White 102 vs Black 401
White starts from setup 102 (QNBRNBKR), Black from setup 401 (BRQBNNKR). In the encyclopedia since 2026-11-01: 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. 102, Black by position No. 401, 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 #102 Q N B R N B K R
King on the g-file, rooks on d, h, queen on the a-file; no 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 102 gives White 0.00 (Morozov Balance Index, 400M nodes).
Black: setup #401 B R Q B N N K R
King on the g-file, rooks on b, h, queen on the c-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 401 gives White -0.07 (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 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 same corridor is required at every deeper budget (8 G, 16 G) at which the pair has been evaluated.
The shallow rungs wandered between -15 and +23 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 102 gives White 0.00 and setup 401 gives White -0.07: 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 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 | 15 | -15 | 1. c4 c5 2. h4 h5 3. e3 a6 4. Nc3 Ng6 |
| S1 | 500 000 | 21 | -4 | 1. c4 c5 2. e3 h5 3. h4 Ng6 4. Nc3 a6 |
| S2 | 2 000 000 | 23 | -9 | 1. c4 h5 2. h4 c5 3. e3 Ng6 4. Nc3 e6 |
| S3 | 8 000 000 | 28 | +10 | 1. c4 c5 2. e3 Ng6 3. b3 a6 4. Nc3 e6 |
| S4 | 32 000 000 | 33 | +23 | 1. c4 c5 2. e3 e6 3. b3 a6 4. Nc3 h5 |
| S5 | 128 000 000 | 38 | +12 | 1. c4 a6 2. d4 h5 3. h4 Ng6 4. b3 b5 |
| S6 | 400 000 000 | 44 | 0 | 1. c4 a6 2. d4 Ng6 3. h4 h5 4. Nc3 b5 |
| S7 | 800 000 000 | 46 | +2 | 1. c4 c5 2. e3 e6 3. Nc3 Ng6 4. d4 cxd4 |
| S8 | 1 600 000 000 | 53 | 0 | 1. c4 a6 2. d4 Ng6 3. b4 e6 4. Nc3 d6 |
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 | +2 |
| 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: +9
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 +81, Black +119, difference -38. 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 | +17 | 41 | 1. c4 c5 2. e3 a6 3. Nc3 Ng6 4. a4 e6 5. d4 cxd4 |
| 2 | -3 | 41 | 1. a4 c5 2. c4 e5 3. e3 Ne6 4. Nc2 O-O 5. Nc3 Nf6 |
| 3 | -31 | 41 | 1. d4 b5 2. a4 b4 3. c3 a5 4. h4 h5 5. cxb4 axb4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 24 cp, mean 5.8 cp, final -2 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | +12 | c5 | +8 |
| 2 | e3 | +4 | e6 | +11 |
| 3 | d4 | -2 | cxd4 | -6 |
| 4 | exd4 | 0 | Ng6 | 0 |
| 5 | Nc3 | +3 | a6 | +16 |
| 6 | a4 | +24 | b6 | +20 |
| 7 | Qb1 | +16 | O-O | +19 |
| 8 | h4 | +18 | Bxh4 | +19 |
| 9 | Qd3 | +18 | h6 | +11 |
| 10 | Qh3 | +17 | Qd8 | +18 |
| 11 | Nd3 | +16 | Bg5 | +11 |
| 12 | f4 | +9 | Be7 | +9 |
| 13 | Ne5 | 0 | Nxe5 | -3 |
| 14 | fxe5 | -2 | Bg5 | -15 |
| 15 | Qg3 | 0 | f5 | 0 |
| 16 | Bd3 | 0 | d6 | +7 |
| 17 | d5 | +5 | Bxc1 | +2 |
| 18 | Rxc1 | 0 | dxe5 | +2 |
| 19 | Qxe5 | 0 | exd5 | 0 |
| 20 | Nxd5 | +6 | Qd6 | +2 |
| 21 | Ne7+ | 0 | Kf7 | 0 |
| 22 | Qxd6 | -1 | Nxd6 | 0 |
| 23 | Nxf5 | 0 | Nxf5 | 0 |
| 24 | Bxf5 | 0 | g6 | 0 |
| 25 | Bd3 | 0 | Kg7 | 0 |
| 26 | Rh3 | -2 | a5 | 0 |
| 27 | Re1 | -2 | h5 | -6 |
| 28 | Re7+ | 0 | Rf7 | 0 |
| 29 | Re6 | 0 | Rf6 | 0 |
| 30 | Re7+ | -7 | Kh6 | -2 |
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 43.0 moves.
Sample game 1 (1/2-1/2)
1. c4 b5 2. cxb5 Rxb5 3. d4 c5 4. e4 Rb8 5. d5 Nf6 6. Nc3 Ng6 7. h4 h5 8. Bg5 Ng4 9. Qc1 c4 10. Nc2 Bb6 11. Be3 O-O 12. Bxb6 Rxb6 13. Be2 N6e5 14. Ne3 e6 15. Rh3 Qb8 16. Rg3 f5 17. exf5 exf5 18. Nxc4 Nxc4 19. Bxc4 Rxb2 20. Ne2 Qb6 21. Rf3 a5 22. Rf1 Qf6 23. Nf4 Rc8 24. Nxh5 Qe5 25. Ng3 Rb4 26. Rf4 Bb7 27. a3 Rcxc4 28. Rxc4 Qxd5 29. Rc8+ Kh7 30. f3 Qd4+ 31. Kh1 Ne3 32. axb4 Nxf1 33. Nxf1 Bxc8 34. bxa5 Ba6 35. Nh2 Qxh4 36. Qb1 Kg8 37. Qa2+ Kh7 38. Qb1 Kg8 39. Qd1 Qc4 40. Qd2 Kh7
Sample game 2 (1/2-1/2)
1. c4 h5 2. e3 c5 3. h4 Ng6 4. Nc3 e6 5. Qb1 Nd6 6. d4 cxd4 7. Rxd4 Nf5 8. Rd1 b6 9. e4 Nh6 10. Be2 Ng4 11. Bg5 f6 12. Bc1 a6 13. a4 O-O 14. Bxg4 hxg4 15. h5 Ne5 16. Bf4 Bc7 17. b3 Nf7 18. Nd3 b5 19. axb5 axb5 20. Nxb5 e5 21. Be3 Bxe4 22. h6 g6 23. Qb2 d6 24. h7+ Kh8 25. Qe2 f5 26. f3 Bxd3 27. Qxd3 gxf3 28. gxf3 Bb6 29. Nxd6 Nxd6 30. Bxb6 Rxb6 31. Qe3 Nxc4 32. bxc4 Qc7 33. Rh2 Rfb8 34. Rhd2 f4 35. Qe4 Qe7 36. Rh2 Re6 37. Qd5 Reb6 38. Qe4 Re8 39. Kh1 Ra6 40. Rg1 Rd8 41. Rh6 Qg7 42. Rh5 Qf6 43. Rh6 Qg7 44. Rh5 Re6 45. c5 Qf6 46. Rh6
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 102 / 401 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): brqbnnkr/pppppppp/8/8/8/8/PPPPPPPP/QNBRNBKR w DHbh - 0 1
Mirror twin: White 854 vs Black 747 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 417.