White 429 vs Black 754

The two setups

White: setup #429 R N Q B N K B R

King on the f-file, rooks on a, h, queen on the c-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 429 gives White 0.00 (Morozov Balance Index, 400M nodes).

Black: setup #754 B R K N N B R Q

King on the c-file, rooks on b, g, queen on the h-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 754 gives White +0.18 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±3 centipawns of equality, reaching search depth 56.

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 -35 and +1 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 429 gives White 0.00 and setup 754 gives White +0.18: 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 h4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (30 moves) the largest swing was 33 cp (around move 10), ending at 0 cp — the position stays playable for both sides.

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: -7
• Lc0 0.32.1: -11

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 +43, Black +80, difference -37. 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| 33 cp, mean 8.8 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 49.5 moves.

1. h4 g6 2. c3 b6 3. d4 e5 4. e3 Ne6 5. Nd2 f5 6. Bh2 exd4 7. cxd4 Bd6 8. Bxd6 Nxd6 9. Bf3 O-O 10. Bxa8 Rxa8 11. Nef3 Qf6 12. Qc2 Rac8 13. O-O c6 14. a4 f4 15. e4 Nxd4 16. Qd3 c5 17. Rfd1 Rce8 18. Nxd4 Qxd4 19. Qxd4 cxd4 20. f3 Rc8 21. a5 Rc2 22. Ra4 bxa5 23. Rxd4 Nb7 24. Nc4 Nc5 25. Na3 Rxb2 26. Rc4 Rc8 27. Rd5 Rb3 28. Nc2 Rb1+ 29. Kh2 Rb5 30. Rxd7 Rbb8 31. Rxa7 Nb3 32. Na3 Nd2 33. Rd4 Nf1+ 34. Kh3 Ne3 35. g3 Rb2 36. Nc4 Nxc4 37. Rdd7 Ne5 38. Rg7+ Kf8 39. Rxh7 Kg8 40. Rhe7 Nxf3

1. h4 b6 2. c3 g6 3. d4 e5 4. e3 Ne6 5. Nd2 f5 6. Bh2 exd4 7. cxd4 Bd6 8. Bxd6 Nxd6 9. Bf3 O-O 10. Bxa8 Rxa8 11. Nef3 Qf6 12. Qc2 Rac8 13. O-O c6 14. a4 f4 15. e4 Nxd4 16. Qd3 c5 17. Rfd1 Rce8 18. Nxd4 Qxd4 19. Qxd4 cxd4 20. f3 Rc8 21. a5 Rc2 22. Ra4 bxa5 23. Rxd4 Nb7 24. Nc4 Nc5 25. Na3 Rxb2 26. Rc4 Rc8 27. Rd5 Rb3 28. Nc2 Rb1+ 29. Kh2 Rb5 30. Rxd7 Rbb8 31. Rxa7 Nb3 32. Na3 Nd2 33. Rd4 Nf1+ 34. Kh3 Ne3 35. g3 Rb2 36. Nc4 Nxc4 37. Rdd7 Ne5 38. Rg7+ Kf8 39. Rxh7 Kg8 40. Rhe7 Nxf3

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 429 / 754 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): brknnbrq/pppppppp/8/8/8/8/PPPPPPPP/RNQBNKBR w AHbg - 0 1

Mirror twin: White 728 vs Black 391 — a different position (castling squares are fixed), not evaluated by the search.