White 13 vs Black 220
White starts from setup 13 (QNNBRKBR), Black from setup 220 (NBQRKNBR). 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. 13, Black by position No. 220, 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 #13 Q N N B R K B R
King on the f-file, rooks on e, 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 13 gives White +0.29 (Morozov Balance Index, 400M nodes).
Black: setup #220 N B Q R K N B R
King on the e-file, rooks on d, h, queen on the c-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 220 gives White +0.20 (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 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 -24 and +11 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 13 gives White +0.29 and setup 220 gives White +0.20: 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 h4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±17 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 | 17 | -24 | 1. e4 f6 2. h4 c5 3. Bh2 Bf7 4. Nc3 Ne6 |
| S1 | 500 000 | 20 | -4 | 1. h4 d5 2. Bh2 Nd7 3. e3 c5 4. Bxb8 Qxb8 |
| S2 | 2 000 000 | 25 | +7 | 1. h4 f6 2. Bh2 c5 3. Bxb8 Qxb8 4. e3 Bf7 |
| S3 | 8 000 000 | 32 | +8 | 1. h4 Ne6 2. Bh2 h6 3. b4 Bh7 4. O-O O-O |
| S4 | 32 000 000 | 36 | +6 | 1. h4 d5 2. Bh2 Ne6 3. O-O h6 4. b4 Bh7 |
| S5 | 128 000 000 | 42 | +11 | 1. h4 d5 2. Bh2 Ne6 3. O-O h6 4. b4 Bh7 |
| S6 | 400 000 000 | 48 | 0 | 1. h4 Ne6 2. Bh2 c5 3. Bxb8 Qxb8 4. e3 f6 |
| S7 | 800 000 000 | 52 | 0 | 1. h4 Ne6 2. Bh2 c5 3. Bxb8 Qxb8 4. e3 f6 |
| S8 | 1 600 000 000 | 53 | 0 | 1. h4 Ne6 2. Bh2 c5 3. Bxb8 Qxb8 4. e3 f6 |
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 | -3 |
| 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: -13
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 +39, Black +83, difference -44. 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 | +12 | 40 | 1. h4 f6 2. Bh2 c5 3. Bxb8 Qxb8 4. e3 Ne6 5. b3 Bf7 |
| 2 | -5 | 40 | 1. d4 d5 2. f3 c6 3. Nd2 h5 4. e4 Nb6 5. c3 f6 |
| 3 | -12 | 40 | 1. f3 d5 2. d4 c6 3. Nd2 h5 4. e4 Nb6 5. Bf2 Bf4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 17 cp, mean 4.2 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | h4 | +8 | Ne6 | 0 |
| 2 | b4 | +13 | d5 | +7 |
| 3 | Bh2 | +3 | h6 | +8 |
| 4 | e3 | +17 | Bh7 | +11 |
| 5 | O-O | +10 | O-O | +12 |
| 6 | d4 | +4 | c6 | +5 |
| 7 | Bxb8 | +5 | Qxb8 | +16 |
| 8 | Nd2 | +15 | Nb6 | +17 |
| 9 | Nd3 | +12 | Nc7 | +8 |
| 10 | a4 | +3 | Ne8 | +5 |
| 11 | a5 | +4 | Nd7 | +1 |
| 12 | Be2 | +3 | Nd6 | 0 |
| 13 | Rc1 | 0 | b5 | +10 |
| 14 | axb6 | +9 | axb6 | +13 |
| 15 | Rfd1 | +11 | e6 | +9 |
| 16 | c4 | +15 | b5 | 0 |
| 17 | cxb5 | 0 | Bxd3 | 0 |
| 18 | Bxd3 | 0 | cxb5 | 0 |
| 19 | Nb3 | 0 | Nc4 | 0 |
| 20 | Qc3 | 0 | Nf6 | 0 |
| 21 | Qe1 | 0 | Qc7 | 0 |
| 22 | Ra1 | 0 | Ra8 | 0 |
| 23 | Rdc1 | 0 | h5 | 0 |
| 24 | g3 | 0 | Rfc8 | 0 |
| 25 | Nc5 | 0 | Qd8 | 0 |
| 26 | Qd1 | 0 | Rc7 | 0 |
| 27 | Rxa8 | 0 | Qxa8 | 0 |
| 28 | Ra1 | 0 | Ra7 | 0 |
| 29 | Rxa7 | 0 | Qxa7 | 0 |
| 30 | Qf3 | 0 | Qa1+ | 0 |
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 43.4 moves.
Sample game 1 (1/2-1/2)
1. e3 f6 2. h4 d5 3. Bh2 Bf7 4. d4 Nd7 5. Nd3 c6 6. Bxb8 Qxb8 7. b3 O-O 8. Bg4 Rfe8 9. Nd2 Nab6 10. a4 e5 11. a5 Nc8 12. a6 b5 13. Bxd7 Rxd7 14. dxe5 fxe5 15. f4 exf4 16. exf4 Rde7 17. O-O Qb6+ 18. Kh2 c5 19. Nf3 h6 20. Nde5 Nd6 21. Qd1 d4 22. Nxf7 Nxf7 23. Rxe7 Rxe7 24. Re1 Re6 25. Rxe6 Qxe6 26. Qd3 Qxa6 27. Qe4 Qc8 28. h5 a5 29. Nh4 Qd7 30. Ng6 c4 31. bxc4 bxc4 32. Ne7+ Kf8 33. Ng6+ Kg8 34. Ne7+ Kf8 35. Ng6+
Sample game 2 (1/2-1/2)
1. f4 c5 2. b4 f6 3. Bxc5 Bxf4 4. O-O Ng6 5. e4 Bb8 6. a4 Bf7 7. Nc3 O-O 8. Nd3 Nb6 9. Bh5 Rde8 10. Qd1 d5 11. exd5 Nxd5 12. Nxd5 Bxd5 13. Bxg6 hxg6 14. Nf4 Qc7 15. g3 Bf7 16. Qf3 Qd7 17. Qd3 Qxd3 18. Nxd3 Rc8 19. Bxe7 Rfe8 20. c3 Bc4 21. Rf3 a5 22. Bc5 Rxe1+ 23. Nxe1 Bb3 24. Re3 Bxa4 25. Kf2 g5 26. Nf3 axb4 27. Bxb4 Bc6 28. Bc5 Bd5 29. Bb4 Kh7 30. h4 g4 31. Nd4 Ba7 32. Re7 Rc4 33. Bd6 Bxd4+ 34. cxd4 Rxd4 35. Ke3 Ra4 36. Rc7 Kg8 37. Rc5 Bf3 38. d3 Ra2 39. Bf4 Bc6 40. Bb8 Kf7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 13 / 220 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): nbqrknbr/pppppppp/8/8/8/8/PPPPPPPP/QNNBRKBR w EHdh - 0 1
Mirror twin: White 952 vs Black 652 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 107.