White 23 vs Black 115
White starts from setup 23 (NQBNRKRB), Black from setup 115 (BNQRNKRB). 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. 23, Black by position No. 115, 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 #23 N Q B N R K R B
King on the f-file, rooks on e, g, queen on the b-file; one 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 23 gives White +0.13 (Morozov Balance Index, 400M nodes).
Black: setup #115 B N Q R N K R B
King on the f-file, rooks on d, g, 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 115 gives White +0.10 (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 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.
For comparison, in symmetric play setup 23 gives White +0.13 and setup 115 gives White +0.10: 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 2 first moves are within 10 cp of it.
Along the engine's main line (28 moves) the evaluation stayed within ±15 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. c4 O-O 2. d4 c5 3. d5 b5 4. cxb5 Bxd5 |
| S1 | 500 000 | 19 | +4 | 1. c4 O-O 2. O-O c5 3. g3 Nc6 4. Nc2 b6 |
| S2 | 2 000 000 | 23 | +11 | 1. c4 g6 2. g3 c5 3. d3 Nc6 4. Bh6+ Bg7 |
| S3 | 8 000 000 | 30 | -9 | 1. c4 c5 2. Qxh7 d5 3. cxd5 Nf6 4. Qh3 Qxh3 |
| S4 | 32 000 000 | 37 | -13 | 1. c4 c5 2. Qxh7 d5 3. cxd5 Nf6 4. Qh3 Qxh3 |
| S5 | 128 000 000 | 42 | -9 | 1. c4 c5 2. Qxh7 d5 3. cxd5 Nf6 4. Qh3 Qxh3 |
| S6 | 400 000 000 | 49 | 0 | 1. c4 c5 2. Qxh7 d5 3. cxd5 Nf6 4. Qh3 Qxh3 |
| S7 | 800 000 000 | 51 | 0 | 1. c4 b6 2. Qxh7 g6 3. d3 Nf6 4. Qh3 Bg7 |
| S8 | 1 600 000 000 | 55 | 0 | 1. c4 b6 2. Qxh7 g6 3. d3 Nf6 4. Qh3 Bg7 |
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: +3
- Lc0 0.32.1: -8
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 +43, Black +104, difference -61. 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 | 43 | 1. c4 c5 2. Qxh7 d5 3. cxd5 Nf6 4. Qh3 Qxh3 5. gxh3 Nxd5 |
| 2 | -9 | 42 | 1. g3 c5 2. c4 Nc6 3. Nc2 b6 4. d3 Nc7 5. b4 d5 |
| 3 | -13 | 42 | 1. O-O b6 2. c3 g6 3. e4 d5 4. e5 d4 5. b4 f6 |
Main-line play-out
28 moves, 5 000 000 nodes per half-move. Largest |evaluation| 15 cp, mean 3.0 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -8 | c5 | -12 |
| 2 | Qxh7 | -5 | d5 | -3 |
| 3 | cxd5 | -8 | Nf6 | -7 |
| 4 | Qh3 | -1 | Qxh3 | 0 |
| 5 | gxh3 | 0 | Nxd5 | -1 |
| 6 | h4 | 0 | g6 | -6 |
| 7 | d3 | -2 | Be5 | -7 |
| 8 | h5 | +1 | Bxh2 | 0 |
| 9 | Rg4 | +2 | b6 | +5 |
| 10 | hxg6 | +7 | Rxg6 | +7 |
| 11 | Rxg6 | +9 | fxg6 | +11 |
| 12 | Bg2 | +5 | Nc6 | +6 |
| 13 | Nc2 | +10 | Nf4 | +12 |
| 14 | Bxf4 | +7 | Bxf4 | +15 |
| 15 | e3 | +7 | Be5 | +4 |
| 16 | Be4 | 0 | g5 | 0 |
| 17 | a3 | 0 | Bf6 | 0 |
| 18 | Ke2 | 0 | c4 | 0 |
| 19 | dxc4 | 0 | Na5 | 0 |
| 20 | Bxa8 | 0 | Rxa8 | 0 |
| 21 | c5 | 0 | bxc5 | 0 |
| 22 | Rg1 | 0 | Nb3 | 0 |
| 23 | Ne1 | 0 | Rd8 | 0 |
| 24 | Nf3 | 0 | Nc1+ | 0 |
| 25 | Ke1 | 0 | Nd3+ | 0 |
| 26 | Kf1 | 0 | Nc1 | 0 |
| 27 | Ke1 | 0 | Nd3+ | 0 |
| 28 | Ke2 | 0 | Nc1+ | 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 32.5 moves.
Sample game 1 (1/2-1/2)
1. c4 O-O 2. g4 g6 3. Nc2 c6 4. d4 d5 5. Bh6 Bg7 6. Bxg7 Nxg7 7. cxd5 cxd5 8. Nde3 b5 9. Qc1 a5 10. h4 b4 11. h5 Qc7 12. Rd1 Ne6 13. Qd2 Kh8 14. Bf3 Ng5 15. Ne1 Qf4 16. Nc4 Qxd2 17. Nxd2 Nd7 18. Nd3 Rc8 19. Rh1 gxh5 20. Rxh5 Rg8 21. Nb3 Rc4 22. Nxa5 Rxd4 23. Nb3 Rc4 24. Nd2 Rd4 25. Nb3 Rc4 26. Nd2 Rd4
Sample game 2 (1/2-1/2)
1. c4 c5 2. Nc3 g5 3. Qxh7 Bf6 4. g4 Rh8 5. Qf5 Ng7 6. Qf3 Nc6 7. d3 Ne5 8. Qg3 Ng6 9. Be4 Be5 10. Qf3 Nh4 11. Qh1 Ne6 12. Bd2 Qb8 13. O-O-O Ng6 14. h3 Nef4 15. Rge1 Rxh3 16. Qf1 Rh2 17. e3 Bxc3 18. Bxc3 d5 19. Bf5 Ng2 20. Bxg6 Nxe1 21. f4 Qd6 22. Bf5 gxf4 23. Rxe1 dxc4 24. dxc4 fxe3 25. Nc2 e2 26. Rxe2 Qh6+ 27. g5 Qxg5+ 28. Ne3 Rxe2 29. Qxe2 b6 30. Kc2 e6 31. Bd3 Qf4 32. Ng2 Qh2 33. Be4 Bxe4+ 34. Qxe4 Qh5 35. Kb3 Qd1+ 36. Ka3 Qd3 37. Qf4 b5 38. cxb5 Qxb5 39. Ne1 Qa6+ 40. Kb3 Qb5+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 23 / 115 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): bnqrnkrb/pppppppp/8/8/8/8/PPPPPPPP/NQBNRKRB w EGdg - 0 1
Mirror twin: White 930 vs Black 835 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 138.