White 168 vs Black 226
White starts from setup 168 (NBRNBKQR), Black from setup 226 (BNRQKBNR). 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 #168 N B R N B K Q R
King on the f-file, rooks on c, h, queen on the g-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 168 gives White +0.07 (Morozov Balance Index, 400M nodes).
Black: setup #226 B N R Q K B N R
King on the e-file, rooks on c, h, queen on the d-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 226 gives White +0.06 (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 62.
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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±14 cp.
For comparison, in symmetric play setup 168 gives White +0.07 and setup 226 gives White +0.06: 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 f3, and 2 first moves are within 10 cp of it.
Along the engine's main line (8 moves) the evaluation stayed within ±0 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 | +14 | 1. f3 b6 2. Qf2 e6 3. O-O c5 4. e4 d5 |
| S1 | 500 000 | 21 | -4 | 1. f3 b6 2. c4 c5 3. Nb3 Nc6 4. d4 cxd4 |
| S2 | 2 000 000 | 27 | 0 | 1. f3 c5 2. c4 e6 3. d4 b6 4. Nb3 cxd4 |
| S3 | 8 000 000 | 38 | 0 | 1. f3 c5 2. c4 b6 3. d4 e6 4. Nb3 cxd4 |
| S4 | 32 000 000 | 44 | 0 | 1. f3 c5 2. c4 e6 3. Nb3 b6 4. d4 cxd4 |
| S5 | 128 000 000 | 50 | 0 | 1. f3 c5 2. c4 e6 3. d4 Nf6 4. Nb3 cxd4 |
| S6 | 400 000 000 | 53 | 0 | 1. f3 c5 2. c4 e6 3. d4 Nf6 4. Nb3 cxd4 |
| S7 | 800 000 000 | 60 | 0 | 1. f3 c5 2. c4 e6 3. d4 Nf6 4. Nb3 cxd4 |
| S8 | 1 600 000 000 | 62 | 0 | 1. f3 c5 2. c4 e6 3. d4 Nf6 4. Nb3 cxd4 |
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: 0
- Lc0 0.32.1: +4
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 +43, Black +49, difference -6. 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 | 0 | 48 | 1. f3 c5 2. c4 b6 3. d4 e6 4. Nb3 cxd4 5. Qxd4 Nc6 |
| 2 | 0 | 47 | 1. c4 c5 2. f3 b6 3. d4 e6 4. Nb3 cxd4 5. Qxd4 Nc6 |
| 3 | -18 | 47 | 1. d4 d5 2. f3 b6 3. c4 dxc4 4. Rxc4 e6 5. Rc1 Be7 |
Main-line play-out
8 moves, 5 000 000 nodes per half-move. Largest |evaluation| 0 cp, mean 0.0 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f3 | 0 | b6 | 0 |
| 2 | c4 | 0 | c5 | 0 |
| 3 | d4 | 0 | e6 | 0 |
| 4 | Nb3 | 0 | cxd4 | 0 |
| 5 | Qxd4 | 0 | Nc6 | 0 |
| 6 | Qd2 | 0 | Ne5 | 0 |
| 7 | Qd4 | 0 | Nc6 | 0 |
| 8 | Qf2 | 0 | Ne5 | 0 |
| 9 | Qd4 | 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 35.1 moves.
Sample game 1 (1/2-1/2)
1. h4 Nf6 2. f3 c5 3. g4 d5 4. c3 b6 5. Bg3 e6 6. Nf2 Bd6 7. h5 h6 8. Qh2 Bxg3 9. Qxg3 Bb7 10. g5 hxg5 11. Qxg5 Ba6 12. Qxg7 Ke7 13. Qg5 Qg8 14. Qxg8 Rcxg8 15. h6 Rg5 16. Nd3 Rg6 17. h7 Rxh7 18. Rxh7 Nxh7 19. Nxc5 Rh6 20. Ncb3 Ng5 21. Kf2 e5 22. Re1 Nh3+ 23. Kg3 Nf4 24. e3 Rh3+ 25. Kf2 Ne2 26. Kg2 Rg3+ 27. Kf2 Rh3 28. Kg2 Rg3+ 29. Kf2
Sample game 2 (1/2-1/2)
1. f3 c5 2. Qf2 b6 3. c4 Nf6 4. Nc2 g6 5. Nc3 Bg7 6. Rd1 O-O 7. h4 h5 8. d4 cxd4 9. Qxd4 Re8 10. b3 d5 11. Qe3 e6 12. O-O Nfd7 13. Nb5 Bf8 14. Qg5 Qxg5 15. hxg5 a6 16. Nba3 Be7 17. f4 Bc5+ 18. Bf2 Bf8 19. Be1 Bb7 20. Nb4 a5 21. Nbc2 Ba6 22. Kh2 Red8 23. Bf2 a4 24. Bg1 Be7 25. g3 Bf8 26. Rfe1 dxc4 27. Nxc4 Bxc4 28. bxc4 Rxc4 29. Ne3 Rb4 30. Nc2 Rc4 31. Ne3 Rc3 32. Nc2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 168 / 226 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): bnrqkbnr/pppppppp/8/8/8/8/PPPPPPPP/NBRNBKQR w CHch - 0 1
Mirror twin (the same position mirrored): White 797 vs Black 631.