White 29 vs Black 723

The two setups

White: setup #29 N Q N B R K B R

King on the f-file, rooks on e, h, queen on the b-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 29 gives White +0.12 (Morozov Balance Index, 400M nodes).

Black: setup #723 B R K N Q N R B

King on the c-file, rooks on b, g, 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 723 gives White +0.28 (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 51.

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 ±11 cp.

For comparison, in symmetric play setup 29 gives White +0.12 and setup 723 gives White +0.28: 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 42 cp (around move 9), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 1, drawn 9, Black won 0 (White scored 55.0%).

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: +8
• Lc0 0.32.1: +13

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 +46, Black +105, difference -59. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.

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| 42 cp, mean 12.9 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 46.5 moves.

1. e4 g5 2. f3 b6 3. d4 d5 4. e5 Nde6 5. c3 O-O-O 6. Bf2 f6 7. exf6 Bxf6 8. O-O Nf4 9. Qf5+ Kb8 10. g3 N4g6 11. a4 h5 12. a5 h4 13. Nc2 hxg3 14. Bxg3 Nf4 15. axb6 axb6 16. Ne3 Qb5 17. Bb3 N8g6 18. Qc2 e5 19. Nxd5 Bxd5 20. c4 Bxf3 21. Rxf3 Qa5 22. c5 e4 23. Rxe4 Rge8 24. Bf2 Rxe4 25. Qxe4 Qa1 26. Qc2 Bxd4 27. Bxd4 Rxd4 28. cxb6 Qxc1+ 29. Qxc1 Ne2+ 30. Kf1 Nxc1 31. bxc7+ Kc8 32. Bc2 Nh4 33. Rc3 Rf4+ 34. Ke1 Na2 35. Rc5 Nb4 36. Ke2 Nxc2 37. Rxc2 Re4+ 38. Kf2 Rf4+ 39. Ke2 Re4+ 40. Kf1 Rf4+

1. f3 b6 2. c3 Nde6 3. d4 O-O-O 4. Bf2 g5 5. O-O h5 6. a4 Ng6 7. a5 g4 8. fxg4 f5 9. e4 fxe4 10. axb6 axb6 11. Nc2 Bb7 12. Qa2 Nef4 13. Nb4 Kb8 14. d5 Be5 15. Bxb6 cxb6 16. Na6+ Bxa6 17. Qxa6 Nxd5 18. Rxe4 Rf8 19. Bf3 Rxf3 20. Rxf3 hxg4 21. Ra4 Kc7 22. Rd3 Bxh2+ 23. Kxh2 e6 24. Rc4+ Kd6 25. Qa3+ Ke5 26. Rxg4 Ra8 27. Ra4 Qf8 28. Qxf8 Rxf8 29. c4 Nf6 30. Rb4 Nf4 31. Rf3 Rc8 32. Nd3+ Nxd3 33. Rxd3 Rc6 34. Kg3 Rc8 35. Kf3 Rf8 36. Ke2 Rg8 37. g3 Rg4 38. Rb5+ d5 39. cxd5 Nxd5 40. Rbb3 Rc4 41. Rd1 Kf6 42. Kf3 Kf5 43. Re1 Kf6 44. Re2 Rd4 45. Re4 Rd1 46. g4 Rd2 47. Kg3 Ke7 48. g5 Rd1 49. Kf2 Rd2+ 50. Re2 Rd4 51. Kg3 Kf7 52. Rf3+ Ke7 53. g6 Nf6 54. Kh3 Rd5 55. Rfe3 Rd6 56. Ra3 Rd5 57. Rg2 Rh5+ 58. Kg3 Rf5 59. Kh2 Rh5+ 60. Kg1 Rh8 61. Ra7+ Kd6 62. Rd2+ Ke5 63. Rf7 Ne8 64. Re2+ Kd6 65. Rd2+ Ke5 66. Re2+ Kd6 67. Rb7 Nc7 68. Rxb6+ Kc5 69. Rb7 Kc6 70. Ra7 Kb6 71. Ra3 Rg8 72. Rg2 e5 73. Re3 Ne6 74. Rxe5 Nf4 75. Rgg5 Rg7 76. Ref5 Nh3+ 77. Kg2 Nxg5 78. Rxg5 Kc6 79. Kf3 Kd6 80. Ke4 Ke6 81. Rg2 Ke7 82. Kf5 Rg8 83. g7 Kd6 84. Kf6 Kd7 85. Kf7 Rb8 86. g8=Q Rxg8 87. Rxg8

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 29 / 723 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): brknqnrb/pppppppp/8/8/8/8/PPPPPPPP/NQNBRKBR w EHbg - 0 1

Mirror twin: White 936 vs Black 419 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 160.