White 126 vs Black 501
White starts from setup 126 (NQRNKBBR), Black from setup 501 (RQBBNKNR). 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. 126, Black by position No. 501, 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 #126 N Q R N K B B R
King on the e-file, rooks on c, h, queen on the b-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 126 gives White +0.27 (Morozov Balance Index, 400M nodes).
Black: setup #501 R Q B B N 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 501 gives White +0.16 (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 54.
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 -19 and -1 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 126 gives White +0.27 and setup 501 gives White +0.16: 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 c4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±24 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 | 18 | -15 | 1. h3 c6 2. Bh2 Bc7 3. Bxc7 Nxc7 4. c4 Nf6 |
| S1 | 500 000 | 20 | -1 | 1. h3 c6 2. Bh2 Bc7 3. Bxc7 Nxc7 4. e3 Nf6 |
| S2 | 2 000 000 | 26 | -19 | 1. c4 c6 2. Nc3 Ngf6 3. f3 O-O 4. Bf2 Nc7 |
| S3 | 8 000 000 | 31 | -13 | 1. c4 c6 2. Nc3 Ngf6 3. e3 O-O 4. Nb3 d5 |
| S4 | 32 000 000 | 36 | -17 | 1. c4 c6 2. Nc3 Ngf6 3. e3 O-O 4. Nb3 d5 |
| S5 | 128 000 000 | 43 | -7 | 1. c4 c6 2. h3 Bc7 3. Nb3 Ngf6 4. e3 b5 |
| S6 | 400 000 000 | 50 | 0 | 1. c4 c6 2. Nc3 Ngf6 3. e3 O-O 4. Nb3 d5 |
| S7 | 800 000 000 | 51 | 0 | 1. c4 c6 2. Nc3 Ngf6 3. e3 O-O 4. Nb3 d5 |
| S8 | 1 600 000 000 | 54 | 0 | 1. c4 c6 2. Nc3 Ngf6 3. f3 d5 4. cxd5 Nxd5 |
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: -5
- 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 +9, Black +21, 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 | +5 | 43 | 1. c4 c6 2. Nc3 Ngf6 3. f3 d5 4. cxd5 cxd5 5. e3 e5 |
| 2 | -7 | 43 | 1. e3 c6 |
| 3 | -8 | 43 | 1. Nb3 c6 2. c4 Ngf6 3. d4 O-O 4. h3 Bc7 5. e4 e5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 24 cp, mean 8.4 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -10 | c6 | -20 |
| 2 | Nc3 | -12 | Ngf6 | -16 |
| 3 | e3 | -15 | O-O | -11 |
| 4 | f3 | -12 | d5 | -12 |
| 5 | Bf2 | -8 | e5 | -21 |
| 6 | Bg3 | -24 | dxc4 | -17 |
| 7 | Bxc4 | -18 | a5 | -17 |
| 8 | Be2 | +1 | Nh5 | -10 |
| 9 | Bf2 | 0 | f5 | -3 |
| 10 | O-O | -8 | Qd6 | -2 |
| 11 | f4 | 0 | Nef6 | -7 |
| 12 | Qd3 | -10 | Qxd3 | -17 |
| 13 | Bxd3 | -12 | e4 | -18 |
| 14 | Bc4+ | -11 | Kh8 | -14 |
| 15 | h3 | -19 | h6 | -8 |
| 16 | Nb3 | -12 | a4 | -10 |
| 17 | Nd4 | -10 | Bb6 | 0 |
| 18 | Nce2 | 0 | Rd8 | -8 |
| 19 | Bh4 | -6 | Rd6 | -3 |
| 20 | b4 | -1 | Nd5 | -10 |
| 21 | Bxd5 | -9 | Rxd5 | -7 |
| 22 | Be7 | -15 | Kg8 | -17 |
| 23 | Bc5 | -12 | Bxc5 | -8 |
| 24 | Rxc5 | -8 | Rxc5 | -8 |
| 25 | bxc5 | -2 | Nf6 | -5 |
| 26 | Nc3 | 0 | g6 | 0 |
| 27 | g4 | 0 | fxg4 | 0 |
| 28 | hxg4 | 0 | Bxg4 | 0 |
| 29 | Rb1 | 0 | Ra7 | 0 |
| 30 | a3 | 0 | h5 | 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 39.1 moves.
Sample game 1 (1/2-1/2)
1. e4 c6 2. c4 e5 3. f3 Ne7 4. b4 O-O 5. Nb3 Nc7 6. Nc3 d5 7. cxd5 cxd5 8. exd5 Ncxd5 9. Nxd5 Nxd5 10. Bc5 Be7 11. Bc4 Bxc5 12. bxc5 Nf4 13. O-O a5 14. d4 a4 15. Nd2 exd4 16. g3 Nh3+ 17. Kh1 Ng5 18. f4 Ne6 19. Ne4 b6 20. cxb6 Bb7 21. Kg1 Bxe4 22. Qxe4 Qxb6 23. Bd3 g6 24. f5 Nc5 25. Qxd4 Rad8 26. Qxc5 Qxc5+ 27. Rxc5 Rxd3 28. fxg6 fxg6 29. Rxf8+ Kxf8 30. Rc8+ Kg7 31. Rc7+ Kg8 32. Rc8+ Kg7 33. Rc7+ Kg8 34. Rc8+
Sample game 2 (1/2-1/2)
1. c4 c6 2. h3 Ngf6 3. Bh2 Bc7 4. Bxc7 Nxc7 5. Nb3 a5 6. d4 b5 7. cxb5 a4 8. Nd2 Nxb5 9. e3 a3 10. b3 Nd5 11. Be2 Nb4 12. Nf3 f6 13. O-O d5 14. Re1 g6 15. Bd3 Qd6 16. e4 dxe4 17. Bxe4 f5 18. Bd3 Nxd4 19. Nxd4 e5 20. Nb5 Qxd3 21. Qa1 O-O 22. Rxe5 Qd7 23. Rc4 Ba6 24. Rxb4 Bxb5 25. Ne3 Rad8 26. Rf4 Qd2 27. Re7 Qb2 28. Qe1 Qd2 29. Qa1 Qb2 30. Qe1 Qd2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 126 / 501 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): rqbbnknr/pppppppp/8/8/8/8/PPPPPPPP/NQRNKBBR w CHah - 0 1
Mirror twin: White 836 vs Black 554 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 496.