White 457 vs Black 505
White starts from setup 457 (RNNBBKQR), Black from setup 505 (RQNBBKNR). In the encyclopedia since 2026-10-03: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #457 R N N B B K Q R
King on the f-file, rooks on a, h, queen on the g-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 457 gives White +0.25 (Morozov Balance Index, 400M nodes).
Black: setup #505 R Q N B B K N R
King on the f-file, rooks on a, h, queen on the b-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 505 gives White +0.26 (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 shallow rungs wandered between -21 and +3 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 457 gives White +0.25 and setup 505 gives White +0.26: 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 (30 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 | 14 | -21 | 1. f3 d5 2. d4 Nf6 3. Nd3 h5 4. Qf2 c6 |
| S1 | 500 000 | 18 | -1 | 1. f3 Nf6 2. g4 d5 3. Kg2 h5 4. g5 Nd7 |
| S2 | 2 000 000 | 23 | -20 | 1. d4 c5 2. dxc5 b6 3. f3 Nf6 4. Bg3 Qb7 |
| S3 | 8 000 000 | 29 | -14 | 1. d4 c5 2. dxc5 b6 3. f3 Nf6 4. c4 bxc5 |
| S4 | 32 000 000 | 33 | -7 | 1. d4 d5 2. f3 e6 3. Nd2 Nge7 4. c3 b6 |
| S5 | 128 000 000 | 41 | +3 | 1. d4 c5 2. dxc5 b6 3. f3 bxc5 4. Qxc5 Qxb2 |
| S6 | 400 000 000 | 51 | 0 | 1. d4 c5 2. dxc5 b6 3. f3 bxc5 4. Qxc5 Qxb2 |
| S7 | 800 000 000 | 53 | 0 | 1. d4 c5 2. dxc5 b6 3. f3 bxc5 4. Qxc5 Qxb2 |
| S8 | 1 600 000 000 | 52 | 0 | 1. d4 c5 2. dxc5 b6 3. f3 bxc5 4. Qxc5 Qxb2 |
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 | not checked |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair held exactly 0.00 up to 1 600 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: -2
- Lc0 0.32.1: +9
Independent confirmations: 2 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 +32, Black +24, difference +8. 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 | 40 | 1. d4 c5 2. dxc5 b6 3. f3 bxc5 4. Qxc5 Bb6 5. Qa3 d5 |
| 2 | +9 | 41 | 1. d4 c5 2. dxc5 b6 3. f3 bxc5 4. Qxc5 Bb6 5. Qa3 d5 |
| 3 | 0 | 40 | 1. c4 b5 2. c5 e5 3. f4 exf4 4. Nd3 d6 5. Qd4 Nf6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 23 cp, mean 5.6 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -23 | c6 | -14 |
| 2 | d4 | -8 | d5 | -18 |
| 3 | cxd5 | -11 | cxd5 | +2 |
| 4 | Nc3 | -1 | e6 | -1 |
| 5 | a4 | +4 | Nge7 | +7 |
| 6 | f3 | +1 | Nd6 | 0 |
| 7 | Nd3 | 0 | a5 | +1 |
| 8 | Qf2 | 0 | O-O | 0 |
| 9 | Bc2 | +4 | Nc6 | 0 |
| 10 | O-O | -1 | Nb4 | -3 |
| 11 | Bb1 | -6 | Nxd3 | -11 |
| 12 | Bxd3 | -9 | b5 | -6 |
| 13 | axb5 | 0 | Nxb5 | 0 |
| 14 | Na4 | 0 | Nd6 | -10 |
| 15 | e4 | -5 | Bb5 | -10 |
| 16 | Qe2 | -7 | Bxd3 | -5 |
| 17 | Qxd3 | -6 | Qb7 | -19 |
| 18 | Nc5 | 0 | Qc6 | 0 |
| 19 | Bf2 | -3 | Be7 | -5 |
| 20 | Rfc1 | -5 | dxe4 | -2 |
| 21 | fxe4 | -3 | Rfc8 | -9 |
| 22 | h3 | -4 | h6 | -5 |
| 23 | Rc3 | -10 | Qb5 | -12 |
| 24 | Qxb5 | -9 | Nxb5 | -8 |
| 25 | Rc4 | -9 | Bf6 | -10 |
| 26 | e5 | -6 | Bd8 | -7 |
| 27 | Rac1 | -15 | Kh7 | -9 |
| 28 | Kf1 | -6 | Ra7 | -8 |
| 29 | Ke2 | 0 | Rb8 | 0 |
| 30 | Na4 | 0 | Rd7 | 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 35.0 moves.
Sample game 1 (1/2-1/2)
1. d4 c5 2. dxc5 b6 3. f3 Nf6 4. Bg3 Qb7 5. Nd3 O-O 6. c4 bxc5 7. e4 Nb6 8. Nd2 d6 9. e5 dxe5 10. Qe3 Nbd7 11. Bc2 a5 12. b3 Bc7 13. Nxe5 Nxe5 14. Bxe5 a4 15. O-O Ra6 16. Rfe1 Re6 17. Qc3 axb3 18. axb3 Bc6 19. Nf1 Re8 20. Ng3 g6 21. Bxc7 Rxe1+ 22. Rxe1 Qxc7 23. Qe3 Bb7 24. Qg5 Qa5 25. Rd1 Qc7 26. Re1 Qa5 27. Rd1 Qc7
Sample game 2 (1/2-1/2)
1. c4 f5 2. g4 fxg4 3. h3 g3 4. Qxg3 c6 5. e4 Qxg3 6. fxg3 e5 7. O-O+ Bf7 8. d3 Nf6 9. Nd2 d6 10. Nf3 a5 11. c5 Nd7 12. cxd6 O-O 13. a4 Nxd6 14. Bc3 Re8 15. Bb3 Nc5 16. Bc2 Nd7 17. Bb3 Nc5 18. Bc2 Nd7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 457 / 505 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): rqnbbknr/pppppppp/8/8/8/8/PPPPPPPP/RNNBBKQR w AHah - 0 1
Mirror twin (the same position mirrored): White 697 vs Black 553.