18 | -2 | 1. d3 c6 2. f4 f5 3. e3 Bf7 4. Ne2 O-O |
| S2 | 2 000 000 | 23 | -10 | 1. d3 d5 2. f4 f6 3. e4 Bf7 4. Nc3 dxe4 |
| S3 | 8 000 000 | 29 | -5 | 1. d3 d5 2. e4 f6 3. Ne2 c5 4. O-O Nc7 |
| S4 | 32 000 000 | 34 | +11 | 1. d3 d5 2. e4 dxe4 3. dxe4 c6 4. Ne2 f6 |
| S5 | 128 000 000 | 40 | 0 | 1. d3 d5 2. e4 dxe4 3. dxe4 c6 4. Ne2 f6 |
| S6 | 400 000 000 | 48 | 0 | 1. d3 d5 2. e4 f6 3. f4 c6 4. Ne2 dxe4 |
| S7 | 800 000 000 | 53 | 0 | 1. d3 d5 2. e4 f6 3. Nc3 dxe4 4. dxe4 c6 |
| S8 | 1 600 000 000 | 57 | 0 | 1. d3 d5 2. e4 f6 3. Nc3 c6 4. f4 dxe4 |
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: -8
- Lc0 0.32.1: +6
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 +62, Black +66, difference -4. 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 | +13 | 43 | 1. e4 d5 2. d3 dxe4 3. dxe4 c6 4. Ne2 f5 5. exf5 Qxf5 |
| 2 | +9 | 43 | 1. d3 d5 2. e4 dxe4 3. dxe4 c6 4. Ne2 f5 5. exf5 Qxf5 |
| 3 | +5 | 43 | 1. f4 d5 2. d3 c6 3. e3 f6 4. Ne2 Bf7 5. O-O O-O |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 23 cp, mean 7.2 cp, final -5 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d3 | -7 | d5 | -8 |
| 2 | f4 | -3 | f6 | +2 |
| 3 | e4 | +8 | c5 | +17 |
| 4 | Ne2 | +23 | Nc7 | +14 |
| 5 | b3 | +15 | Bf7 | 0 |
| 6 | c4 | 0 | dxc4 | +1 |
| 7 | dxc4 | -3 | Ne6 | 0 |
| 8 | Nbc3 | -6 | O-O | -8 |
| 9 | Nd5 | -11 | Rfe8 | -6 |
| 10 | O-O | -6 | Nd4 | -19 |
| 11 | Nxd4 | -6 | cxd4 | -10 |
| 12 | Nb4 | -11 | d3 | -15 |
| 13 | Kh1 | -21 | Qd7 | -21 |
| 14 | Be3 | -5 | g5 | -9 |
| 15 | Nd5 | 0 | gxf4 | -8 |
| 16 | Bxf4 | -10 | Bxf4 | -5 |
| 17 | Rxf4 | -9 | Qd6 | -11 |
| 18 | Rf3 | 0 | Qe5 | 0 |
| 19 | Rb1 | 0 | Bg6 | -4 |
| 20 | Qf2 | -3 | Kg7 | -3 |
| 21 | Rxd3 | -10 | Bxe4 | -11 |
| 22 | Re3 | -5 | Qf5 | -9 |
| 23 | Qxf5 | -12 | Bxf5 | -11 |
| 24 | Rc1 | -16 | e6 | -8 |
| 25 | g4 | 0 | exd5 | 0 |
| 26 | Rxe8 | -6 | Rxe8 | -8 |
| 27 | gxf5 | -2 | dxc4 | -2 |
| 28 | Kg2 | -1 | Rd8 | -1 |
| 29 | Bf3 | 0 | Rd2+ | -12 |
| 30 | Kg3 | -3 | Nf7 | -5 |
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 37.2 moves.
Sample game 1 (1/2-1/2)
1. e3 c5 2. b4 cxb4 3. Ne2 f5 4. O-O Nb6 5. Bb2 Bd5 6. f4 Qc6 7. Rf2 O-O 8. d3 Ng6 9. Nd4 Qd6 10. c4 Bc6 11. Bb3 Kh8 12. Nxc6 Qxc6 13. h4 Nxh4 14. Qxb4 Bd6 15. Qb5 Qxb5 16. cxb5 e6 17. g3 Ng6 18. Kg2 Bc5 19. Rc2 Rc8 20. e4 h5 21. exf5 Rxf5 22. d4 Bd6 23. Rxc8+ Nxc8 24. d5 Bxf4 25. dxe6 dxe6 26. gxf4 Nxf4+ 27. Kg1 Ne2+ 28. Kh1 Rf2 29. Be5 Rf5 30. Bb2 Rf2 31. Be5 Rf5
Sample game 2 (1/2-1/2)
1. Nh3 f6 2. d3 Be6 3. Nf4 Bf7 4. e4 e5 5. Nh5 O-O 6. Ng3 d5 7. Nf5 Rde8 8. Bh6 gxh6 9. Nxh6+ Kg7 10. Nf5+ Kg8 11. Nh6+ Kg7 12. Nf5+ Kg8
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 517 / 316 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): nbqrkrbn/pppppppp/8/8/8/8/PPPPPPPP/RNBBQKNR w AHdf - 0 1
Mirror twin: White 538 vs Black 364 — a different position (castling squares are fixed), not evaluated by the search.