White 72 vs Black 12
White starts from setup 72 (NBNRBKQR), Black from setup 12 (QBNNRKBR). In the encyclopedia since 2026-10-21: 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. 72, Black by position No. 12, 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 #72 N B N R B K Q R
King on the f-file, rooks on d, h, queen on the g-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 72 gives White +0.37 (Morozov Balance Index, 400M nodes).
Black: setup #12 Q B N N R K B R
King on the f-file, rooks on e, h, queen on the a-file; no 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 12 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 is exactly 0.00 each time, 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.
For comparison, in symmetric play setup 72 gives White +0.37 and setup 12 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 f3, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±16 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 | 13 | +10 | 1. f4 f6 2. Qe3 e5 3. fxe5 Rxe5 4. Qa3+ c5 |
| S1 | 500 000 | 18 | +4 | 1. d4 f6 2. f3 Bf7 3. Qf2 d5 4. Nab3 b6 |
| S2 | 2 000 000 | 22 | -7 | 1. d4 f6 2. f3 Bf7 3. Nab3 b6 4. c3 d5 |
| S3 | 8 000 000 | 29 | +13 | 1. d4 f6 2. f3 Bf7 3. c3 d5 4. Bg3 c6 |
| S4 | 32 000 000 | 36 | -3 | 1. d4 f6 2. f3 Bf7 3. Nab3 b6 4. c3 d5 |
| S5 | 128 000 000 | 40 | -9 | 1. f3 f6 2. c3 Bf7 3. d4 d5 4. Bg3 O-O |
| S6 | 400 000 000 | 45 | 0 | 1. f3 f6 2. d4 d5 3. c3 c6 4. Nab3 Nd6 |
| S7 | 800 000 000 | 49 | 0 | 1. f3 f6 2. d4 d5 3. c3 e5 4. dxe5 fxe5 |
| S8 | 1 600 000 000 | 53 | 0 | 1. f3 f6 2. d4 Bf7 3. Nab3 b6 4. Nd2 O-O |
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 | -2 |
| 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: +10
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 +59, Black +47, difference +12. 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 | -13 | 43 | 1. f3 f6 2. d4 Bf7 3. Nab3 c6 4. c3 d5 5. Bg3 Nd6 |
| 2 | -17 | 43 | 1. Nab3 f6 2. f3 Bf7 3. d4 c6 4. c3 d5 5. Bg3 Nd6 |
| 3 | -18 | 43 | 1. d4 f6 2. c3 Bf7 3. Nab3 c6 4. f3 d5 5. Bg3 Nd6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 16 cp, mean 4.1 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +13 | f6 | +3 |
| 2 | f3 | -16 | Bf7 | -13 |
| 3 | c3 | -16 | d5 | -11 |
| 4 | Bg3 | -12 | O-O | -1 |
| 5 | Nab3 | -7 | b6 | -2 |
| 6 | Qf2 | -2 | e5 | 0 |
| 7 | O-O | +1 | Nd6 | +2 |
| 8 | dxe5 | +2 | fxe5 | 0 |
| 9 | Nd2 | 0 | Bg6 | 0 |
| 10 | Bxg6 | +4 | hxg6 | +3 |
| 11 | Qe1 | +6 | c5 | 0 |
| 12 | e4 | 0 | c4 | 0 |
| 13 | exd5 | 0 | Qxd5 | 0 |
| 14 | Qe2 | +4 | Qb5 | +2 |
| 15 | Ne4 | 0 | N8f7 | 0 |
| 16 | b3 | 0 | Qc6 | 0 |
| 17 | Rfe1 | 0 | Rc8 | 0 |
| 18 | bxc4 | 0 | Qxc4 | 0 |
| 19 | Nd3 | +2 | Nxe4 | 0 |
| 20 | Qxe4 | +15 | Qxe4 | +5 |
| 21 | Rxe4 | 0 | Rxc3 | +7 |
| 22 | Nxe5 | +9 | Bxe5 | +8 |
| 23 | Bxe5 | +14 | Rc2 | +10 |
| 24 | a4 | +8 | Re8 | 0 |
| 25 | Rde1 | +8 | Rxe5 | +4 |
| 26 | Rxe5 | +6 | Nxe5 | 0 |
| 27 | Rxe5 | +9 | Ra2 | +6 |
| 28 | Re4 | +6 | g5 | 0 |
| 29 | Rc4 | +8 | Kh7 | +3 |
| 30 | h4 | 0 | gxh4 | 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 42.4 moves.
Sample game 1 (1/2-1/2)
1. d4 f6 2. Nd3 c6 3. f3 Bf7 4. Bg3 d5 5. c3 e5 6. Nc5 Bd6 7. dxe5 fxe5 8. Nd7+ Kg8 9. Qe3 Bg6 10. O-O Bxb1 11. Rxb1 h5 12. Qg5 Rh6 13. Bxe5 Ne6 14. Qc1 Be7 15. Bd4 Nb6 16. Nxb6 axb6 17. Be5 Qxa2 18. Nc2 Qc4 19. Qd2 Bc5+ 20. Kh1 Nf8 21. b3 Qh4 22. Bf4 Bd6 23. e3 Rf6 24. Bxd6 Rxd6 25. Rbe1 Qf6 26. Nd4 Qg6 27. h3 Rd7 28. Qc1 b5 29. f4 Qd3 30. Kh2 h4 31. b4 Rf7 32. Rf3 Qe4 33. f5 Qe5+ 34. Kg1 Nh7 35. Rf4 Ng5 36. Rg4 Ne4 37. Rxh4 Ng3 38. Qb1 Nxf5 39. Rh5 g6 40. Rg5 Kg7 41. h4 Kh6 42. Qd1 Qg7 43. e4 Rxe4 44. Rxe4 dxe4 45. Qd2 e3 46. Nxf5+ Rxf5 47. Qxe3 Rxg5 48. Qxg5+ Kh7 49. h5 Qxc3 50. Qxg6+ Kh8 51. Qe8+ Kg7 52. Qg6+ Kh8 53. Qh6+ Kg8 54. Qg5+
Sample game 2 (1/2-1/2)
1. f4 b6 2. d4 f6 3. Qf2 Nd6 4. Nab3 Bd5 5. O-O O-O 6. Nd2 Ne4 7. Nxe4 Bxe4 8. a3 d5 9. Nb3 e5 10. Nd2 Bg6 11. f5 Bf7 12. dxe5 Rxe5 13. c4 Re7 14. cxd5 Qxd5 15. e4 Qb5 16. Nf3 Bc4 17. e5 Bxf1 18. Ba2+ Bc4 19. Qe2 Qc5+ 20. Bf2 Qxf2+ 21. Kxf2 Bxa2 22. Qc2 fxe5 23. b3 e4 24. f6 Ree8 25. Ng5 Rxf6+ 26. Kg1 Nf7 27. Nxe4 Rfe6 28. Nd2 Bxb3 29. Qxb3 c6 30. Nf3 h6 31. Kf1 Kf8 32. Re1 Ne5 33. Kg1 Rf6 34. Nd2 Bd6 35. Kh1 Re7 36. Qc3 Ke8 37. Ne4 Rfe6 38. Ng3 Rf7 39. a4 Kd8 40. a5 Ref6 41. Kg1 Bc5+ 42. Kh1
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 72 / 12 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): qbnnrkbr/pppppppp/8/8/8/8/PPPPPPPP/NBNRBKQR w DHeh - 0 1
Mirror twin: White 893 vs Black 956 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 316.