White 106 vs Black 40
White starts from setup 106 (QNRNBBKR), Black from setup 40 (NBNQBRKR). In the encyclopedia since 2026-10-03: 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. 106, Black by position No. 40, 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 #106 Q N R N B B K R
King on the g-file, rooks on c, 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 106 gives White +0.26 (Morozov Balance Index, 400M nodes).
Black: setup #40 N B N Q B R K R
King on the g-file, rooks on f, h, queen on the d-file; no bishop starts in a corner; the knights start away from the centre. The king already stands on a castled square, so one of the castlings moves only the rook. In ordinary symmetric play setup 40 gives White +0.34 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 57.
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 ±14 cp.
For comparison, in symmetric play setup 106 gives White +0.26 and setup 40 gives White +0.34: 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 (30 moves) the largest swing was 58 cp (around move 13), ending at 0 cp — the position stays playable for both sides.
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 | +14 | 1. d4 h5 2. h4 d5 3. b3 c6 4. c4 f6 |
| S1 | 500 000 | 21 | 0 | 1. d4 h5 2. h4 d5 3. b3 c6 4. c4 Nc7 |
| S2 | 2 000 000 | 26 | +1 | 1. d4 h5 2. h4 d5 3. e3 Nd6 4. b3 c6 |
| S3 | 8 000 000 | 33 | +3 | 1. d4 h5 2. h4 d5 3. e3 Nab6 4. b3 Nd7 |
| S4 | 32 000 000 | 35 | +5 | 1. d4 d5 2. e3 c6 3. c4 h5 4. h4 Nab6 |
| S5 | 128 000 000 | 42 | +3 | 1. d4 d5 2. h4 h5 3. e3 c6 4. c4 Nab6 |
| S6 | 400 000 000 | 51 | 0 | 1. d4 d5 2. h4 c6 3. e3 f5 4. c4 Nc7 |
| S7 | 800 000 000 | 55 | 0 | 1. d4 d5 2. h4 c6 3. e3 f5 4. c4 Nc7 |
| S8 | 1 600 000 000 | 54 | 0 | 1. d4 d5 2. h4 c6 3. e3 f5 4. c4 Nc7 |
| S9 | 3 200 000 000 | 57 | 0 | 1. d4 d5 2. e3 c6 3. c4 Nc7 4. h4 f5 |
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: +9
- Lc0 0.32.1: +15
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 +27, Black +52, difference -25. 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 | +7 | 42 | 1. d4 h5 2. h4 d5 3. e3 c6 4. c4 Nab6 5. b3 Nd7 |
| 2 | 0 | 42 | 1. b3 c6 2. d4 f6 3. h4 h5 4. c4 d5 5. cxd5 cxd5 |
| 3 | -16 | 41 | 1. h4 e5 2. d4 e4 3. Bb4 Ne7 4. a4 f5 5. Qa3 Rf7 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 58 cp, mean 19.5 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +1 | h5 | -12 |
| 2 | h4 | -2 | d5 | -1 |
| 3 | e3 | +8 | c6 | +15 |
| 4 | c4 | +13 | Bd7 | +3 |
| 5 | Nd2 | +18 | Nd6 | +13 |
| 6 | cxd5 | +12 | cxd5 | +19 |
| 7 | a4 | +24 | Bg4 | +18 |
| 8 | f3 | +20 | Bf5 | +23 |
| 9 | Nc3 | +18 | Nc7 | +13 |
| 10 | Bg3 | +24 | Rh6 | +19 |
| 11 | b4 | +26 | Re6 | +29 |
| 12 | Bf2 | +18 | Bg6 | +36 |
| 13 | b5 | +49 | Nf5 | +58 |
| 14 | e4 | +42 | dxe4 | +34 |
| 15 | Ndxe4 | +36 | Nd6 | +44 |
| 16 | Ng5 | +43 | Rf6 | +27 |
| 17 | g3 | +32 | Ne6 | +34 |
| 18 | Bg2 | +35 | a6 | +38 |
| 19 | bxa6 | +30 | bxa6 | +32 |
| 20 | Qb2 | +32 | Qa5 | +34 |
| 21 | f4 | +32 | Nf5 | +24 |
| 22 | Nge4 | +37 | Ba7 | +20 |
| 23 | Nd5 | +16 | Rb8 | +15 |
| 24 | Qa2 | +14 | Nexd4 | +12 |
| 25 | Nexf6+ | 0 | gxf6 | 0 |
| 26 | Kh2 | +7 | e6 | +5 |
| 27 | Nxf6+ | 0 | Kg7 | 0 |
| 28 | Nd7 | 0 | Rb4 | +4 |
| 29 | Rc4 | 0 | Rxc4 | 0 |
| 30 | Qxc4 | 0 | Nf3+ | 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 46.4 moves.
Sample game 1 (1/2-1/2)
1. d4 c6 2. c4 h5 3. h4 d5 4. e3 Nab6 5. b3 Nd7 6. Ndc3 e6 7. Nd2 Ne7 8. Nf3 Rh6 9. Bd2 e5 10. cxd5 cxd5 11. e4 Rg6 12. Re1 exd4 13. Nxd5 Ne5 14. Nxe5 Bxe5 15. Bd3 Bc6 16. Nf4 Bxf4 17. Bxf4 Re6 18. Bg5 Re8 19. O-O Qb6 20. f4 Bb5 21. f5 Bxd3 22. fxe6 Bxf1 23. exf7+ Kxf7 24. Rxf1+ Kg8 25. Qd1 Ng6 26. Qxh5 d3+ 27. Kh1 Qc6 28. Qf3 Qxe4 29. Rd1 Nxh4 30. Qxe4 Rxe4 31. Rxd3 Rg4 32. Rd8+ Kf7 33. Rd7+ Ke8 34. Rd8+ Kf7 35. Rd7+ Ke8 36. Rd8+
Sample game 2 (1/2-1/2)
1. d4 h5 2. h4 d5 3. b3 c6 4. c4 f6 5. e3 Bg6 6. cxd5 cxd5 7. Bb4 Nd6 8. Nbc3 Nc7 9. Ne2 Rh6 10. Qb2 Na6 11. Ba3 Nb5 12. Nf4 Nxa3 13. Qxa3 Bf7 14. Bxa6 bxa6 15. Qxa6 Qd7 16. Qc6 Qf5 17. Qc2 Qd7 18. Qd2 e5 19. dxe5 fxe5 20. Nh3 Bc7 21. Ng5 Bd8 22. O-O Rd6 23. f4 exf4 24. Rxf4 Bxg5 25. hxg5 Qe7 26. Nc3 Re8 27. g6 Rxg6 28. Nxd5 Qg5 29. Rc5 Rd6 30. Rd4 Kh8 31. b4 h4 32. a4 h3 33. Nf4 Rxd4 34. Qxd4 Qg3 35. Nxh3 Rxe3 36. Rf5 Rd3 37. Qe4 Re3 38. Qd4 Rd3 39. Qxa7 Bd5 40. Rxd5 Qe1+ 41. Kh2 Qg3+ 42. Kg1 Qe1+ 43. Kh2 Qg3+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 106 / 40 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): nbnqbrkr/pppppppp/8/8/8/8/PPPPPPPP/QNRNBBKR w CHfh - 0 1
Mirror twin: White 853 vs Black 925 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 25.