White 33 vs Black 35

The two setups

White: setup #33 B N N B Q R K R

King on the g-file, rooks on f, 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 33 gives White +0.39 (Morozov Balance Index, 400M nodes).

Black: setup #35 B N N Q R K R B

King on the f-file, rooks on e, g, queen on the d-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 35 gives White +0.06 (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 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 wandered between -15 and +46 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 33 gives White +0.39 and setup 35 gives White +0.06: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.

The engine's first choice for White is b4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (30 moves) the largest swing was 51 cp (around move 9), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 0, drawn 9, Black won 1 (White scored 45.0%).

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 +107. 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: -5
• Lc0 0.32.1: -12

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 +100, Black +81, difference +19. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 7 White wins, 135 draws, 18 Black wins, White scored 46.6%.

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| 51 cp, mean 16.2 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 0, drawn 9, Black won 1 — White scored 45.0%. Average length 44.8 moves.

1. e4 g5 2. c3 Nd6 3. b4 b6 4. f3 c5 5. h4 gxh4 6. Rxh4 cxb4 7. e5 Nf5 8. Rxh7 e6 9. cxb4 Nc6 10. Nd3 Qe7 11. Nc3 d6 12. Ne4 Nxe5 13. Be2 Bb7 14. g4 Nxd3 15. Bxd3 Bxa1 16. Qxa1 e5 17. Qe1 O-O-O 18. Nc5 Nd4 19. Nxb7 Kxb7 20. Kg2 Kb8 21. Qe3 Qe6 22. a4 f5 23. a5 Rh8 24. Rfh1 Rxh7 25. Rxh7 Qg8 26. Rh4 fxg4 27. fxg4 Rf8 28. axb6 Rf4 29. bxa7+ Kxa7 30. Be2 Kb6 31. Kh2 Qg6 32. Rh3 Re4 33. Bd3 Rxe3 34. Bxg6 Re2+ 35. Kg3 Rxd2 36. Rh1 Kb5 37. g5 Kxb4 38. Be4 Ne2+ 39. Kf3 Nf4 40. g6 Kc5

1. b4 d5 2. d3 Nd6 3. Nd2 Qd7 4. e4 dxe4 5. dxe4 b6 6. h4 O-O-O 7. Nd3 Bb7 8. Bf3 g6 9. e5 Bxf3 10. Nxf3 Nf5 11. Ng5 Qd5 12. e6 Bxa1 13. exf7 Rgf8 14. Nf4 Qd6 15. Qe6+ Qxe6 16. Nfxe6 Bf6 17. Nxd8 Rxd8 18. Ne6 Nd7 19. g4 Nd6 20. Nxd8 Kxd8 21. Rh3 Nxf7 22. g5 Be5 23. Ra3 b5 24. Rxa7 Nb6 25. Re1 Bd6 26. Ra5 c6 27. Ra6 Bxb4 28. Rb1 Bc5 29. c4 Nd6 30. cxb5 cxb5 31. Kg2 Bd4 32. Rd1 Bc5 33. Rc1 Bd4 34. Rd1 Bc5 35. Ra5 Kc7 36. Ra7+ Kd8 37. Rb7 Nd7 38. Rxd6 exd6 39. Rxb5 Nb6 40. Ra5 Nc8 41. Rb5 Nb6 42. f4 Kd7 43. Kf3 Ke6 44. Rb2 Kf5 45. Re2 Nc4 46. a4 Bb4 47. Re7 Nd2+ 48. Ke2 Kxf4 49. Kd3 Ba5 50. Ra7 Nb3 51. Kc4 Nd2+ 52. Kd5 Nb3 53. Kxd6 Kg4 54. Rxh7 Be1 55. Kd5 Bxh4 56. Rxh4+ Kxh4 57. Kc4 Na5+ 58. Kb5 Kxg5 59. Kxa5 Kf6 60. Kb5 Ke7 61. a5 Kd7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 33 / 35 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): bnnqrkrb/pppppppp/8/8/8/8/PPPPPPPP/BNNBQRKR w FHeg - 0 1

Mirror twin: White 923 vs Black 915 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 5.