White 82 vs Black 609

The two setups

White: setup #82 B N N R K B R Q

King on the e-file, rooks on d, g, queen on the h-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 82 gives White +0.28 (Morozov Balance Index, 400M nodes).

Black: setup #609 B R N B Q K R N

King on the f-file, rooks on b, g, queen on the e-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 609 gives White +0.28 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 59.

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 -17 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 82 gives White +0.28 and setup 609 gives White +0.28: 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 b3, and 2 first moves are within 10 cp of it.

Along the engine's main line (15 moves) the evaluation stayed within ±11 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 1, drawn 7, Black won 2 (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 16 000 000 000 nodes.

Swap the two setups, giving White the black back rank and Black the white one, and the evaluation jumps to +101. The same two armies dealt the other way round are no longer balanced at all: that is how precisely this pair pays for the first move.

Independent engines, run on the same position:

• Berserk 14: +3
• Lc0 0.32.1: +12

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 +49, Black +137, difference -88. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 11 White wins, 104 draws, 45 Black wins, White scored 39.4%.

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| 11 cp, mean 2.3 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 7, Black won 2 — White scored 45.0%. Average length 49.0 moves.

1. g3 b5 2. Bg2 Bxg2 3. Qxg2 e5 4. e4 O-O 5. b3 d6 6. O-O f6 7. Kh1 Nf7 8. f4 c6 9. d4 Bb6 10. Ne2 Ne7 11. c4 bxc4 12. bxc4 Ba5 13. c5 exf4 14. gxf4 d5 15. Bc3 Bc7 16. Nd2 dxe4 17. Nxe4 Nd5 18. Bd2 Qd7 19. N4c3 Rfd8 20. Nxd5 Qxd5 21. Qxd5 Rxd5 22. Rb1 Re8 23. Rf2 Nd8 24. Rb3 f5 25. Ra3 Ne6 26. Rxa7 Bb8 27. Ra5 Nxd4 28. Nxd4 Rxd4 29. Ra6 Red8 30. Rxc6 Rxd2 31. Rxd2 Rxd2 32. Rc8+ Kf7 33. Rxb8 Rxa2 34. c6 Rc2 35. Rb7+ Kg6 36. c7 h6 37. Kg1 Kh5 38. c8=R Rxc8 39. Rxg7 Rc2 40. Rg3 Rc4 41. Kg2 Rxf4 42. Rg7 Kh4 43. Rf7 Rg4+ 44. Kf3 Kg5 45. Rg7+ Kh5 46. Rf7 Kg6 47. Ra7 Kg5 48. Rg7+ Kh5

1. b3 b5 2. e3 O-O 3. d4 e5 4. dxe5 Ng6 5. Be2 Nxe5 6. Bf3 Nb6 7. Nd2 d5 8. Nd3 Nxd3+ 9. cxd3 c5 10. O-O Qe6 11. h4 Be7 12. h5 h6 13. Qh2 Bd6 14. Qh4 a5 15. e4 d4 16. Bg4 Qe7 17. Qh3 Bc6 18. Nf3 Bd7 19. Nh4 Bxg4 20. Qxg4 Qg5 21. Qxg5 hxg5 22. Nf5 Rfd8 23. Bb2 Bf8 24. Bc1 g6 25. Ng3 Be7 26. hxg6 fxg6 27. Ne2 a4 28. f4 c4 29. bxc4 bxc4 30. fxg5 c3 31. Nf4 Nd7 32. Nxg6 Bd6 33. Rf5 Rb1 34. Rdf1 Kh7 35. Nf4 Rxc1 36. Rxc1 Bxf4 37. Rxf4 Ne5 38. Rb1 Nxd3 39. Rf7+ Kg6 40. Rf6+ Kh5

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 82 / 609 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): brnbqkrn/pppppppp/8/8/8/8/PPPPPPPP/BNNRKBRQ w DGbg - 0 1

Mirror twin: White 871 vs Black 251 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 23.