White 32 vs Black 211

The two setups

White: setup #32 B B N N Q R K R

King on the g-file, rooks on f, 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 32 gives White +0.50 (Morozov Balance Index, 400M nodes).

Black: setup #211 B N Q R K N R B

King on the e-file, rooks on d, g, queen on the c-file; one bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 211 gives White +0.18 (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 59.

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 -13 and +20 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 32 gives White +0.50 and setup 211 gives White +0.18: 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 e4, and 2 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the largest swing was 32 cp (around move 3), ending at -12 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 0, drawn 6, Black won 4 (White scored 30.0%).

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: -7

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 +111, Black +78, difference +33. 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, 6 draws, 4 Black wins, White scored 30.0%.

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| 32 cp, mean 4.8 cp, final -12 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 0, drawn 6, Black won 4 — White scored 30.0%. Average length 71.3 moves.

1. b4 d5 2. d4 g6 3. c3 b6 4. h4 c5 5. Nb3 c4 6. Nd2 Nbd7 7. e4 dxe4 8. Bxe4 b5 9. a4 a6 10. Bb2 Ne6 11. Bc1 Nf6 12. Bxa8 Qxa8 13. Nf3 Bg7 14. Ng5 Nc7 15. f4 bxa4 16. f5 Nb5 17. fxg6 hxg6 18. Rh3 Qc6 19. Ne3 a3 20. Bd2 Nd6 21. Qa1 Nb5 22. Qe1 Rh8 23. Qe2 Ne4 24. Nxf7 Nexc3 25. Bxc3 Nxc3 26. Qd2 Bxd4 27. Nxh8 Ne4 28. Qc2 Bxh8 29. Rhf3 Bg7 30. Nxc4 Nd2 31. Nxa3 Nxf3+ 32. Rxf3 Qe6 33. Qa4+ Rd7 34. Nc2 Qe4 35. Rf1 Be5 36. Rd1 Bd6 37. Rd4 Qe6 38. Rd1 Kd8 39. Qa1 Qe4 40. Qh8+ Kc7 41. Qc3+ Kb7 42. Rd4 Qf5 43. Ne3 Qf6 44. Rd3 Qxh4 45. Nc4 Bh2+ 46. Kf1 Rc7 47. Rd4 Qf6+ 48. Qf3+ Qxf3+ 49. gxf3 g5 50. Ke2 Kc6 51. Re4 Kb5 52. Ne5 Bf4 53. Kd3 Ka4 54. Nf7 Kb3 55. Re6 Ra7 56. Rg6 Kxb4 57. Rb6+ Ka5 58. Rg6 Rd7+ 59. Ke4 Rd1 60. Nxg5 Bd6 61. Nf7 Bc5 62. Rg2 Rd4+ 63. Ke5 Kb5 64. Ng5 Rd1 65. Ke4 Rd6 66. Rb2+ Kc4 67. Rc2+ Kb4 68. Nf7 Rd4+ 69. Ke3 a5 70. Ne5 Kb5 71. Ke2 a4 72. Nd3 Rc4 73. Ra2 Bb4 74. Ke3 a3 75. Ra1 Ka5 76. Rg1 a2 77. Ra1 Rc2 78. Nc1 Rxc1 79. Rxa2+ Kb5 80. Kd4 Bc5+ 81. Kd5 Rd1+ 82. Ke5 Re1+ 83. Kf5 Kc4 84. Ra4+ Kd3 85. Ra6 Bd6 86. Rb6 Kd4 87. Rb7 Rf1 88. Rb3 Kc4 89. Re3 Bc5 90. Re4+ Kd3 91. Kg4 Rg1+ 92. Kf5 Rf1 93. Kg4 Bd6 94. Ra4 Rc1 95. Ra2 Rg1+ 96. Kf5 Rg3 97. Rf2 Ke3 98. Ra2 Rxf3+ 99. Ke6 Rf6+ 100. Kd7 Kd3 101. Ra1 e5 102. Rd1+ Kc4 103. Rc1+ Kd4 104. Rg1 e4 105. Rd1+ Kc3 106. Re1 Kd3 107. Rd1+ Ke2 108. Rh1 e3 109. Kc6 Bg3+ 110. Kc5 Kf3 111. Rc1 e2 112. Rc3+ Kg4 113. Rc4+ Rf4 114. Rxf4+ Kxf4

1. b4 d5 2. c3 b6 3. d4 g6 4. Nb3 Ne6 5. h4 Bb7 6. f3 c5 7. bxc5 bxc5 8. Qf2 Nd7 9. e4 Nf6 10. Ne3 Nh5 11. exd5 Bxd5 12. c4 Bb7 13. d5 Bxa1 14. Nxa1 Nd4 15. Rd1 Ng3 16. Rh3 Nge2+ 17. Kh1 Qc7 18. Nb3 Nf4 19. Rh2 Nxb3 20. axb3 e6 21. g3 Nh5 22. g4 Nf4 23. Qg1 O-O-O 24. Rhd2 f5 25. Qf2 h5 26. g5 Rd7 27. Ng2 exd5 28. Nxf4 Qxf4 29. cxd5 Kb8 30. Kg2 Re8 31. Qg3 Qe5 32. Bd3 Qxg3+ 33. Kxg3 Rxd5 34. Bc4 f4+ 35. Kf2 Rxd2+ 36. Rxd2 Kc7 37. Re2 Rxe2+ 38. Kxe2 a5 39. Bf7 Ba6+ 40. Kd2 Bb7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 32 / 211 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): bnqrknrb/pppppppp/8/8/8/8/PPPPPPPP/BBNNQRKR w FHdg - 0 1

Mirror twin: White 927 vs Black 643 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 173.