White 237 vs Black 87

The two setups

White: setup #237 N R Q B K N B R

King on the e-file, rooks on b, 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 237 gives White +0.39 (Morozov Balance Index, 400M nodes).

Black: setup #87 N N B R K R Q B

King on the e-file, rooks on d, f, queen on the g-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 87 gives White +0.25 (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 52.

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 -21 and +29 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 237 gives White +0.39 and setup 87 gives White +0.25: 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 f3, and 3 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the largest swing was 34 cp (around move 7), ending at 0 cp — the position stays playable for both sides.

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: +6
• Lc0 0.32.1: +15

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 -21, Black +60, difference -81. 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| 34 cp, mean 9.5 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 40.1 moves.

1. b4 g5 2. f3 a6 3. b5 d5 4. c4 g4 5. Bf2 f5 6. cxd5 gxf3 7. gxf3 Qxd5 8. a4 axb5 9. axb5 Qd6 10. Nb3 Nd7 11. d4 Nab6 12. e4 fxe4 13. fxe4 Rxf2 14. Kxf2 Bxd4+ 15. Kg2 Nf6 16. Ng3 Be5 17. Re1 Bf4 18. Qc3 Be5 19. Qc1 Ng4 20. Bxg4 Bxg4 21. Qg5 Qe6 22. Nf5 Bxf5 23. Qxf5 Qxf5 24. exf5 Rd5 25. Rec1 Nd7 26. b6 Nxb6 27. Nc5 Rd2+ 28. Kf3 Bxh2 29. Ne6 Kf7 30. Nxc7 Bxc7 31. Rxc7 Nd5 32. Rd7 Kf6 33. Rb5 Rd3+ 34. Kf2 Rd2+ 35. Kg3 Rd3+ 36. Kf2 Rd2+ 37. Kg1 Rd1+ 38. Kh2 Rd2+ 39. Kg1 Rd1+ 40. Kh2 Rd2+

1. f3 Nb6 2. c4 g5 3. Ne3 d6 4. b4 f5 5. c5 dxc5 6. bxc5 N6d7 7. Bb3 Qg6 8. Nd5 Na6 9. Qa3 Ndb8 10. Nc3 g4 11. Bf2 Qh6 12. Rd1 Nc6 13. Nc2 Bxc3 14. dxc3 Rxd1+ 15. Kxd1 f4 16. fxg4 Ne5 17. g5 Qxg5 18. Ne1 Ng4 19. Bd4 c6 20. Nf3 Qh5 21. Re1 e5 22. Bg1 e4 23. Qa4 Nxc5 24. Bxc5 Qxc5 25. Qxe4+ Qe7 26. Qxe7+ Kxe7 27. Rg1 Kd6 28. Kd2 Nf6 29. Rf1 Ne4+ 30. Kc2 b5 31. Kb2 c5 32. Nh4 Ke7 33. Bc2 Bb7 34. Bd3 a6 35. Nf3 Kd6 36. a3 Bd5 37. Nh4 Rf6 38. Nf3 Rg6 39. Ne1 Rg4 40. h3 Rh4 41. Bxe4 Bxe4 42. Rf2 Ke5 43. Nf3+ Bxf3 44. exf3 Rh5 45. Re2+ Kd6 46. Re4 Rg5 47. Rxf4 Rxg2+ 48. Kb3 Re2 49. a4 Re3 50. Kc2 c4

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 237 / 87 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): nnbrkrqb/pppppppp/8/8/8/8/PPPPPPPP/NRQBKNBR w BHdf - 0 1

Mirror twin: White 632 vs Black 866 — a different position (castling squares are fixed), not evaluated by the search.