White 162 vs Black 241
White starts from setup 162 (BNRNKBQR), Black from setup 241 (BNRBKQNR). 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 #162 B N R N K B Q R
King on the e-file, rooks on c, h, queen on the g-file; one 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 162 gives White +0.25 (Morozov Balance Index, 400M nodes).
Black: setup #241 B N R B K Q N R
King on the e-file, rooks on c, h, queen on the f-file; one 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 241 gives White +0.22 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±1 centipawns of equality, reaching search depth 61.
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 -23 and +7 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 162 gives White +0.25 and setup 241 gives White +0.22: 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 Nbc3, and 3 first moves are within 10 cp of it.
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 | 15 | -23 | 1. g3 Nc6 2. f4 e6 3. Bg2 Bf6 4. Bxc6 bxc6 |
| S1 | 500 000 | 21 | +2 | 1. g4 e6 2. h4 Nc6 3. Bg2 b6 4. b3 Be7 |
| S2 | 2 000 000 | 24 | -1 | 1. f3 b6 2. e4 e6 3. Ne3 Bf6 4. O-O-O Nc6 |
| S3 | 8 000 000 | 28 | +4 | 1. g4 e6 2. h4 h5 3. g5 c5 4. b3 d5 |
| S4 | 32 000 000 | 36 | +7 | 1. e4 b6 2. Nbc3 e6 3. Ne3 Bf6 4. f3 O-O-O |
| S5 | 128 000 000 | 44 | 0 | 1. e4 b6 2. Nbc3 e6 3. Ne3 Bf6 4. f3 O-O-O |
| S6 | 400 000 000 | 51 | +1 | 1. e4 b6 2. Nbc3 e6 3. Ne3 Bf6 4. f3 O-O-O |
| S7 | 800 000 000 | 59 | 0 | 1. e4 b6 2. Nbc3 e6 3. Ne3 Bf6 4. f3 O-O-O |
| S8 | 1 600 000 000 | 61 | 0 | 1. e4 b6 2. Nbc3 e6 3. Ne3 Bf6 4. f3 O-O-O |
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: +6
- Lc0 0.32.1: +3
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 0, Black +43, difference -43. 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 | 43 | 1. Nbc3 |
| 2 | 0 | 43 | 1. e4 b6 2. Nbc3 e6 3. Ne3 Bf6 4. f3 O-O-O 5. O-O-O Nc6 |
| 3 | -8 | 42 | 1. f3 b6 2. e4 f5 3. exf5 Nh6 4. Ne3 Nxf5 5. O-O-O e6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 24 cp, mean 7.2 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f3 | +14 | b6 | -20 |
| 2 | Nf2 | -7 | e6 | -17 |
| 3 | O-O-O | -12 | h5 | -20 |
| 4 | Nc3 | -15 | d5 | -23 |
| 5 | Kb1 | -15 | Nc6 | -18 |
| 6 | d4 | -17 | Bf6 | -22 |
| 7 | e4 | -24 | O-O-O | -12 |
| 8 | e5 | -19 | Be7 | -13 |
| 9 | b3 | -15 | f6 | -12 |
| 10 | exf6 | -10 | Qxf6 | -10 |
| 11 | h4 | -7 | Kb8 | +4 |
| 12 | Nd3 | +6 | Nh6 | 0 |
| 13 | Ne2 | -12 | Nf5 | -7 |
| 14 | g3 | -11 | a5 | -11 |
| 15 | Bh3 | -8 | Bb7 | -6 |
| 16 | a4 | -10 | g5 | -8 |
| 17 | hxg5 | -5 | Qxg5 | -7 |
| 18 | Nef4 | 0 | Rdg8 | -2 |
| 19 | Nxe6 | -2 | Qf6 | -2 |
| 20 | Bxf5 | -1 | Qxf5 | -2 |
| 21 | Nef4 | -2 | Nb4 | 0 |
| 22 | g4 | -2 | Nxd3 | -2 |
| 23 | Nxd3 | 0 | Qxf3 | 0 |
| 24 | Ne5 | 0 | Qe4 | 0 |
| 25 | Re1 | 0 | Qh7 | 0 |
| 26 | Bc3 | 0 | Bd6 | 0 |
| 27 | g5 | 0 | Bc8 | 0 |
| 28 | g6 | 0 | Qg7 | 0 |
| 29 | Nf7 | 0 | Bf5 | 0 |
| 30 | Nxh8 | 0 | Rxh8 | 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 35.1 moves.
Sample game 1 (1/2-1/2)
1. g4 c5 2. Bg2 e6 3. c4 h5 4. h3 Ne7 5. b3 Nbc6 6. Ndc3 a6 7. f4 b6 8. O-O-O Bc7 9. e3 O-O-O 10. Na3 d5 11. d3 Nb4 12. Nc2 Nxc2 13. Kxc2 Kb8 14. Kb1 f6 15. Bb2 Bb7 16. f5 Qf7 17. Qf2 Bc6 18. fxe6 Qxe6 19. Nxd5 Nxd5 20. cxd5 Bxd5 21. Bxd5 Qxd5 22. Qf5 hxg4 23. Qxg4 Rd7 24. h4 a5 25. h5 Re7 26. d4 cxd4 27. Bxd4 Qb5 28. Qf3 Rd7 29. Kb2 a4 30. Rc1 Be5 31. Qc6 Qxc6 32. Rxc6 Bxd4+ 33. exd4 Kb7 34. Re6 axb3 35. Kxb3 Rxd4 36. Re7+ Ka6 37. Rxg7 Rh6 38. Rg3 Kb5 39. Kc3 Rc4+ 40. Kb3 Rb4+
Sample game 2 (1/2-1/2)
1. g4 e6 2. b3 c5 3. c4 b6 4. Bg2 Nc6 5. Nbc3 h5 6. h3 Nge7 7. Nb5 Ng6 8. Qh2 e5 9. gxh5 Rxh5 10. Ne3 Nh4 11. Bd5 a6 12. Nc3 f5 13. Ng2 g5 14. Nxh4 Rxh4 15. Qg2 d6 16. a3 Kd7 17. Rb1 Bf6 18. d3 Qh8 19. Kd2 b5 20. cxb5 axb5 21. Nxb5 e4 22. Bxf6 Qxf6 23. dxe4 Nd4 24. Nc3 fxe4 25. e3 Qf5 26. Bxa8 Rxa8 27. exd4 cxd4 28. Nxe4 Rxe4 29. Rbe1 Qa5+ 30. b4 Qxa3 31. Qxe4 Qxb4+ 32. Ke2 Re8 33. Qxe8+ Kxe8 34. Rd1 Qc4+ 35. Kf3 Kd7 36. Kg4 Qd5 37. f4 Qg2+ 38. Kf5 Qd5+ 39. Kg4 gxf4 40. h4 f3
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 162 / 241 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): bnrbkqnr/pppppppp/8/8/8/8/PPPPPPPP/BNRNKBQR w CHch - 0 1
Mirror twin (the same position mirrored): White 791 vs Black 619.
Current place in the live balance rating: 370.