White 164 vs Black 216

The two setups

White: 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).

Black: setup #216 N B Q R B K N R

King on the f-file, rooks on d, h, queen on the c-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 216 gives White +0.32 (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 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±14 cp.

For comparison, in symmetric play setup 164 gives White +0.39 and setup 216 gives White +0.32: 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 ±12 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: +5

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 +112, difference -49. 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| 12 cp, mean 1.4 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 39.5 moves.

1. f3 d5 2. c3 c5 3. d4 cxd4 4. cxd4 e6 5. Nd3 Ne7 6. Qf2 f6 7. Bf4 O-O 8. Bxb8 Qxb8 9. Qg3 Qxg3 10. hxg3 Bg6 11. Kf2 Kf7 12. Nb3 b6 13. g4 h6 14. Rc1 Rc8 15. Nd2 Rxc1 16. Nxc1 Nc6 17. e3 Rc8 18. Bxg6+ Kxg6 19. Nb1 Nc7 20. Nc3 Ne8 21. Nd3 Nd6 22. Ra1 Ne7 23. Rc1 Kf7 24. Ke2 Kf8 25. Nf4 Kf7 26. Nd3 Kf8 27. b3 Nc6 28. Kd2 Kf7 29. Rh1 Kf8 30. Rc1 Kf7 31. Rh1 Ke7 32. Rh3 Ke8 33. Rh5 Kf8 34. Rh4 Rc7 35. Rh1 Kf7 36. Nf4 Rc8

1. d4 c5 2. c3 cxd4 3. cxd4 Nb6 4. f3 e6 5. Qf2 d5 6. Nd3 Ne7 7. b3 Bd6 8. Bf4 f6 9. O-O O-O 10. Nc2 Bg6 11. Bxd6 Rxd6 12. e3 Qc7 13. Nf4 Bf7 14. Nb4 Nd7 15. Qd2 Qb6 16. Rc1 e5 17. Ne2 Re8 18. Rfe1 Bg6 19. Bxg6 hxg6 20. Nd3 Rc6 21. Nb2 Qa6 22. dxe5 Rxc1 23. Nxc1 Nxe5 24. Nbd3 Qd6 25. Nxe5 fxe5 26. e4 Rc8 27. h3 Kh7 28. Rd1 Qb6+ 29. Kh2 dxe4 30. fxe4 Ng8 31. Ne2 Nf6 32. Ng1 Nxe4 33. Qe1 Nf6 34. Qxe5 Qf2 35. Nf3 Rc2 36. Ng5+ Kh6 37. Nf7+ Kh7 38. Ng5+ Kh6 39. Nf7+ Kh7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 164 / 216 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): nbqrbknr/pppppppp/8/8/8/8/PPPPPPPP/NBBRNKQR w DHdh - 0 1

Mirror twin: White 798 vs Black 653 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 460.