White 14 vs Black 641

The two setups

White: setup #14 Q N N R K B B R

King on the e-file, rooks on d, h, queen on the a-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 14 gives White +0.14 (Morozov Balance Index, 400M nodes).

Black: setup #641 B R N B K R Q N

King on the e-file, rooks on b, f, queen on the g-file; one 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 641 gives White +0.16 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±3 centipawns of equality, reaching search depth 54.

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 +26 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 14 gives White +0.14 and setup 641 gives White +0.16: 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 2 first moves are within 10 cp of it.

Along the engine's main line (15 moves) the evaluation stayed within ±29 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.

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: -1

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 +11, Black +49, difference -38. 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.

Main-line play-out

15 moves, 5 000 000 nodes per half-move. Largest |evaluation| 29 cp, mean 7.9 cp, final 0 cp.

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 45.7 moves.

1. d4 f5 2. e3 e6 3. Nd3 b6 4. a4 g5 5. h4 gxh4 6. Bh2 h3 7. Rg1 hxg2 8. Bxg2 Bxg2 9. Nf4 Rf7 10. Rxg2 Rg7 11. Rxg7 Qxg7 12. Nc3 Nd6 13. Ke2 Be7 14. Rg1 Qf7 15. Qd1 Ne4 16. Qd3 Nxc3+ 17. Qxc3 Bd6 18. Bg3 O-O-O 19. a5 Kb8 20. Kd2 Ng6 21. axb6 cxb6 22. Nxg6 Bxg3 23. Rxg3 hxg6 24. Qa3 Kb7 25. Qd6 Rg8 26. Rg5 Qh7 27. c3 a5 28. Rg2 Rh8 29. d5 Rg8 30. dxe6 dxe6 31. Kc2 Qf7 32. Rh2 Re8 33. Rh6 g5 34. Qg3 Qd7 35. Qxg5 Qa4+ 36. Kc1 Qa1+ 37. Kc2 Qa4+ 38. Kc1 Qa1+ 39. Kc2

1. d4 b6 2. f3 f5 3. Nd3 Qe6 4. g3 Nd6 5. h4 Qh6 6. Bg2 e6 7. Bf2 Ne4 8. fxe4 fxe4 9. Nf4 Rxf4 10. gxf4 e3 11. Bxa8 exf2+ 12. Kf1 Rxa8 13. Nc3 Ng6 14. Qc1 Nxf4 15. Qe3 Bf6 16. Qf3 c6 17. h5 Ke7 18. e3 Nd5 19. Nxd5+ exd5 20. Rh3 Re8 21. Rd2 Bg5 22. Qg3 Kd8 23. Qb8+ Ke7 24. Qe5+ Kd8 25. Qb8+ Ke7 26. Qc7 Qd6 27. Qxd6+ Kxd6 28. Kxf2 b5 29. Ke2 a5 30. Rd1 a4 31. Rg1 h6 32. c3 Re4 33. Kd3 Ke6 34. b3 axb3 35. axb3 Bf6 36. Rg6 Kd6 37. Rh1 Ke6 38. Rh3 Kd6 39. Rh2 Ke6

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 14 / 641 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): brnbkrqn/pppppppp/8/8/8/8/PPPPPPPP/QNNRKBBR w DHbf - 0 1

Mirror twin: White 948 vs Black 219 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 117.