White 461 vs Black 241

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 #241 B N R B K Q N R

King on the e-file, rooks on c, h, queen on the f-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 241 gives White +0.22 (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 60.

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 -23 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 461 gives White +0.47 and setup 241 gives White +0.22: 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 f3, and 3 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the evaluation stayed within ±27 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: +3

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 +32, Black +43, difference -11. 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

30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 27 cp, mean 9.6 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 34.0 moves.

1. f4 b6 2. Nc3 f5 3. e3 c5 4. Nd3 Nf6 5. Bf3 Bxf3 6. Qxf3 Nc6 7. Bf2 Qf7 8. Ne5 Qe6 9. Nxc6 Qxc6 10. Qxc6 Rxc6 11. a4 a6 12. Bh4 e6 13. Ke2 Kf7 14. Nd1 Ne4 15. Bxd8 Rxd8 16. Nf2 Nxf2 17. Kxf2 e5 18. fxe5 Re8 19. Ke2 Rxe5 20. Raf1 Rf6 21. Rf3 d5 22. Rhf1 d4 23. h4 Kg6 24. Rg3+ Kf7 25. Rgf3 Ke6 26. Rf4 h5 27. g3 dxe3 28. dxe3 Kd5 29. Rd1+ Kc6 30. Kf3 Rd5 31. Rxd5 Kxd5 32. Ke2 Ke5 33. Rf1 Rg6 34. Kf3 Rg4 35. b3 c4 36. Rd1 a5 37. Rd7 cxb3 38. cxb3 g6 39. Re7+ Kf6 40. Rc7 Rb4

1. a4 c5 2. Nc3 e6 3. e4 Nc6 4. f4 b6 5. Bf3 Qe7 6. Qa6 Rb8 7. Qe2 Nb4 8. d4 f5 9. Bf2 Nh6 10. dxc5 bxc5 11. e5 Bxf3 12. gxf3 O-O 13. O-O Nf7 14. a5 Rc8 15. Nd3 Nxd3 16. Qxd3 Bc7 17. Rad1 Rfd8 18. Qb5 Bb8 19. Na4 d6 20. exd6 Bxd6 21. Qc4 Nh8 22. Rfe1 Ng6 23. Qxe6+ Qxe6 24. Rxe6 Bc7 25. Rxd8+ Rxd8 26. Bxc5 Bxa5 27. Rd6 Rxd6 28. Bxd6 Bd2 29. Bb8 Be3+ 30. Kf1 Kf7 31. b4 Nxf4 32. c4 Ke8 33. Nc3 a6 34. Bxf4 Bxf4 35. h4 h5 36. Nd5 Bg3 37. Kg2 Bb8 38. f4 Kd7 39. Kg3 Kd6 40. Kf2 Ba7+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 461 / 241 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): bnrbkqnr/pppppppp/8/8/8/8/PPPPPPPP/RNNBKQBR w AHch - 0 1

Mirror twin: White 696 vs Black 619 — a different position (castling squares are fixed), not evaluated by the search.