White 93 vs Black 81
White starts from setup 93 (NNRBKRBQ), Black from setup 81 (BNNBRKRQ). In the encyclopedia since 2026-10-15: 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. 93, Black by position No. 81, 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 #93 N N R B K R B Q
King on the e-file, rooks on c, f, queen on the h-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 93 gives White +0.42 (Morozov Balance Index, 400M nodes).
Black: setup #81 B N N B R K R Q
King on the f-file, rooks on e, g, queen on the h-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 81 gives White +0.35 (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 57.
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 93 gives White +0.42 and setup 81 gives White +0.35: 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 2 first moves are within 10 cp of it.
Along the engine's main line (26 moves) the evaluation stayed within ±23 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 | 15 | -3 | 1. f3 O-O 2. e4 b6 3. Be2 e6 4. O-O-O d5 |
| S1 | 500 000 | 19 | +5 | 1. f3 b6 2. c3 O-O 3. Bc2 d5 4. O-O-O h5 |
| S2 | 2 000 000 | 23 | +11 | 1. e4 b6 2. f3 O-O 3. Be2 c5 4. O-O-O h5 |
| S3 | 8 000 000 | 26 | +7 | 1. g3 h5 2. f4 e6 3. c3 Nc6 4. Bb3 Nd6 |
| S4 | 32 000 000 | 32 | -3 | 1. g3 e6 2. c3 h5 3. Bc2 d5 4. f4 b6 |
| S5 | 128 000 000 | 38 | -6 | 1. e4 b6 2. Nc3 e6 3. f4 g5 4. fxg5 Bxg5 |
| S6 | 400 000 000 | 50 | 0 | 1. e4 b6 2. Nc3 e6 3. f4 g5 4. fxg5 Bxg5 |
| S7 | 800 000 000 | 54 | 0 | 1. e4 b6 2. Nc3 e6 3. f4 g5 4. fxg5 Bxg5 |
| S8 | 1 600 000 000 | 57 | 0 | 1. e4 b6 2. Nc3 e5 3. Be2 Nd6 4. f3 h5 |
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: +1
- Lc0 0.32.1: -17
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 +44, Black +56, 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 | 0 | 41 | 1. f3 b6 2. e4 h5 3. Be2 c5 4. O-O-O e5 5. Nc3 Nd6 |
| 2 | 0 | 41 | 1. e4 b6 2. f3 h5 3. Be2 c5 4. O-O-O e5 5. Nc3 Nd6 |
| 3 | -22 | 40 | 1. Nb3 b6 2. e3 g6 3. Nc3 c5 4. f4 e5 5. Be2 Bh4+ |
Main-line play-out
26 moves, 5 000 000 nodes per half-move. Largest |evaluation| 23 cp, mean 7.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g3 | +15 | h5 | -14 |
| 2 | e4 | -13 | e5 | -9 |
| 3 | Be2 | -20 | O-O | -10 |
| 4 | O-O-O | -13 | b6 | -15 |
| 5 | Nc3 | -17 | Nd6 | -23 |
| 6 | Nb3 | -21 | Qh7 | -7 |
| 7 | f3 | +6 | c5 | -2 |
| 8 | d3 | -7 | Nc6 | -12 |
| 9 | Rde1 | -12 | f5 | -15 |
| 10 | Be3 | 0 | Nd4 | -8 |
| 11 | Bd1 | -12 | Qg6 | 0 |
| 12 | Qg1 | -10 | Bc6 | -19 |
| 13 | Kb1 | -22 | h4 | -21 |
| 14 | Bc1 | -14 | Ne6 | -20 |
| 15 | Nd2 | -9 | f4 | -5 |
| 16 | Ne2 | 0 | fxg3 | 0 |
| 17 | hxg3 | 0 | hxg3 | -4 |
| 18 | Qxg3 | -6 | Qxg3 | 0 |
| 19 | Nxg3 | 0 | Kf7 | 0 |
| 20 | Rg1 | 0 | Nf4 | 0 |
| 21 | Ndf1 | 0 | Bh4 | 0 |
| 22 | Ne3 | 0 | Rh8 | 0 |
| 23 | Ref1 | 0 | Nh3 | 0 |
| 24 | Rg2 | 0 | Nf4 | 0 |
| 25 | Rgg1 | 0 | Nh3 | 0 |
| 26 | Rg2 | 0 | Nf4 | 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 25.0 moves.
Sample game 1 (1/2-1/2)
1. f3 b6 2. e4 c5 3. Be2 h5 4. O-O-O e5 5. Nc3 Nd6 6. Be3 O-O 7. h4 Qh7 8. Qh3 f5 9. Nb3 Kh8 10. d3 Nc6 11. g4 f4 12. Bf2 Nd4 13. Rh1 Bc6 14. Rdg1 Nxe2+ 15. Nxe2 c4 16. Nd2 cxd3 17. cxd3 Nb5 18. gxh5 Bf6 19. Kb1 d5 20. Rc1 Bb7 21. Qd7 Ba6 22. Qxd5 Rd8 23. Qb3 Na3+ 24. Ka1 Rxd3 25. Nc3 Nb5 26. Qb4 Rfd8 27. Nd5 Bb7 28. Nxf6 gxf6 29. Nb1 Nc7 30. Rhg1 Qf7 31. Rg6 Na6 32. Qa4 Kh7 33. Rcg1 Rxf3 34. Rg7+ Qxg7 35. Rxg7+ Kxg7 36. Qc4 Rfd3 37. Qe6 Bxe4 38. Qe7+ Kg8 39. Qxf6 Rd1 40. Qe6+ Kf8
Sample game 2 (1/2-1/2)
1. f3 b6 2. e4 O-O 3. Be2 c5 4. O-O-O h5 5. Nc3 e5 6. Bc4 Nd6 7. Bd5 Bxd5 8. Nxd5 f5 9. g3 h4 10. d3 Nc6 11. Nb3 Ne7 12. Ne3 Ng6 13. Qg2 f4 14. Nd5 h3 15. Qe2 Qh5 16. Kb1 Bg5 17. Nd2 Ne7 18. Nc3 Nc6 19. Nd5 Ne7 20. Nc3 Nc6 21. Nd5
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 93 / 81 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): bnnbrkrq/pppppppp/8/8/8/8/PPPPPPPP/NNRBKRBQ w CFeg - 0 1
Mirror twin: White 872 vs Black 875 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 406.