White 172 vs Black 244
White starts from setup 172 (NBRNKQBR), Black from setup 244 (NBBRKQNR). In the encyclopedia since 2026-10-15: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #172 N B R N K Q B R
King on the e-file, rooks on c, h, queen on the f-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 172 gives White +0.15 (Morozov Balance Index, 400M nodes).
Black: setup #244 N B B R K Q N R
King on the e-file, rooks on d, h, queen on the f-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 244 gives White +0.33 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±1 centipawns of equality, reaching search depth 53.
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 -5 and +16 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 172 gives White +0.15 and setup 244 gives White +0.33: 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 c4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 47 cp (around move 12), ending at +7 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.
| Stage | Nodes | Depth | Eval, cp | Main line |
|---|---|---|---|---|
| S0 | 100 000 | 11 | +10 | 1. c4 f5 2. f4 d6 3. Bd4 c6 4. Ne3 Nh6 |
| S1 | 500 000 | 17 | -3 | 1. c4 f5 2. f3 d6 3. Bf2 Nf6 4. Ne3 f4 |
| S2 | 2 000 000 | 23 | +16 | 1. c4 c6 2. e4 e5 3. f3 d6 4. Nc2 Qe7 |
| S3 | 8 000 000 | 27 | -2 | 1. c4 d6 2. f4 f5 3. h3 Qf7 4. g4 e6 |
| S4 | 32 000 000 | 30 | -5 | 1. f4 f5 2. Nb3 d6 3. Ne3 g6 4. h3 Bd7 |
| S5 | 128 000 000 | 39 | +1 | 1. f4 f5 2. Nb3 c6 3. c3 g6 4. g3 Nb6 |
| S6 | 400 000 000 | 47 | -1 | 1. f4 f5 2. Nb3 c6 3. c3 Qf7 4. h3 e6 |
| S7 | 800 000 000 | 48 | 0 | 1. f4 f5 2. Nb3 c6 3. c3 Qf7 4. h3 Nb6 |
| S8 | 1 600 000 000 | 53 | +1 | 1. e4 f5 2. e5 f4 3. f3 d6 4. exd6 exd6 |
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: +11
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 +52, Black +68, difference -16. 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.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | -9 | 41 | 1. c4 f5 2. g4 d5 3. cxd5 fxg4 4. h3 gxh3 5. Rxh3 Qf6 |
| 2 | -12 | 41 | 1. f4 f5 2. Nb3 Qf7 3. Ne3 d6 4. c3 c6 5. Qf3 g6 |
| 3 | -17 | 41 | 1. Nb3 f5 2. f4 Qf7 3. Ne3 d6 4. c3 c6 5. Qf3 g6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 47 cp, mean 22.4 cp, final +7 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f4 | -1 | f5 | -9 |
| 2 | Nb3 | -20 | d6 | -22 |
| 3 | c4 | -8 | Qf7 | 0 |
| 4 | g4 | 0 | fxg4 | 0 |
| 5 | h3 | +21 | g3 | +29 |
| 6 | Rc3 | +35 | Nf6 | +32 |
| 7 | Rxg3 | +20 | c5 | +20 |
| 8 | Bh2 | +24 | Nb6 | +31 |
| 9 | Rhg1 | +43 | Rg8 | +34 |
| 10 | Na5 | +36 | Bc7 | +38 |
| 11 | e4 | +40 | Nbd7 | +38 |
| 12 | Nb3 | +47 | e5 | +30 |
| 13 | Rf3 | +25 | b6 | +25 |
| 14 | Ne3 | +20 | Bb7 | +18 |
| 15 | fxe5 | +25 | Nxe5 | +17 |
| 16 | Bxe5 | +22 | dxe5 | +30 |
| 17 | Nd5 | +22 | O-O-O | +20 |
| 18 | Nc1 | +17 | Kb8 | +15 |
| 19 | Ne2 | +15 | Rdf8 | +18 |
| 20 | Kd1 | +21 | Bd8 | +26 |
| 21 | Nec3 | +22 | Qe8 | +24 |
| 22 | Bc2 | +22 | Bc6 | +24 |
| 23 | Nxf6 | +26 | Rxf6 | +22 |
| 24 | Rxf6 | +25 | Bxf6 | +25 |
| 25 | Kc1 | +23 | Rf8 | +24 |
| 26 | Qd3 | +28 | Qd7 | +20 |
| 27 | Nd5 | +21 | g6 | +21 |
| 28 | Qg3 | +25 | Qd6 | +15 |
| 29 | Rf1 | +19 | Kb7 | +18 |
| 30 | Bd3 | +18 | Be7 | +7 |
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 41.7 moves.
Sample game 1 (1/2-1/2)
1. Nb3 f5 2. c3 e5 3. g4 fxg4 4. h3 g3 5. Qg2 Nf6 6. Qxg3 c6 7. Bh2 d6 8. Qh4 Qf7 9. f4 Nb6 10. fxe5 dxe5 11. Nf2 Qh5 12. Qxh5+ Nxh5 13. Bc2 Nc4 14. Ne4 h6 15. O-O-O Nf4 16. Bxf4 exf4 17. h4 Ne5 18. Nd4 O-O 19. Rdf1 Rde8 20. h5 b6 21. b4 Kh8 22. a4 Bc7 23. Rf2 Bd7 24. Nf3 Bg4 25. Nd4 Bd7 26. Rg1 Re7 27. Rfg2 Bb8 28. Rf2 Ng4 29. Rfg2 Ne5 30. Rh2 Be8 31. Rf1 Bd7 32. Rg1 Ng4 33. Rhg2
Sample game 2 (1-0)
1. c4 Nh6 2. Nc3 f5 3. f3 Qf7 4. e4 c6 5. O-O-O O-O 6. Nb3 e5 7. Be3 d6 8. c5 dxc5 9. Bg5 Rd6 10. Nxc5 Nc7 11. f4 exf4 12. Bxf4 Rg6 13. g3 b6 14. Nd3 Qe8 15. Re1 Re6 16. Qg2 fxe4 17. Nxe4 Nf7 18. Nd6 Qd7 19. Nxc8 Rxc8 20. Bc2 Rce8 21. Qf2 c5 22. Rhf1 Nb5 23. Rxe6 Qxe6 24. Re1 Qc8 25. Rxe8+ Qxe8 26. Ba4 Bxf4 27. Nxf4 g6 28. Qf1 a6 29. Nd5 Qd8 30. Bb3 Nd4 31. Bc4 Ne5 32. Nxb6+ Kg7 33. Nd5 h5 34. Ne3 a5 35. Bd5 a4 36. Be4 h4 37. Kb1 hxg3 38. hxg3 Qd6 39. Nd5 Nf5 40. Bg2 Nxg3 41. Qf4 Nf5 42. Qxa4 Nd4 43. Qa7+ Kh6 44. Qb6 Qd7 45. Ne3 Nc4 46. Qf6 Nxe3 47. Qf4+ g5 48. Qxe3 Qg4 49. Qh3+ Qxh3 50. Bxh3 Kg6 51. b3 Kf6 52. Kb2 Ke5 53. Kc3 Kd5 54. Kd3 Kd6 55. Bg4 Kd5 56. Bh5 Nf5 57. Bf3+ Kd6 58. Be4 Ng3 59. Bg6 Kc7 60. Ke3 Nf1+ 61. Ke2 Nh2 62. Bf5 g4 63. Be4 g3 64. Bg2 Ng4 65. Kf3 Nh6 66. Kxg3 Nf5+ 67. Kf4 Nd4 68. Ke5 Ne2 69. Bd5 Nc1 70. a3 Nd3+ 71. Ke4 Nf2+ 72. Ke3 Ng4+ 73. Kf4 Nf6 74. Be4 Kb6 75. Kf5 Ng8 76. Bd5 Ne7+ 77. Ke6 Ng6 78. Kd6 Nf4 79. Bc4 Nh5 80. Ke5 Ka5 81. a4 Ng3 82. Kd5 Kb6 83. d4 cxd4 84. b4 Nf5 85. a5+ Kc7 86. Bd3 Ne7+ 87. Kxd4 Nc6+ 88. Kc5 Nd8 89. Be4 Ne6+ 90. Kc4 Kd6 91. a6 Ke5 92. Bh1 Nd4 93. b5 Nc2 94. a7 Nd4 95. b6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 172 / 244 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): nbbrkqnr/pppppppp/8/8/8/8/PPPPPPPP/NBRNKQBR w CHdh - 0 1
Mirror twin: White 796 vs Black 622 — a different position (castling squares are fixed), not evaluated by the search.