White 39 vs Black 164

The two setups

White: setup #39 N N B 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 away from the centre. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 39 gives White +0.10 (Morozov Balance Index, 400M nodes).

Black: setup #164 N B B R N K Q R

King on the f-file, rooks on d, h, queen on the g-file; no bishop starts in a corner; the knights start away from the centre. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 164 gives White +0.39 (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 61.

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 -20 and +12 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 39 gives White +0.10 and setup 164 gives White +0.39: 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 e4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (30 moves) the evaluation stayed within ±22 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: +7
• Lc0 0.32.1: +2

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 +63, Black +63, difference 0. 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| 22 cp, mean 5.9 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 35.4 moves.

1. g3 f6 2. Nb3 d5 3. O-O c6 4. d4 b6 5. f4 Nd6 6. N1d2 Ba6 7. Rf3 f5 8. Rff1 Qe6 9. Nf3 O-O 10. Nbd2 Qe3+ 11. Rf2 Qe6 12. Rff1 Ne4 13. c3 Bd6 14. Ne5 c5 15. Nc6 Rc8 16. Nxe4 dxe4 17. d5 Qf6 18. Ne5 Rcd8 19. Nc6 Rde8 20. Ne5 Rd8 21. Nc6 Rde8 22. Ne5

1. e4 f5 2. Nc3 fxe4 3. O-O d5 4. f3 e3 5. dxe3 Qf7 6. Nb3 O-O 7. g3 a6 8. Nc5 Nf6 9. Nd3 c6 10. Qe2 e5 11. Bg2 Rfe8 12. e4 Nc7 13. exd5 Ncxd5 14. Ne4 Bc7 15. Ndf2 Bb6 16. Kh1 Nxe4 17. Nxe4 h6 18. Rd1 Qe7 19. c4 Nf6 20. Rxd8 Rxd8 21. f4 Nxe4 22. Qxe4 Rd4 23. Qc2 exf4 24. Bxf4 Rd8 25. h3 Rf8 26. Kh2 Bc5 27. a3 Bf5 28. Qc3 Qe2 29. Re1 Qf2 30. Be3 Bxe3 31. Rxe3 Rd8 32. Re7 Rd4 33. Re2 Qxe2 34. Qxd4 Be6 35. b3 Bf5 36. Kg1 Qe1+ 37. Kh2 Qe2 38. c5 a5 39. h4 Qa2 40. b4 a4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 39 / 164 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): nbbrnkqr/pppppppp/8/8/8/8/PPPPPPPP/NNBQRKRB w EGdh - 0 1

Mirror twin: White 914 vs Black 798 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 185.