White 108 vs Black 156
White starts from setup 108 (QBNRNKBR), Black from setup 156 (NBRNQKBR). 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. 108, Black by position No. 156, 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 #108 Q B N R N K B R
King on the f-file, rooks on d, 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 108 gives White +0.14 (Morozov Balance Index, 400M nodes).
Black: setup #156 N B R N Q K B R
King on the f-file, rooks on c, h, queen on the e-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 156 gives White +0.10 (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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±13 cp.
For comparison, in symmetric play setup 108 gives White +0.14 and setup 156 gives White +0.10: 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 d4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the evaluation stayed within ±25 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 | 12 | +7 | 1. d4 f6 2. h4 c5 3. dxc5 Rxc5 4. c3 Rc8 |
| S1 | 500 000 | 19 | +3 | 1. d4 f6 2. f3 Bf7 3. Bf2 c6 4. c3 O-O |
| S2 | 2 000 000 | 25 | +11 | 1. d4 f6 2. f3 Bf7 3. c3 O-O 4. Bf2 e5 |
| S3 | 8 000 000 | 33 | +8 | 1. d4 f6 2. f3 d5 3. c3 c6 4. e4 Nb6 |
| S4 | 32 000 000 | 35 | -1 | 1. d4 f6 2. f3 c6 3. c3 Nb6 4. e4 d5 |
| S5 | 128 000 000 | 42 | +13 | 1. d4 c6 2. f3 d5 3. c3 Nb6 4. e4 f6 |
| S6 | 400 000 000 | 51 | 0 | 1. d4 d5 2. h3 c6 3. Nf3 c5 4. dxc5 f6 |
| S7 | 800 000 000 | 51 | 0 | 1. d4 d5 2. h3 c6 3. Nf3 c5 4. dxc5 f6 |
| S8 | 1 600 000 000 | 53 | 0 | 1. d4 d5 2. h3 c6 3. Nf3 c5 4. dxc5 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 | 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: 0
- Lc0 0.32.1: +7
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 +47, Black +63, difference -16. 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 | +15 | 43 | 1. d4 f6 2. f3 c6 3. c3 Nb6 4. e4 d5 5. Ne2 Bf7 |
| 2 | -7 | 43 | 1. b3 c5 2. e4 f6 3. Ne2 d5 4. exd5 b5 5. c4 bxc4 |
| 3 | -8 | 42 | 1. e4 c5 2. b3 f6 3. Ne2 d5 4. exd5 b5 5. c4 bxc4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 25 cp, mean 6.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | +2 | f6 | +9 |
| 2 | f3 | +21 | c6 | +16 |
| 3 | c3 | +10 | d5 | +14 |
| 4 | e4 | +17 | h5 | +13 |
| 5 | Be3 | +17 | h4 | +21 |
| 6 | Ne2 | +15 | Nb6 | +16 |
| 7 | O-O | +15 | Bh7 | +15 |
| 8 | exd5 | +22 | Nc4 | +12 |
| 9 | Bc1 | +21 | cxd5 | +25 |
| 10 | Bxh7 | +21 | Rxh7 | +20 |
| 11 | Qb1 | +16 | Kg8 | +20 |
| 12 | Nd3 | +13 | Ne6 | +13 |
| 13 | Qc2 | +21 | Qg6 | +11 |
| 14 | b3 | 0 | Nd6 | 0 |
| 15 | Nef4 | 0 | Nxf4 | 0 |
| 16 | Bxf4 | 0 | Qf5 | 0 |
| 17 | h3 | 0 | Bc7 | 0 |
| 18 | Rc1 | 0 | Bb6 | 0 |
| 19 | Kh1 | 0 | Nb5 | 0 |
| 20 | Qd2 | 0 | Ba5 | 0 |
| 21 | b4 | 0 | Bc7 | 0 |
| 22 | Rfe1 | 0 | Bxf4 | 0 |
| 23 | Nxf4 | 0 | Nd6 | 0 |
| 24 | Rxe7 | 0 | g5 | 0 |
| 25 | Rxh7 | 0 | Kxh7 | 0 |
| 26 | Nd3 | 0 | Re8 | 0 |
| 27 | Re1 | 0 | Rxe1+ | 0 |
| 28 | Qxe1 | 0 | Qxd3 | 0 |
| 29 | Qe7+ | 0 | Kg6 | 0 |
| 30 | Qxd6 | 0 | Qxc3 | 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 40.6 moves.
Sample game 1 (1/2-1/2)
1. f3 c5 2. c4 f6 3. b3 d5 4. cxd5 Bxd5 5. Bf2 e5 6. Bd3 Bf7 7. Qb1 Ne6 8. a4 h5 9. O-O Nb6 10. a5 Nd5 11. Bc4 Qc6 12. Ned3 h4 13. e4 Ndc7 14. Ne2 h3 15. g3 b5 16. axb6 axb6 17. Rc1 O-O 18. b4 Ng5 19. Bxf7+ Rxf7 20. Be3 Nce6 21. bxc5 bxc5 22. Nxc5 Ba7 23. Nxe6 Qxe6 24. Rxc8+ Qxc8 25. Kf2 Bxe3+ 26. dxe3 Kh7 27. Rc1 Qa8 28. Qd3 Qa7 29. g4 Rd7 30. Qc2 Qa5 31. Rd1 Rc7 32. Qd2 Qa4 33. Qd5 Rc2 34. Rd2 Qa1 35. Rxc2 Qh1 36. Rc8 Qg2+ 37. Ke1 Nxf3+ 38. Kd1 Qf1+ 39. Kc2 Qxe2+ 40. Kb1 Qf1+
Sample game 2 (1/2-1/2)
1. d4 c6 2. a4 f6 3. f3 h5 4. h4 Bh7 5. Bf2 d5 6. a5 O-O 7. O-O b6 8. Ned3 Nf7 9. Qa2 Nc7 10. c4 e5 11. dxe5 fxe5 12. axb6 axb6 13. cxd5 cxd5 14. Bxb6 Qe7 15. Bc5 Qxh4 16. e4 dxe4 17. Bxf8 exd3 18. Bc5 e4 19. Bf2 Qg5 20. Qc4 Re8 21. fxe4 Bxe4 22. Qxf7+ Kxf7 23. Bh4+ Qf5 24. Nxd3 g6 25. Nc5 Bxb1 26. Rxb1 Nd5 27. Rxf5+ gxf5 28. Bf2 Re2 29. Nd3 Rd2 30. Ne1 f4 31. Nf3 Rc2 32. Ne1 Rd2 33. Nf3 Rc2 34. Ne1
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 108 / 156 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): nbrnqkbr/pppppppp/8/8/8/8/PPPPPPPP/QBNRNKBR w DHch - 0 1
Mirror twin: White 860 vs Black 812 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 438.