White 202 vs Black 931
White starts from setup 202 (QNRKBBNR), Black from setup 931 (BRKRNQNB). In the encyclopedia since 2026-10-15: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #202 Q N R K B B N R
King on the d-file, rooks on c, h, queen on the a-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 202 gives White +0.30 (Morozov Balance Index, 400M nodes).
Black: setup #931 B R K R N Q N B
King on the c-file, rooks on b, d, queen on the f-file; one bishop starts in a corner; the knights start on central files. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 931 gives White +0.27 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±2 centipawns of equality, 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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±7 cp.
For comparison, in symmetric play setup 202 gives White +0.30 and setup 931 gives White +0.27: 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 (23 moves) the evaluation stayed within ±25 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 | +5 | 1. a4 g6 2. Qa3 Nd6 3. e3 e5 4. f3 b6 |
| S1 | 500 000 | 19 | +3 | 1. a4 g6 2. e3 c5 3. Na3 b6 4. f3 f5 |
| S2 | 2 000 000 | 23 | +7 | 1. a4 g6 2. e3 c5 3. d4 cxd4 4. exd4 Bxd4 |
| S3 | 8 000 000 | 28 | +7 | 1. d4 g6 2. e3 Ngf6 3. a4 Qh6 4. Qa3 Nd6 |
| S4 | 32 000 000 | 33 | +5 | 1. e3 e5 2. a4 g6 3. Qa3 Qxa3 4. Nxa3 b6 |
| S5 | 128 000 000 | 41 | 0 | 1. d4 g6 2. e3 Ngf6 3. a4 Nd6 4. Qa3 Qh6 |
| S6 | 400 000 000 | 47 | 0 | 1. d4 g6 2. e3 Ngf6 3. a4 Nd6 4. Qa3 Qh6 |
| S7 | 800 000 000 | 49 | -1 | 1. a4 e5 2. Qa3 Qxa3 3. Nxa3 Ne7 4. f3 b6 |
| S8 | 1 600 000 000 | 54 | +2 | 1. a4 e5 2. Qa3 Qxa3 3. Nxa3 g6 4. Nh3 Ne7 |
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 0, Black +39, difference -39. 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 | -4 | 40 | 1. d4 g6 2. e3 c5 3. Nf3 Nc7 4. dxc5 Nf6 5. Bd3 Qh6 |
| 2 | -7 | 40 | 1. a4 e5 2. Qa3 Qxa3 3. Nxa3 Ne7 4. f3 b6 5. e3 g6 |
| 3 | -24 | 39 | 1. f3 d5 2. a4 b6 3. e3 e5 4. Bh4 Ne7 5. Ba6+ Bb7 |
Main-line play-out
23 moves, 5 000 000 nodes per half-move. Largest |evaluation| 25 cp, mean 5.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +3 | g6 | +5 |
| 2 | e3 | -6 | c5 | -8 |
| 3 | dxc5 | +6 | Ngf6 | -19 |
| 4 | Nf3 | -13 | Ne4 | -19 |
| 5 | a4 | -11 | b6 | -21 |
| 6 | Ba6+ | -25 | Bb7 | -14 |
| 7 | Bxb7+ | -19 | Rxb7 | -13 |
| 8 | cxb6 | -11 | Rxb6 | -11 |
| 9 | Qa2 | -7 | d5 | -14 |
| 10 | b4 | -12 | Nc7 | -13 |
| 11 | c3 | -9 | Qe8 | -9 |
| 12 | Nfd2 | +11 | Ra6 | 0 |
| 13 | a5 | 0 | Qb5 | 0 |
| 14 | f3 | 0 | Nxd2 | 0 |
| 15 | Bxd2 | 0 | Rc6 | 0 |
| 16 | Ke1 | 0 | O-O | 0 |
| 17 | Kf2 | 0 | Rc8 | 0 |
| 18 | Na3 | 0 | Qa4 | 0 |
| 19 | Rc2 | 0 | a6 | 0 |
| 20 | Rhc1 | 0 | Ne8 | 0 |
| 21 | Nb1 | 0 | Qb5 | 0 |
| 22 | Na3 | 0 | Qa4 | 0 |
| 23 | Nb1 | 0 | Qb5 | 0 |
| 24 | Na3 | 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 44.4 moves.
Sample game 1 (1/2-1/2)
1. e3 g6 2. d4 e5 3. dxe5 b5 4. a4 b4 5. c3 Bxe5 6. Ba6+ Bb7 7. Bxb7+ Rxb7 8. Nf3 Qd6+ 9. Bd2 bxc3 10. Nxc3 Bxc3 11. Rxc3 Qa6 12. Rc1 Qd3 13. Qa2 Ngf6 14. Ne1 Qd5 15. Qxd5 Nxd5 16. Nd3 f5 17. f3 Nef6 18. g4 fxg4 19. e4 Ne7 20. Bg5 O-O 21. O-O gxf3 22. Nc5 Rxb2 23. Rxf3 Ng4 24. Rxf8+ Kxf8 25. Nxd7+ Kf7 26. h3 h6 27. hxg4 hxg5 28. Rxc7 a5 29. Ra7 Re2 30. Ne5+ Kf6 31. Nd7+ Kf7 32. Nc5 Rc2 33. Rxa5 Nc6 34. Rb5 Nd4 35. Rb7+ Ke8 36. Nd3 Ra2 37. Ra7 Nf3+ 38. Kf1 Nh2+ 39. Kg1 Nf3+ 40. Kf1 Nh2+
Sample game 2 (1/2-1/2)
1. d4 e5 2. dxe5 b5 3. O-O-O g5 4. e3 Bxe5 5. Nf3 Bh8 6. Nxg5 Qe7 7. h4 h6 8. Nh3 c5 9. Ba5 Nc7 10. a3 Nf6 11. Nc3 d5 12. Bd3 O-O 13. Ne2 Ng4 14. Bf5 Nxf2 15. Nxf2 Qxe3+ 16. Bd2 Qxf2 17. Nf4 c4 18. c3 Be5 19. Rhf1 Qb6 20. Qb1 d4 21. cxd4 Qxd4 22. Qc2 b4 23. axb4 a5 24. Rde1 axb4 25. Be3 Qd6 26. Qxc4 Rfe8 27. Nd3 Ne6 28. Qg4+ Ng7 29. Nxe5 h5 30. Qd4 Qxe5 31. Qxe5 Rxe5 32. Bf4 Rc5+ 33. Kb1 Rd8 34. Bg5 Rb8 35. Bf4 Rd8 36. Bg5 Rb8
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 202 / 931 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): brkrnqnb/pppppppp/8/8/8/8/PPPPPPPP/QNRKBBNR w CHbd - 0 1
Mirror twin: White 661 vs Black 19 — a different position (castling squares are fixed), not evaluated by the search.