White 88 vs Black 420

The two setups

White: setup #88 N B N R B K R Q

King on the f-file, rooks on d, g, queen on the h-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 88 gives White +0.35 (Morozov Balance Index, 400M nodes).

Black: setup #420 R B B N Q N K R

King on the g-file, rooks on a, h, queen on the e-file; no 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 420 gives White +0.27 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±4 centipawns of equality, reaching search depth 54.

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 +5 and +17 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 88 gives White +0.35 and setup 420 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 (26 moves) the evaluation stayed within ±20 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 +24, Black +50, difference -26. 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

26 moves, 5 000 000 nodes per half-move. Largest |evaluation| 20 cp, mean 4.8 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 36.0 moves.

1. c4 c6 2. d4 d5 3. cxd5 cxd5 4. h4 h5 5. g3 Nh7 6. Bd2 Nf6 7. O-O Nc6 8. Bg5 Qd8 9. Nab3 g6 10. a3 Kg7 11. Nc5 Nh7 12. Be3 b6 13. Na4 e6 14. Nc3 Ba6 15. Bd3 Bb7 16. Qg2 Bd6 17. Nb5 Bb8 18. f3 Qd7 19. Nc3 Bd6 20. Bb1 Rac8 21. Nd3 Ba6 22. Qf2 Bc4 23. Bc2 Nf6 24. Bg5 Nh7 25. Bd2 Nf6 26. Kg2 Rhe8 27. Rfe1 Qb7 28. Bg5 Nh7 29. Bd2 Nf6 30. Bg5 Nh7 31. Bd2

1. h4 h5 2. d4 c6 3. c4 d5 4. g3 dxc4 5. Nc2 b5 6. Ne3 Bc7 7. b3 Rb8 8. Bc2 Be6 9. f4 Nh7 10. bxc4 bxc4 11. f5 Bd7 12. g4 hxg4 13. Nxg4 Nf6 14. Qf3 Rh7 15. Bc3 Nxg4 16. Rxg4 f6 17. e4 Nf7 18. e5 fxe5 19. dxe5 Bxe5 20. Ne2 Bxc3 21. Qxc3 Nd6 22. Ng3 Qf8 23. O-O-O Kh8 24. Qd4 Rh6 25. a4 Rf6 26. Qxa7 Bxf5 27. Nxf5 Nxf5 28. Qc5 c3 29. Rg5 Nh6 30. Qxc3 e5 31. Qd3 e4 32. Qxe4 Qa3+ 33. Kd2 Rf2+ 34. Ke1 Rxc2 35. Qxc2 Re8+ 36. Kf1 Rf8+ 37. Kg1 Qe3+ 38. Kg2 Qf3+ 39. Kg1 Qe3+ 40. Kg2 Qf3+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 88 / 420 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): rbbnqnkr/pppppppp/8/8/8/8/PPPPPPPP/NBNRBKRQ w DGah - 0 1

Mirror twin: White 877 vs Black 734 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 384.