White 411 vs Black 26

The two setups

White: setup #411 R Q N N B K R B

King on the f-file, rooks on a, g, queen on the b-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 411 gives White +0.32 (Morozov Balance Index, 400M nodes).

Black: setup #26 N Q N R B B K R

King on the g-file, rooks on d, h, queen on the b-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 26 gives White +0.36 (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 shallow rungs agreed early: from 100 thousand to 128 million nodes the evaluation never left ±9 cp.

For comparison, in symmetric play setup 411 gives White +0.32 and setup 26 gives White +0.36: 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 (30 moves) the evaluation stayed within ±24 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 9, Black won 0 (White scored 55.0%).

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: -1
• 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 +22, Black +82, difference -60. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.

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| 24 cp, mean 4.3 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 37.4 moves.

1. d4 g6 2. O-O h5 3. c4 Bg7 4. d5 c6 5. Bc3 b5 6. b3 bxc4 7. bxc4 Qxb1 8. Rxb1 Ncb6 9. c5 Nxd5 10. Ba5 Rc8 11. g3 f5 12. Bxd5+ cxd5 13. Rb7 Rxc5 14. Nb3 Rc8 15. Ne3 e6 16. Rxa7 g5 17. Rc1 Rb8 18. Nc5 f4 19. Nf1 Bd4 20. e3 Bxc5 21. Rxc5 fxe3 22. fxe3 O-O 23. Nd2 Nb6 24. Rb5 Nc8 25. Rxb8 Nxa7 26. Bb4 Nc6 27. Bxf8 Nxb8 28. Bd6 Nc6 29. e4 d4 30. Bc7 e5 31. Nc4 Kf7 32. Nxe5+ Ke6 33. Nf3 g4 34. Ng5+ Kf6 35. h4 gxh3 36. Nxh3 Bf7 37. a3 Ne5 38. Ng5 Bg8 39. Bxe5+ Kxe5 40. Kf2 d5 41. Nf3+ Kxe4

1. d4 d5 2. O-O h5 3. g3 c6 4. Nd3 Nd6 5. f3 f6 6. e4 dxe4 7. fxe4 Nf7 8. c3 e5 9. Ne3 exd4 10. cxd4 Rxd4 11. Qc2 Nb6 12. a4 Rd8 13. Nf4 Ne5 14. a5 Nbd7 15. Ne6 Rc8 16. Nxf8 Nxf8 17. Rd1 Ne6 18. Bc3 Rd8 19. Rxd8 Nxd8 20. Nf5 b6 21. Bf3 Ndf7 22. Qf2 c5 23. Ne7+ Kf8 24. Nf5 Bb5 25. Be2 Ng5 26. Qe3 Bxe2 27. Qxe2 g6 28. axb6 axb6 29. Ne3 Kg7 30. Nd5 Rf8 31. Kg2 b5 32. b4 cxb4 33. Bxb4 Rf7 34. Bc3 Ng4 35. h3 Ne5 36. h4 Nh7 37. Rb1 Qc8 38. Rxb5 Nf8 39. Bxe5 fxe5 40. Qb2 Nd7 41. Qe2 Nf8 42. Qb2 Nd7 43. Qe2

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 411 / 26 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): nqnrbbkr/pppppppp/8/8/8/8/PPPPPPPP/RQNNBKRB w AGdh - 0 1

Mirror twin (the same position mirrored): White 737 vs Black 933.