White 71 vs Black 851

The two setups

White: setup #71 N N B R K Q R B

King on the e-file, rooks on d, g, queen on the f-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 71 gives White +0.37 (Morozov Balance Index, 400M nodes).

Black: setup #851 B R K N R N Q B

King on the c-file, rooks on b, e, queen on the g-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 851 gives White +0.17 (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 wandered between -10 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 71 gives White +0.37 and setup 851 gives White +0.17: 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 g4, and 3 first moves are within 10 cp of it.

Along the engine's main line (26 moves) the evaluation stayed within ±18 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: +17

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 +78, Black +120, difference -42. 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| 18 cp, mean 3.4 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 40.1 moves.

1. g4 e5 2. Nb3 Nc6 3. c3 g5 4. d3 b6 5. Be4 h6 6. h4 gxh4 7. Bxh6 O-O-O 8. c4 Ne6 9. Nc3 Bf6 10. Bd2 Kb8 11. O-O-O Bb7 12. Kb1 Ng5 13. Bxg5 Bxg5 14. e3 Qg7 15. a3 Rh8 16. Ka2 Bc8 17. Qh3 Rde8 18. c5 Bb7 19. Rc1 f6 20. Kb1 Qf7 21. Qf1 Nd4 22. Nxd4 exd4 23. Bxb7 dxc3 24. c6 cxb2 25. Rc3 f5 26. cxd7 Qxd7 27. Bc6 Qc8 28. Bxe8 Rxe8 29. gxf5 Qxf5 30. Qg2 Bd8 31. Rh1 Rh8 32. Kxb2 Bf6 33. d4 c5 34. Qh2+ Kb7 35. Qg2+ Kb8 36. Qh3 Rh5 37. Kc1 cxd4 38. Rc2 dxe3 39. Qxf5 Rxf5 40. fxe3 Ra5 41. Ra2 Be7 42. Kd2 Ra4 43. Kd3 a5 44. Rf1 Rxa3+ 45. Rxa3 Bxa3 46. Rf4 Be7 47. Rf7 Bd6 48. Kc4 a4 49. Rh7

1. g4 e5 2. c4 g6 3. d3 b6 4. Bxa8 Rxa8 5. Qg2 Nc6 6. Nc2 a5 7. Nc3 Ne6 8. Bd2 Kb7 9. O-O-O f5 10. gxf5 gxf5 11. Qd5 Qf7 12. Kb1 Rg8 13. a3 Raf8 14. b4 Rxg1 15. Rxg1 Kb8 16. Na4 axb4 17. Bxb4 Rd8 18. c5 b5 19. Nc3 Qh5 20. e3 Qxh2 21. Rc1 Qxf2 22. Nxb5 e4 23. d4 Qe2 24. Nc3 Qd3 25. Qb3 Ka8 26. Qa4+ Na7 27. Qb3 Nb5 28. Kb2 Nxc3 29. Bxc3 c6 30. Qa4+ Kb7 31. Rb1 Rb8 32. Kc1+ Kc8 33. Rb6 Nc7 34. Qa7 Ra8 35. Qb7+ Kd8 36. Be1 Qf1 37. Kb2 Qh3 38. a4 Qh2 39. Kb3 Bf6 40. a5 f4 41. a6 f3 42. a7 Ke8 43. Qb8+ Bd8 44. Rb7 Kf7 45. d5 Qe5 46. dxc6 Qe6+ 47. Kb2 Qxc6 48. Nd4 Qxc5 49. Rxc7 Bxc7 50. Qxa8 f2 51. Qe8+ Kxe8 52. a8=Q+ Kf7 53. Qa2+ Kg7 54. Bxf2 Qa5 55. Qc4 Qd2+ 56. Kb1 Bd8 57. Qb5 Qd1+ 58. Kb2 Qd2+ 59. Kb1

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 71 / 851 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): brknrnqb/pppppppp/8/8/8/8/PPPPPPPP/NNBRKQRB w DGbe - 0 1

Mirror twin: White 882 vs Black 99 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 315.