White 45 vs Black 459
White starts from setup 45 (NNQBRKBR), Black from setup 459 (RNNKBQRB). In the encyclopedia since 2026-10-09: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #45 N N Q B R K B R
King on the f-file, rooks on e, h, queen on the c-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 45 gives White +0.31 (Morozov Balance Index, 400M nodes).
Black: setup #459 R N N K B Q R B
King on the d-file, rooks on a, g, queen on the f-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 459 gives White +0.32 (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 56.
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 -3 and +25 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 45 gives White +0.31 and setup 459 gives White +0.32: 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 d4, and 2 first moves are within 10 cp of it.
Along the engine's main line (20 moves) the evaluation stayed within ±22 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 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 | +1 | 1. h4 Nc6 2. c3 f5 3. d4 g6 4. Nb3 Nd6 |
| S1 | 500 000 | 20 | -3 | 1. h4 Nc6 2. Nb3 g6 3. c3 Nb6 4. d4 e5 |
| S2 | 2 000 000 | 22 | +4 | 1. d4 g5 2. f3 f5 3. Bf2 d6 4. O-O f4 |
| S3 | 8 000 000 | 28 | +25 | 1. f3 f5 2. Bf2 g5 3. d4 d6 4. e4 Nb6 |
| S4 | 32 000 000 | 34 | +9 | 1. f3 f5 2. Bf2 g5 3. d4 f4 4. e4 fxe3 |
| S5 | 128 000 000 | 44 | -1 | 1. f3 f5 2. Bf2 f4 3. e4 fxe3 4. Bxe3 g5 |
| S6 | 400 000 000 | 51 | 0 | 1. f3 f5 2. Bf2 g5 3. d4 f4 4. e4 fxe3 |
| S7 | 800 000 000 | 56 | 0 | 1. f3 f5 2. Bf2 g5 3. d4 f4 4. e4 fxe3 |
| S8 | 1 600 000 000 | 55 | 0 | 1. f3 f5 2. Bf2 g5 3. d4 f4 4. e4 fxe3 |
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 +50, Black +76, difference -26. 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 | -4 | 43 | 1. d4 f5 2. f3 g5 3. Bf2 f4 4. c3 Nb6 5. e4 fxe3 |
| 2 | -8 | 43 | 1. f3 f5 2. Bf2 f4 3. c3 g5 4. d4 Nb6 5. e4 fxe3 |
| 3 | -16 | 42 | 1. e4 f5 2. f3 fxe4 3. Bf2 exf3 4. Bxf3 Nd6 5. Nb3 Bf7 |
Main-line play-out
20 moves, 5 000 000 nodes per half-move. Largest |evaluation| 22 cp, mean 4.4 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f3 | +15 | g5 | +13 |
| 2 | Bf2 | +10 | f5 | +3 |
| 3 | e4 | +11 | Nc6 | -8 |
| 4 | c3 | -6 | g4 | -15 |
| 5 | fxg4 | -22 | fxe4 | -7 |
| 6 | Rxe4 | -11 | Nd6 | -10 |
| 7 | Re3 | -2 | Bf6 | 0 |
| 8 | h4 | 0 | Qg7 | 0 |
| 9 | d4 | 0 | e5 | 0 |
| 10 | Nb3 | 0 | exd4 | 0 |
| 11 | cxd4 | 0 | a5 | 0 |
| 12 | a4 | -2 | Bf7 | +16 |
| 13 | O-O | +13 | Bc4 | +15 |
| 14 | Rfe1 | 0 | Bxb3 | 0 |
| 15 | Bxb3 | 0 | Rf8 | 0 |
| 16 | Rd3 | 0 | Qxg4 | 0 |
| 17 | Rg3 | 0 | Qh5 | 0 |
| 18 | Bd1 | 0 | Qf7 | 0 |
| 19 | Bb3 | 0 | Qh5 | 0 |
| 20 | Bd1 | 0 | Qf7 | 0 |
| 21 | Bb3 | 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 36.5 moves.
Sample game 1 (1/2-1/2)
1. d4 d6 2. f3 Nb6 3. Bf2 g5 4. e4 Bb5+ 5. Kg1 f5 6. exf5 Qxf5 7. c3 Bd7 8. Nc2 Nc6 9. Ne3 Qf7 10. b4 e6 11. h4 gxh4 12. Bxh4+ Ne7 13. Nd2 O-O-O 14. Ng4 Bg7 15. Ne4 Nbd5 16. Bxe7 Qxe7 17. Bb3 Qf7 18. Ng5 Qf5 19. Nxh7 Nxb4 20. Qb1 Qf7 21. Qe4 Nd5 22. Ng5 Bxd4+ 23. Qxd4 Rxg5 24. Bxd5 exd5 25. Qxa7 Bxg4 26. Qa8+ Kd7 27. Qa4+ Kc8 28. Qa8+ Kd7 29. Qa4+ Kc8
Sample game 2 (1/2-1/2)
1. d4 g5 2. f3 Nc6 3. c3 f5 4. Bf2 f4 5. e4 fxe3 6. Bxe3 Nb6 7. O-O O-O-O 8. f4 gxf4 9. Bxf4 Bf6 10. Bb3 Bf7 11. Bg3 Qg7 12. Qf4 d6 13. Nd2 Rdf8 14. Qf5+ Kb8 15. Bxf7 Qxf7 16. Nab3 Rg6 17. Qh5 Qg8 18. Ne4 Bg7 19. Rxf8+ Qxf8 20. Rf1 Qg8 21. Nc1 Bh6 22. b3 Qe6 23. Qf3 Rg8 24. Ne2 Rf8 25. Qd3 Rxf1+ 26. Kxf1 a5 27. Nf2 Nd5 28. Qxh7 Ne3+ 29. Kg1 Nf5 30. Kf1 Ne3+ 31. Kg1 Nf5 32. Kf1
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 45 / 459 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): rnnkbqrb/pppppppp/8/8/8/8/PPPPPPPP/NNQBRKBR w EHag - 0 1
Mirror twin: White 920 vs Black 689 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 165.