White 51 vs Black 516

The two setups

White: setup #51 B N N R Q K R B

King on the f-file, rooks on d, g, 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 51 gives White +0.24 (Morozov Balance Index, 400M nodes).

Black: setup #516 R B B N 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 516 gives White +0.21 (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 55.

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 -20 and 0 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 51 gives White +0.24 and setup 516 gives White +0.21: 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 g3, and 3 first moves are within 10 cp of it.

Along the engine's main line (13 moves) the evaluation stayed within ±0 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.

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.

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: +17

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 +81, Black +63, difference +18. 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.

Main-line play-out

13 moves, 5 000 000 nodes per half-move. Largest |evaluation| 0 cp, mean 0.0 cp, final 0 cp.

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 41.4 moves.

1. e4 f6 2. d4 a5 3. b3 e5 4. Nd3 d6 5. g4 a4 6. Nd2 Ne7 7. g5 Bh3+ 8. Bg2 Bxg2+ 9. Rxg2 fxg5 10. dxe5 axb3 11. axb3 Ne6 12. exd6 cxd6 13. Nf3 h6 14. Nd4 Nxd4 15. Bxd4 O-O 16. h4 Nc6 17. Bb2 Qh5 18. hxg5 Ba7 19. gxh6 Qh1+ 20. Rg1 Qh3+ 21. Rg2 Qh1+ 22. Rg1 Qh3+ 23. Ke2 Qh5+ 24. Kf1 Qh3+ 25. Rg2 Qh1+ 26. Rg1 Qh3+ 27. Ke2 Qh5+ 28. Kf1

1. g3 h5 2. e4 c5 3. b3 e5 4. Nc3 d6 5. Nd5 Nc6 6. O-O h4 7. Nd3 hxg3 8. fxg3 Nce7 9. Ne3 Bc7 10. Bg2 f6 11. Qe2 Nc6 12. Ne1 Nge7 13. c3 Qg6 14. Rf2 Be6 15. Nd5 O-O-O 16. d3 Bb6 17. Bb2 Bxd5 18. exd5 Nb8 19. Nf3 Qh7 20. Nh4 f5 21. Bc1 Rde8 22. d4 Nd7 23. dxe5 Nxe5 24. c4 g6 25. Nf3 Ng8 26. h4 Nf6 27. Ng5 Qd7 28. Ne6 Nh5 29. Bb2 Nxg3 30. Qe3 Nh5 31. Bxe5 dxe5 32. Qxe5 Bd8 33. d6 Qxe6 34. Qxc5+ Kb8 35. Qb5 Bb6 36. c5 Nf4 37. cxb6 Nxg2 38. Qa4 axb6 39. d7 Rd8 40. Kxg2 Qc6+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 51 / 516 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): rbbnqknr/pppppppp/8/8/8/8/PPPPPPPP/BNNRQKRB w DGah - 0 1

Mirror twin: White 899 vs Black 542 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 227.