White 250 vs Black 533
White starts from setup 250 (NRKQBBNR), Black from setup 533 (RNBBKQNR). 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 #250 N R K Q B B N R
King on the c-file, rooks on b, h, queen on the d-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 250 gives White +0.38 (Morozov Balance Index, 400M nodes).
Black: setup #533 R N B B K Q N R
King on the e-file, rooks on a, h, queen on the f-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 533 gives White +0.39 (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 59.
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 250 gives White +0.38 and setup 533 gives White +0.39: 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 ±19 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 | -8 | 1. d4 Nf6 2. Qd3 d5 3. O-O-O e6 4. f3 c5 |
| S1 | 500 000 | 19 | +2 | 1. e4 e5 2. d4 d6 3. f3 Qe7 4. Ne2 c5 |
| S2 | 2 000 000 | 24 | +13 | 1. e4 e5 2. d4 d6 3. Ne2 f5 4. exf5 Qxf5 |
| S3 | 8 000 000 | 28 | -7 | 1. e4 e5 2. d4 d6 3. f3 exd4 4. Qxd4 Nc6 |
| S4 | 32 000 000 | 42 | 0 | 1. e4 e5 2. d4 exd4 3. Qxd4 Nc6 4. Qc3 d6 |
| S5 | 128 000 000 | 45 | 0 | 1. e4 e5 2. d4 exd4 3. Qxd4 Nc6 4. Qc3 Bf6 |
| S6 | 400 000 000 | 52 | 0 | 1. e4 e5 2. d4 exd4 3. Qxd4 Nc6 4. Qc3 Bf6 |
| S7 | 800 000 000 | 53 | 0 | 1. e4 e5 2. d4 exd4 3. Qxd4 Nc6 4. Qc3 Bf6 |
| S8 | 1 600 000 000 | 59 | 0 | 1. e4 e5 2. d4 exd4 3. Qxd4 Nc6 4. Qc3 Bf6 |
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: +4
- Lc0 0.32.1: +12
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 +11, Black +25, difference -14. 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 | 44 | 1. d4 d5 2. f3 f5 3. Nh3 Nf6 4. e3 Qf7 5. Qd2 O-O |
| 2 | -1 | 44 | 1. e4 e5 |
| 3 | -13 | 43 | 1. f4 d5 2. d3 f5 3. Nf3 Nf6 4. e3 e6 5. Be2 Qd6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 19 cp, mean 3.5 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | -11 | e5 | +2 |
| 2 | d4 | +10 | exd4 | -11 |
| 3 | Qxd4 | 0 | Nc6 | 0 |
| 4 | Qc3 | 0 | Bf6 | -8 |
| 5 | Qe3 | +17 | Bd4 | +7 |
| 6 | Qg3 | +7 | f5 | +10 |
| 7 | Nf3 | +11 | f4 | +12 |
| 8 | Qh4 | 0 | Bf6 | 0 |
| 9 | Qh5+ | 0 | g6 | 0 |
| 10 | Qb5 | 0 | d6 | 0 |
| 11 | O-O-O | 0 | Ne7 | 0 |
| 12 | Qb3 | 0 | g5 | 0 |
| 13 | h3 | 0 | Qg7 | 0 |
| 14 | c3 | 0 | h5 | 0 |
| 15 | Nc2 | 0 | a6 | +19 |
| 16 | Nfd4 | +7 | Ne5 | +8 |
| 17 | Ne6 | +11 | Bxe6 | +6 |
| 18 | Qxe6 | +7 | Qf7 | +8 |
| 19 | Qxf7+ | +12 | Kxf7 | +5 |
| 20 | a4 | 0 | Rab8 | 0 |
| 21 | Nb4 | -1 | f3 | 0 |
| 22 | Kc2 | +2 | Rbe8 | 0 |
| 23 | Bd2 | 0 | N7g6 | 0 |
| 24 | Nd5 | 0 | Bd8 | 0 |
| 25 | Ne3 | +8 | fxg2 | 0 |
| 26 | Nxg2 | 0 | Kg7 | 0 |
| 27 | Be3 | +2 | Rhf8 | +5 |
| 28 | Be2 | 0 | h4 | 0 |
| 29 | Rhf1 | 0 | Nf3 | 0 |
| 30 | Bd3 | 0 | Nge5 | 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 37.6 moves.
Sample game 1 (1/2-1/2)
1. e4 d6 2. d4 e5 3. Ne2 Nc6 4. Nb3 f5 5. dxe5 dxe5 6. Nc3 a6 7. Bd3 Be6 8. f4 fxe4 9. Nxe4 Be7 10. Qh5+ g6 11. Qe2 Bxb3 12. axb3 Nd4 13. Qd2 Qxf4 14. Bg3 Qxd2+ 15. Kxd2 Bd6 16. Rbe1 O-O-O 17. Rhf1 Nh6 18. Bh4 Rd7 19. Nf6 Rdd8 20. Ne4 Rd7 21. Nf6 Rg7 22. g4 Rf8 23. Bg3 Rgf7 24. g5 b5 25. Bxe5 Bxe5 26. Rxe5 Ng4 27. Re4 Nxf6 28. Rxd4 c5 29. Rdf4 Ne4+ 30. Rxe4 Rxf1 31. Bxf1 Rxf1 32. Rh4 Rf7 33. Ke3 Kd7 34. Rf4 Rxf4 35. Kxf4 Kd6 36. Ke4 b4 37. c3 a5 38. Kd3 Kd5 39. Ke3 bxc3 40. bxc3 Ke5
Sample game 2 (1/2-1/2)
1. e4 d6 2. d4 e5 3. Ne2 Nc6 4. Nb3 f5 5. dxe5 dxe5 6. Nc3 a6 7. Bd3 Be6 8. f4 fxe4 9. Nxe4 Be7 10. Qh5+ g6 11. Qe2 Bxb3 12. axb3 Nd4 13. Qd2 Qxf4 14. Bg3 Qxd2+ 15. Kxd2 Bd6 16. Rbe1 O-O-O 17. Rhf1 Nh6 18. Bh4 Rd7 19. Nf6 Rdd8 20. Ne4 Rd7 21. Nf6 Rg7 22. g4 Rf8 23. Bg3 Rgf7 24. g5 b5 25. Bxe5 Bxe5 26. Rxe5 Ng4 27. Re4 Nxf6 28. Rxd4 c5 29. Rdf4 Ne4+ 30. Rxe4 Rxf1 31. Bxf1 Rxf1 32. Rh4 Rf7 33. Ke3 Kd7 34. Rf4 Rxf4 35. Kxf4 Kd6 36. Ke4 b4 37. c3 a5 38. Kd3 Kd5 39. Ke3 bxc3 40. bxc3 Ke5
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 250 / 533 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): rnbbkqnr/pppppppp/8/8/8/8/PPPPPPPP/NRKQBBNR w BHah - 0 1
Mirror twin: White 613 vs Black 522 — a different position (castling squares are fixed), not evaluated by the search.