White 109 vs Black 53

The two setups

White: setup #109 Q N R B N K B R

King on the f-file, rooks on c, h, queen on the a-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 109 gives White +0.10 (Morozov Balance Index, 400M nodes).

Black: setup #53 N N B B R Q K R

King on the g-file, rooks on e, h, queen on the f-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 53 gives White +0.27 (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 57.

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 -17 and +2 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 109 gives White +0.10 and setup 53 gives White +0.27: 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 c4, and 2 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the evaluation stayed within ±15 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 2, drawn 6, Black won 2 (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 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 +30. 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: -1

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 +32, Black +78, difference -46. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 8 White wins, 144 draws, 8 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| 15 cp, mean 2.0 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 2, drawn 6, Black won 2 — White scored 50.0%. Average length 51.8 moves.

1. f3 Na6 2. a3 c6 3. c4 e5 4. b4 d6 5. Bf2 h5 6. O-O Rh6 7. Nc3 h4 8. Qa2 Nb6 9. Bb3 Be6 10. Be3 Rg6 11. Nd3 Nd7 12. f4 Bh3 13. Ne1 Bxg2 14. Nxg2 h3 15. Rf3 hxg2 16. Qb1 Rg4 17. Rh3 Nf6 18. Bc2 g6 19. f5 e4 20. fxg6 fxg6 21. Nd1 Nd5 22. Nf2 Nxe3 23. Rxe3 Rf4 24. Nxe4 d5 25. Ng3 Bb6 26. c5 Nxc5 27. Rxe8 Ne6+ 28. e3 Qxe8 29. Bxg6 Qf8 30. Bh5 Rf6 31. Kxg2 Rf2+ 32. Kh1 Rxd2 33. Ne2 Qf6 34. Rg1+ Ng7 35. Rf1 Qh6 36. Qe1 Bxe3 37. Bf7+ Kh7 38. Rf3 Bf4 39. Rxf4 Rxe2 40. Bg6+ Kg8 41. Qg3 Rxh2+ 42. Qxh2 Qxg6 43. Qf2 Ne6 44. Rf6 Qe4+ 45. Kg1 Ng5 46. Rf8+ Kh7 47. Qh2+ Kg6 48. Qd6+

1. c4 e5 2. f3 Nc6 3. c5 h5 4. Bf2 h4 5. O-O Bg5 6. a3 d5 7. e4 d4 8. b4 Rh6 9. Nd3 Qe7 10. h3 Rg6 11. Kh1 Bh6 12. b5 Na5 13. Qb2 c6 14. Qb4 Qe6 15. Rg1 b6 16. a4 Nc7 17. cxb6 axb6 18. Be2 Qd6 19. bxc6 Ba6 20. Qxd6 Rxd6 21. Bxh4 f6 22. Rc2 Ra8 23. Rb2 Nc4 24. Rc2 Na5 25. Rb2 Nc4 26. Rc2

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 109 / 53 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): nnbbrqkr/pppppppp/8/8/8/8/PPPPPPPP/QNRBNKBR w CHeh - 0 1

Mirror twin: White 856 vs Black 906 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 27.