White 461 vs Black 722

The two setups

White: setup #461 R N N B K Q B R

King on the e-file, rooks on a, h, queen on the f-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 461 gives White +0.47 (Morozov Balance Index, 400M nodes).

Black: setup #722 B R K N Q B N R

King on the c-file, rooks on b, h, queen on the e-file; one 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 722 gives White +0.26 (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 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 shallow rungs wandered between 0 and +24 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 461 gives White +0.47 and setup 722 gives White +0.26: 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 2 first moves are within 10 cp of it.

Along the engine's main line (22 moves) the evaluation stayed within ±28 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 held exactly 0.00 up to 1 600 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: +5

Independent confirmations: 2 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 +32, Black +86, difference -54. 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

22 moves, 5 000 000 nodes per half-move. Largest |evaluation| 28 cp, mean 5.6 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 38.5 moves.

1. e4 b6 2. Nc3 f5 3. e5 e6 4. f4 d6 5. Nd3 Nf7 6. h4 dxe5 7. Nxe5 Nxe5 8. fxe5 Ne7 9. Rh3 Nc6 10. Be2 O-O-O 11. O-O-O Nxe5 12. d4 Ng4 13. a4 Bb4 14. Nb5 Kb8 15. Kb1 Bd5 16. c3 Be7 17. c4 Be4+ 18. Bd3 Bxd3+ 19. Rhxd3 a6 20. Nc3 Qc6 21. c5 bxc5 22. d5 Qb6 23. a5 Qb4 24. dxe6 Rxd3 25. Qxd3 Rd8 26. Qxa6 Rxd1+ 27. Nxd1 Qe4+ 28. Kc1 Bxh4 29. Qb5+ Ka8 30. Qa6+ Kb8 31. Qb5+ Ka8 32. Qa6+

1. f3 b6 2. e4 e5 3. Be2 f5 4. exf5 Ne7 5. Nc3 Nxf5 6. Nb3 Nc6 7. O-O-O O-O-O 8. Bc4 Qg6 9. a3 h5 10. Bf2 h4 11. Re1 Kb8 12. Qd3 Nce7 13. g3 hxg3 14. hxg3 Rxh1 15. Rxh1 Qf6 16. Nd5 Bxd5 17. Bxd5 Nxd5 18. Qxd5 Nd6 19. Kb1 Re8 20. a4 c6 21. Qd3 Kb7 22. Rf1 Be7 23. Qe2 Rf8 24. f4 exf4 25. gxf4 Qf7 26. Rg1 Bf6 27. Qd3 Ne8 28. Bd4 Nc7 29. Be5 Qd5 30. Qxd5 Nxd5 31. c3 c5 32. d4 cxd4 33. Bxf6 gxf6 34. Rd1 Rh8 35. Rxd4 Kc6 36. Rc4+ Kb7 37. Rd4 Kc6 38. Rc4+ Kb7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 461 / 722 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): brknqbnr/pppppppp/8/8/8/8/PPPPPPPP/RNNBKQBR w AHbh - 0 1

Mirror twin (the same position mirrored): White 696 vs Black 423.

Current place in the live balance rating: 238.