White 78 vs Black 527
White starts from setup 78 (NNRKQBBR), Black from setup 527 (RNQKNRBB). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
How to play with different setups
White sets up the pieces by position No. 78, Black by position No. 527, mirrored on their own side; the pawns stand as usual.
Moves as usual: White starts; everything else follows the Chess960 rules.
The two setups
White: setup #78 N N R K Q B B R
King on the d-file, rooks on c, h, queen on the e-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 78 gives White +0.21 (Morozov Balance Index, 400M nodes).
Black: setup #527 R N Q K N R B B
King on the d-file, rooks on a, f, 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 527 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 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 -17 and +3 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 78 gives White +0.21 and setup 527 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 d4, and 2 first moves are within 10 cp of it.
Along the engine's main line (21 moves) the evaluation stayed within ±25 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.
| Stage | Nodes | Depth | Eval, cp | Main line |
|---|---|---|---|---|
| S0 | 100 000 | 14 | +1 | 1. e4 c5 2. O-O-O f5 3. e5 g5 4. Nc3 Qc7 |
| S1 | 500 000 | 19 | +2 | 1. e4 c5 2. Nc3 f5 3. e5 g5 4. f3 Qc7 |
| S2 | 2 000 000 | 24 | -17 | 1. e4 f5 2. e5 c5 3. O-O-O Qc7 4. h4 f4 |
| S3 | 8 000 000 | 26 | -7 | 1. d4 f5 2. c4 c5 3. e3 b6 4. f3 g5 |
| S4 | 32 000 000 | 36 | +2 | 1. d4 f5 2. c4 c5 3. e3 g5 4. f3 g4 |
| S5 | 128 000 000 | 40 | +3 | 1. d4 f5 2. c4 c5 3. e3 g5 4. f3 g4 |
| S6 | 400 000 000 | 50 | 0 | 1. d4 f5 2. c4 g5 3. e3 c5 4. Nc2 Nc6 |
| S7 | 800 000 000 | 55 | 0 | 1. d4 f5 2. c4 g5 3. e3 c5 4. Nc2 Nc6 |
| S8 | 1 600 000 000 | 59 | 0 | 1. d4 f5 2. c4 g5 3. e3 c5 4. Nc2 Nc6 |
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.
| Nodes | Eval, cp |
|---|---|
| 4 000 000 000 | 0 |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
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: +5
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 +61, Black +34, difference +27. 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.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 41 | 1. d4 f5 2. c4 c5 3. e3 g5 4. Qd2 Nc6 5. f3 g4 |
| 2 | -6 | 40 | 1. f3 f5 2. c4 c5 3. e3 g5 4. d4 g4 5. Qd2 gxf3 |
| 3 | -21 | 40 | 1. e4 f5 2. e5 c5 3. O-O-O Qc7 4. f3 g5 5. h4 Qxe5 |
Main-line play-out
21 moves, 5 000 000 nodes per half-move. Largest |evaluation| 25 cp, mean 2.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | -7 | f5 | -3 |
| 2 | c4 | 0 | c5 | +1 |
| 3 | e3 | +25 | g5 | +25 |
| 4 | Qd2 | +25 | b6 | +24 |
| 5 | h4 | +12 | f4 | 0 |
| 6 | f3 | 0 | g4 | 0 |
| 7 | exf4 | 0 | cxd4 | 0 |
| 8 | Nb3 | 0 | Nc6 | 0 |
| 9 | fxg4 | 0 | e5 | 0 |
| 10 | Be2 | 0 | Rxf4 | 0 |
| 11 | Bh2 | 0 | Rf2 | 0 |
| 12 | Qg5+ | 0 | Nf6 | 0 |
| 13 | Bxe5 | 0 | Nxe5 | 0 |
| 14 | Qxe5 | 0 | Qc6 | 0 |
| 15 | N1d2 | 0 | Qxg2 | 0 |
| 16 | Re1 | 0 | Rc8 | 0 |
| 17 | Nxd4 | 0 | Nxg4 | 0 |
| 18 | Qg5+ | 0 | Nf6 | 0 |
| 19 | Qe3 | 0 | Ng4 | 0 |
| 20 | Qg5+ | 0 | Nf6 | 0 |
| 21 | Qe3 | 0 | Ng4 | 0 |
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 60.7 moves.
Sample game 1 (1/2-1/2)
1. f3 f5 2. Nc3 c5 3. O-O-O g6 4. d4 cxd4 5. Bxd4 Bxd4 6. Rxd4 Nc6 7. Rd2 Nf6 8. e4 fxe4 9. Nxe4 Qc7 10. Bb5 Ne5 11. Nxf6 Rxf6 12. Qe4 a6 13. Qa4 Bc4 14. Bxc4 Nxc4 15. Rd4 b5 16. Qb4 Re6 17. Rhd1 Ke8 18. g3 d6 19. R4d3 Rc8 20. Nb3 Re3 21. Qc3 Rxd3 22. Qxd3 Ne5 23. Qe2 Nxf3 24. Nd4 Nxd4 25. Rxd4 Qc5 26. Rf4 Qd5 27. b3 Rc5 28. Kb1 Qh1+ 29. Kb2 Qd5 30. Kb1 Qh5 31. g4 Qg5 32. Qf2 Qd5 33. Qe2 Qg5 34. Qf3 Kd7 35. a3 Qd5 36. Qe2 Qe6 37. Qf2 a5 38. h4 Qe5 39. h5 b4 40. a4 Rc3 41. Rf3 Qd5 42. Rf4 Qe5 43. Rf3 Qe4 44. Rxc3 bxc3 45. hxg6 hxg6 46. Qb6 Qe1+ 47. Ka2 Qe4 48. Kb1 Qxg4 49. Qb7+ Ke8 50. Qc6+ Kf7 51. Qxc3 Qg1+ 52. Kb2 Qc5 53. Qf3+ Qf5 54. Qa8 Qe5+ 55. Ka2 Qc3 56. Qe4 g5 57. Qf5+ Ke8 58. Kb1 Qc5 59. Qg6+ Kf8 60. Qe6 Qg1+ 61. Ka2 Qf2 62. Qc8+ Kg7 63. b4 Qd4 64. Qb7 Kf6 65. Qb8 Qe4 66. Kb3 Qd5+ 67. Kb2 Qe5+ 68. Ka2 Qd5+ 69. Kb2 Qe5+ 70. Ka2 Kf7 71. Qb6 Qe6+ 72. Ka3 axb4+ 73. Qxb4 g4 74. a5 Qe3+ 75. Qb3+ Qxb3+ 76. Kxb3 g3 77. a6 g2 78. a7 g1=Q 79. a8=Q Qb1+ 80. Kc3 Qe1+ 81. Kb3 Qe6+ 82. c4 Qe3+ 83. Ka4 Kf6 84. Qf8+ Kg6 85. Kb4 Qe1+ 86. Kb5 Qe5+ 87. Kb4 Qb2+ 88. Ka4 Qc2+ 89. Kb4 Qb2+ 90. Ka4 Qf6 91. Qg8+ Kf5 92. Qd5+ Qe5 93. Qf3+ Qf4 94. Qh5+ Kf6 95. Qh8+ Ke6 96. Qh3+ Qf5 97. Qe3+ Kf7 98. Qd4 Ke8 99. Kb4 Qf3 100. Qb6 Qe4 101. Qa7 Qb1+ 102. Kc3 Qf5 103. Kb4 Qf4 104. Qa8+ Kf7 105. Qh8 Qd2+ 106. Kb5 Qg5+ 107. Ka4 Qf5 108. Qd4 Qf3 109. Kb4 Ke8 110. Qg1 Qb7+ 111. Kc3 Qe4 112. Qf2 Qe5+ 113. Kb3 Qe4 114. Kc3 Qc6 115. Kb4 Qb7+ 116. Kc3 Qe4 117. Kb3 Kd8 118. Qa7 Ke8 119. Qf2 Qd3+ 120. Kb4 Qb1+ 121. Kc3 Qg6 122. Qa7 Qf6+ 123. Kb3 Qf3+ 124. Ka4 Qd1+ 125. Kb4 Qb1+ 126. Kc3 Qc1+ 127. Kb3 Qd1+ 128. Kb4
Sample game 2 (1/2-1/2)
1. f3 f5 2. Nb3 d6 3. d4 a5 4. a4 Nc6 5. e3 Nf6 6. O-O-O Nb4 7. Na3 Qd7 8. Bb5 c6 9. Bc4 Bxc4 10. Nxc4 Qc7 11. Na3 b5 12. axb5 cxb5 13. Kb1 O-O 14. e4 fxe4 15. fxe4 Rfc8 16. Qe2 a4 17. Nc1 g6 18. h4 Bg7 19. c3 Na6 20. Na2 Rab8 21. e5 Nd5 22. exd6 Qd7 23. Qe4 e6 24. Ka1 b4 25. cxb4 Naxb4 26. Nxb4 Rxb4 27. Bh2 Rcb8 28. Rd2 Rb3 29. Rb1 Bf8 30. Re2 Re8 31. Rc1 Bxd6 32. Bxd6 Qxd6 33. Rc5 Nb4 34. Re3 Rf8 35. Rf3 Rfxf3 36. gxf3 Kg7 37. Nc4 Qg3 38. Qe5+ Qxe5 39. Nxe5 Re3 40. Kb1 Re1+ 41. Rc1 Re2 42. Rc7+ Kf8 43. Kc1 Na2+ 44. Kb1 Nb4 45. Kc1 Na2+ 46. Kb1
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 78 / 527 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): rnqknrbb/pppppppp/8/8/8/8/PPPPPPPP/NNRKQBBR w CHaf - 0 1
Mirror twin: White 884 vs Black 528 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 346.