White 468 vs Black 49

The two setups

White: setup #468 R B B N N K R Q

King on the f-file, rooks on a, g, queen on the h-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 468 gives White +0.16 (Morozov Balance Index, 400M nodes).

Black: setup #49 B N N B R Q K R

King on the g-file, rooks on e, h, queen on the f-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 49 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 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 -7 and +16 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 468 gives White +0.16 and setup 49 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 c3, and 2 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the evaluation stayed within ±21 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 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 +41. 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: 0
• Lc0 0.32.1: +8

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 +10, Black +96, difference -86. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 9 White wins, 151 draws, 0 Black wins, White scored 52.8%.

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| 21 cp, mean 3.3 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 38.9 moves.

1. h4 c5 2. Qh3 b6 3. c3 h5 4. d3 e6 5. e4 d5 6. Nf3 Nd7 7. Bf4 dxe4 8. dxe4 Nd6 9. e5 Nc4 10. Bd3 Bxf3 11. Bxc4 Bc6 12. O-O b5 13. Be2 f6 14. a4 bxa4 15. exf6 Nxf6 16. Be5 Ng4 17. Bg3 Qf5 18. f3 Nh6 19. Nf2 Bb6 20. Bc4 O-O 21. Bd6 Qxh3 22. Nxh3 Nf5 23. Bxf8 Ne3 24. b3 Nxf1 25. Kxf1 Kxf8 26. Nf4 Ba5 27. Nxe6+ Ke7 28. Nxc5 Bxc3 29. Ra2 Bf6 30. Nxa4 Kd6 31. Nb2 Bxh4 32. Nd3 Bf6 33. Nb4 Bc3 34. Nxc6 Kxc6 35. g3 Re7 36. Rh2 Be1 37. Rh3 Re5 38. Be2 Bb4 39. Bc4 Be1 40. Be2 Bb4 41. Rh4 Bd6 42. Rc4+ Kd7

1. c3 e5 2. g4 a5 3. g5 Na6 4. h4 Nd6 5. d4 Qe7 6. dxe5 Qxe5 7. Ne3 O-O 8. Bc2 a4 9. Bxa4 Nc5 10. Bc2 Qe6 11. Nf3 b5 12. Nd4 Bxh1 13. Nxe6 Rxe6 14. Rxh1 f6 15. g6 hxg6 16. Ng2 g5 17. Be3 Na4 18. O-O-O Rf7 19. Rh2 g4 20. Nf4 Ree7 21. h5 f5 22. h6 g5 23. Nh5 Rxe3 24. fxe3 Nc5 25. Ng3 f4 26. exf4 gxf4 27. Nf1 Bg5 28. Rh5 Ne6 29. Kb1 Kh8 30. Bd3 g3 31. Nd2 Rf8 32. Nf3 Bf6 33. Bxb5 Nxb5 34. Rxb5 c6 35. Rb4 d5 36. a4 Ra8 37. Rb6 Rc8 38. a5 Bd8 39. Rb7 Bc7 40. a6 Nd8 41. Ra7 Kh7 42. Rh1 Nf7 43. Kc2 Nxh6 44. Rb7 Kg6 45. a7 Bd6 46. Rb6 Nf5 47. Rxc6 Ra8 48. Ra6 Kf7 49. Rh5 Kf6 50. Kd3 g2 51. Rh2 g1=Q 52. Nxg1 Kg7 53. Nf3 Bc5 54. Ng5 Bd6 55. Rh1 f3 56. exf3 Kf6 57. f4 Kg6 58. Ne6 Kf7 59. Nd4 Ne7 60. Rxd6 Rxa7 61. f5 Ke8 62. Rh8+ Kf7 63. f6 Nc8 64. Rxc8 Kg6

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 468 / 49 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): bnnbrqkr/pppppppp/8/8/8/8/PPPPPPPP/RBBNNKRQ w AGeh - 0 1

Mirror twin: White 686 vs Black 907 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 67.