White 73 vs Black 782
White starts from setup 73 (NNRBBKQR), Black from setup 782 (QRKNRBBN). 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. 73, Black by position No. 782, 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 #73 N N R B B K Q R
King on the f-file, rooks on c, 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 73 gives White +0.31 (Morozov Balance Index, 400M nodes).
Black: setup #782 Q R K N R B B N
King on the c-file, rooks on b, e, queen on the a-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 782 gives White +0.20 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±5 centipawns of equality, reaching search depth 55.
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 -20 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 73 gives White +0.31 and setup 782 gives White +0.20: with both sides on the same rank the first move is worth something. In this pair Black's own setup absorbs that edge completely.
The engine's first choice for White is f4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the largest swing was 32 cp (around move 4), ending at 0 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 0, drawn 9, Black won 1 (White scored 45.0%).
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 | -20 | 1. f4 e5 2. fxe5 Ng6 3. Qf2 Nxe5 4. O-O b5 |
| S1 | 500 000 | 18 | -2 | 1. c4 e5 2. f3 f5 3. Qf2 Ng6 4. O-O b5 |
| S2 | 2 000 000 | 23 | -13 | 1. c4 e5 2. f3 f5 3. Qe3 Ng6 4. O-O a6 |
| S3 | 8 000 000 | 26 | -16 | 1. c4 e5 2. f3 f5 3. Qe3 Ng6 4. d4 b5 |
| S4 | 32 000 000 | 32 | +16 | 1. f4 b5 2. e3 f6 3. Qf2 e5 4. fxe5 Ng6 |
| S5 | 128 000 000 | 37 | +9 | 1. f4 b5 2. e3 f6 3. Qf2 e5 4. fxe5 fxe5 |
| S6 | 400 000 000 | 45 | +5 | 1. f4 b5 2. e3 f6 3. Qf2 e5 4. fxe5 fxe5 |
| S7 | 800 000 000 | 51 | 0 | 1. f4 b5 2. e3 f6 3. Qf2 e5 4. fxe5 fxe5 |
| S8 | 1 600 000 000 | 55 | 0 | 1. f4 b5 2. e3 f6 3. Qf2 e5 4. fxe5 fxe5 |
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: -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 +18, Black +23, difference -5. 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, 9 draws, 1 Black wins, White scored 45.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +7 | 39 | 1. f4 b5 2. e3 f6 3. Qf2 e5 4. fxe5 fxe5 5. O-O Ng6 |
| 2 | -17 | 39 | 1. c4 e5 2. f3 Nc6 3. Qe3 f5 4. O-O b6 5. Bf2 Ng6 |
| 3 | -18 | 39 | 1. f3 e5 2. c4 Nc6 3. Qe3 f5 4. O-O Ng6 5. Bf2 b6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 32 cp, mean 3.7 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -26 | e5 | -23 |
| 2 | f3 | -8 | f5 | -8 |
| 3 | d4 | -8 | Ng6 | 0 |
| 4 | Nb3 | -32 | exd4 | -15 |
| 5 | Nxd4 | 0 | Nc6 | +1 |
| 6 | b3 | 0 | Nge7 | +1 |
| 7 | Bc2 | +3 | g6 | +3 |
| 8 | Nc3 | +3 | b6 | 0 |
| 9 | g4 | 0 | fxg4 | 0 |
| 10 | Qxg4 | +10 | Nxd4 | +5 |
| 11 | Qxd4 | +8 | Qc6 | +16 |
| 12 | Bg3 | +19 | Qe6 | +7 |
| 13 | Qf4 | +4 | Qh3+ | +1 |
| 14 | Kf2 | +7 | d6 | 0 |
| 15 | Qh4 | +7 | Qe6 | 0 |
| 16 | Nb5 | 0 | Nf5 | 0 |
| 17 | Qe4 | 0 | Bh6 | 0 |
| 18 | Nxa7+ | 0 | Kd7 | 0 |
| 19 | Qc6+ | 0 | Kd8 | 0 |
| 20 | Be4 | 0 | Nd4 | 0 |
| 21 | Qa4 | 0 | Qf6 | 0 |
| 22 | Kg2 | 0 | Bxc1 | 0 |
| 23 | Rxc1 | 0 | Be6 | -5 |
| 24 | Nc6+ | 0 | Nxc6 | 0 |
| 25 | Bxc6 | 0 | Re7 | 0 |
| 26 | Qb5 | 0 | Kc8 | 0 |
| 27 | b4 | 0 | Qb2 | 0 |
| 28 | Re1 | 0 | Qd2 | 0 |
| 29 | a4 | 0 | Bd7 | 0 |
| 30 | Bxd7+ | 0 | Rxd7 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 9, Black won 1 — White scored 45.0%. Average length 34.9 moves.
Sample game 1 (1/2-1/2)
1. c4 e5 2. f3 a6 3. d4 exd4 4. Qxd4 Nc6 5. Qd2 Qa7 6. Nc3 Qd4 7. Qxd4 Nxd4 8. Nd5 Ng6 9. h4 Ne5 10. h5 f6 11. h6 b5 12. hxg7 Bxg7 13. b3 f5 14. Bc3 bxc4 15. Nxc7 Kxc7 16. Bxd4 Bf8 17. Bf2 Ba3 18. Rb1 Bd6 19. Bc2 f4 20. g4 fxg3 21. Bxg3 Ng6 22. Bxd6+ Kxd6 23. Kf2 Kc7 24. Rbc1 Kd8 25. Be4 Nf4 26. Rcd1 Rb5 27. Rh4 Ng6 28. Rh6 Ra5 29. Rd2 c3 30. Rc2 Nf4 31. Rh4 Rf8 32. Rxc3 Rxa2 33. Nc2 h5 34. b4 Rf6 35. Rc5 Bb3 36. Nd4 Bd1 37. Bd5 Rb2 38. Bc4 Rxb4 39. Nf5 d6 40. Nxd6 Rb2 41. Ne4 Bxe2 42. Nxf6 Bxc4+ 43. Kg1 Rb1+
Sample game 2 (0-1)
1. c4 e5 2. f3 f5 3. Qe3 a6 4. Bb3 b6 5. Bf2 Ng6 6. Qg5 Be6 7. Qh5 Nf7 8. Qxh7 Nf4 9. Be3 g5 10. c5 Qc6 11. g3 bxc5 12. Nc3 Nxe2 13. Kxe2 g4 14. Rhf1 f4 15. Ba4 gxf3+ 16. Kd1 Qd6 17. Bg1 Bh6 18. Ne4 Qd3 19. Rf2 fxg3 20. hxg3 Rh8 21. Qg6 Be3 22. Rc3 Qb1+ 23. Rc1 Qxa2 24. Nc3 Bxf2 25. Nxa2 Bxg1 26. Nc3 Rxb2 27. Qe4 c6 28. Bxc6 f2 29. Bb7+ Rxb7 30. Kc2 Nd6 31. Qf3 Nf5 32. Ne2 Rf8 33. Kc3 Rf7 34. Nxg1 Nd4 35. Qg2 e4 36. g4 fxg1=Q 37. Rxg1 Rf3+ 38. Qxf3 exf3 39. Kd3 d6 40. Rh1 Bxg4 41. Kc3 f2 42. Rh8+ Kd7 43. Rh7+ Kc6 44. Rh1 Kd5 45. d3 Rf7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 73 / 782 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): qrknrbbn/pppppppp/8/8/8/8/PPPPPPPP/NNRBBKQR w CHbe - 0 1
Mirror twin: White 889 vs Black 180 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 320.