White 155 vs Black 722

The two setups

White: setup #155 N R N Q B K R B

King on the f-file, rooks on b, 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 155 gives White +0.14 (Morozov Balance Index, 400M nodes).

Black: setup #722 B R K N Q B N R

King on the c-file, rooks on b, 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 722 gives White +0.26 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation never left ±2 centipawns of equality, 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.

For comparison, in symmetric play setup 155 gives White +0.14 and setup 722 gives White +0.26: 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 d4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (13 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: 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 +4, Black +86, difference -82. 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

13 moves, 5 000 000 nodes per half-move. Largest |evaluation| 12 cp, mean 1.6 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 32.2 moves.

1. d4 b6 2. g3 Bxh1 3. Rxh1 d5 4. Qd3 h5 5. h4 e5 6. dxe5 Qxe5 7. b4 Qe4 8. f3 Qxd3 9. Nxd3 Bd6 10. Kg2 Ne7 11. Bf2 Ndc6 12. c3 Ne5 13. Nb2 a5 14. bxa5 bxa5 15. Na4 Rxb1 16. Rxb1 Nc4 17. Bc5 Nf5 18. Bxd6 Nfxd6 19. Nc2 Re8 20. Nd4 c6 21. Nc5 Nb5 22. Nxb5 cxb5 23. Kf2 Kc7 24. Rxb5 Kc6 25. a4 Nd6 26. Rxa5 Nc4 27. Rb5 Nd6 28. Ra5 Nc4 29. Rb5 Nd6

1. d4 b6 2. g3 e5 3. Bxa8 Rxa8 4. dxe5 Qxe5 5. Bc3 Qe6 6. Nd3 Nf6 7. Nf4 Qc6 8. Qd3 Ne4 9. Nd5 Nxc3 10. Nxc3 g6 11. O-O h5 12. b4 Qe6 13. Nd5 Bd6 14. c4 h4 15. c5 Be5 16. Nb3 c6 17. Qa6+ Kb8 18. cxb6 axb6 19. Qxb6+ Kc8 20. e4 hxg3 21. fxg3 cxd5 22. Rbc1+ Nc6 23. b5 Bxg3 24. hxg3 Rxa2 25. Rf2 Rh1+ 26. Kxh1 Qh3+ 27. Kg1 Qxg3+ 28. Kf1 Qh3+ 29. Kg1 Qg3+ 30. Kf1 Qh3+ 31. Kg1

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 155 / 722 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): brknqbnr/pppppppp/8/8/8/8/PPPPPPPP/NRNQBKRB w BGbh - 0 1

Mirror twin: White 801 vs Black 423 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 33.