White 291 vs Black 405

The two setups

White: setup #291 B Q N R K R N B

King on the e-file, rooks on d, f, 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 291 gives White +0.19 (Morozov Balance Index, 400M nodes).

Black: setup #405 R Q B B N N K R

King on the g-file, rooks on a, h, queen on the b-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 405 gives White +0.26 (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 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±11 cp.

For comparison, in symmetric play setup 291 gives White +0.19 and setup 405 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 g3, and 3 first moves are within 10 cp of it.

Along the engine's main line (14 moves) the evaluation stayed within ±14 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: -1
• Lc0 0.32.1: -6

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 +67, Black +72, difference -5. 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

14 moves, 5 000 000 nodes per half-move. Largest |evaluation| 14 cp, mean 1.2 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 32.1 moves.

1. g3 c6 2. f4 e5 3. Nd3 exf4 4. Nxf4 d5 5. b3 h5 6. e4 h4 7. Nge2 dxe4 8. Bxe4 Qd6 9. O-O-O Bf6 10. Bd3 hxg3 11. hxg3 Ne6 12. Nxe6 Bxe6 13. Nc3 Rd8 14. Rde1 Rh5 15. Ne4 Qa3+ 16. Bb2 Bxb2+ 17. Qxb2 Qxb2+ 18. Kxb2 Nc7 19. Bc4 Bxc4 20. bxc4 b5 21. g4 Re5 22. cxb5 Rxb5+ 23. Ka1 Ne6 24. Rb1 Rdb8 25. Rxb5 Rxb5 26. Nd6 Rd5 27. Nxf7 Rxd2 28. Kb1 Nd4 29. Ne5 Rxc2 30. Rc1 Rxc1+ 31. Kxc1 Kf8 32. Kd2 Ke7 33. Kd3 c5 34. Kc4 Kd6 35. Nf7+ Kc6 36. Ne5+ Kb6 37. Nd7+ Ka5 38. Nxc5 Nf3 39. Kb3 Nd2+ 40. Kc3 Nf3

1. c4 h5 2. h4 Ng6 3. g3 c6 4. b3 Bc7 5. Bg2 Rh6 6. e4 d5 7. exd5 Bxg3 8. fxg3 Qxg3+ 9. Rf2 Nxh4 10. Nce2 Nxg2+ 11. Kf1 Qd6 12. Qe4 cxd5 13. cxd5 Nh4 14. Qxh4 Bg4 15. Re1 Qxd5 16. Qxe7 Nd6 17. Nf4 Qb5+ 18. d3 Re8 19. Qc7 Rc8 20. Qe7 Re8 21. Qc7 Rc8 22. Qe7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 291 / 405 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): rqbbnnkr/pppppppp/8/8/8/8/PPPPPPPP/BQNRKRNB w DFah - 0 1

Mirror twin: White 371 vs Black 746 — a different position (castling squares are fixed), not evaluated by the search.