White 31 vs Black 573

The two setups

White: setup #31 N Q N R K R B B

King on the e-file, rooks on d, f, queen on the b-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 31 gives White +0.26 (Morozov Balance Index, 400M nodes).

Black: setup #573 R N K B N R B Q

King on the c-file, rooks on a, f, queen on the h-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 573 gives White +0.33 (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 same corridor is required at every deeper budget (8 G, 16 G) at which the pair has been evaluated.

The shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±8 cp.

For comparison, in symmetric play setup 31 gives White +0.26 and setup 573 gives White +0.33: 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 (21 moves) the evaluation stayed within ±20 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: -7

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 +6, Black +88, difference -82. 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

21 moves, 5 000 000 nodes per half-move. Largest |evaluation| 20 cp, mean 4.1 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 38.4 moves.

1. f4 f5 2. g3 a5 3. Nd3 h5 4. b4 h4 5. Bf3 g5 6. bxa5 c6 7. Nb3 g4 8. Bg2 d6 9. Bd4 Qh7 10. Qb2 Bc4 11. Qc3 Qf7 12. Nb2 Bd5 13. Bxd5 Qxd5 14. Nc4 hxg3 15. hxg3 c5 16. Bg7 Rg8 17. Bh8 Nc6 18. Ne3 Qe4 19. Kf2 Nc7 20. d3 Qxe3+ 21. Kxe3 Nd5+ 22. Kd2 Nxc3 23. Bxc3 Nxa5 24. a4 Nxb3+ 25. cxb3 b5 26. Ra1 bxa4 27. Rxa4 Rxa4 28. bxa4 d5 29. e3 Kd7 30. Rh1 Re8 31. Kc2 e6 32. Rh7+ Re7 33. Rh8 Re8 34. Rh7+ Kc6 35. Rf7 Re7 36. Rf8 Bb6 37. Rc8+ Kd7 38. Rh8 Kc6 39. Rc8+ Kb7 40. Rh8 c4

1. f4 f5 2. g3 a5 3. Nd3 h5 4. b4 h4 5. Bf3 g5 6. bxa5 c6 7. Nb3 g4 8. Bg2 d6 9. Bd4 Qh7 10. Qb2 Bc4 11. Qc3 Qf7 12. Nb2 Bd5 13. Bxd5 Qxd5 14. Nc4 hxg3 15. hxg3 c5 16. Bg7 Rg8 17. Bh8 Nc6 18. Ne3 Qe4 19. Kf2 Nc7 20. d3 Qxe3+ 21. Kxe3 Nd5+ 22. Kd2 Nxc3 23. Bxc3 Nxa5 24. a4 Nxb3+ 25. cxb3 b5 26. Ra1 bxa4 27. Rxa4 Rxa4 28. bxa4 d5 29. e3 Kd7 30. Rh1 Re8 31. Kc2 e6 32. Rh7+ Re7 33. Rh8 Re8 34. Rh7+ Kc6 35. Rf7 Re7 36. Rf8 Bb6 37. Rc8+ Kd7 38. Rh8 Kc6 39. Rc8+ Kb7 40. Rh8 c4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 31 / 573 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): rnkbnrbq/pppppppp/8/8/8/8/PPPPPPPP/NQNRKRBB w DFaf - 0 1

Mirror twin: White 928 vs Black 488 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 170.