White 186 vs Black 247
White starts from setup 186 (NRNKBBRQ), Black from setup 247 (NRBKQNRB). In the encyclopedia since 2026-09-21: 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. 186, Black by position No. 247, 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 #186 N R N K B B R Q
King on the d-file, rooks on b, g, queen on the h-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 186 gives White +0.23 (Morozov Balance Index, 400M nodes).
Black: setup #247 N R B K Q N R B
King on the d-file, rooks on b, g, queen on the e-file; one 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 247 gives White +0.18 (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 60.
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 -10 and +19 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 186 gives White +0.23 and setup 247 gives White +0.18: 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 g4, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±22 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 | 13 | -10 | 1. f4 f5 2. Bf2 Nb6 3. g4 fxg4 4. e4 d6 |
| S1 | 500 000 | 18 | 0 | 1. f4 d6 2. g4 g5 3. f5 h5 4. e4 e6 |
| S2 | 2 000 000 | 24 | +13 | 1. g4 d6 2. d4 g5 3. Nab3 Nb6 4. e3 Ng6 |
| S3 | 8 000 000 | 28 | +19 | 1. g4 d6 2. e3 g5 3. Nab3 Bd7 4. d4 e5 |
| S4 | 32 000 000 | 33 | +17 | 1. g4 d6 2. e3 Nb6 3. Nab3 g5 4. Ne2 h5 |
| S5 | 128 000 000 | 41 | +4 | 1. Nab3 Nb6 2. g4 d6 3. e3 g5 4. Ne2 e5 |
| S6 | 400 000 000 | 48 | 0 | 1. g4 Nb6 2. e3 d6 3. Nab3 g5 4. d4 e5 |
| S7 | 800 000 000 | 55 | 0 | 1. g4 Nb6 2. e3 d6 3. Nab3 g5 4. d4 e5 |
| S8 | 1 600 000 000 | 56 | 0 | 1. g4 Nb6 2. e3 d6 3. h4 Bd7 4. Nab3 Bc6 |
| S9 | 3 200 000 000 | 60 | 0 | 1. g4 Nb6 2. e3 g5 3. d4 d6 4. Nab3 e5 |
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 | 0 |
| 16 000 000 000 | 0 |
This pair stays within the ±5 cp corridor up to 16 000 000 000 nodes.
Swap the two setups, giving White the black back rank and Black the white one, and the evaluation jumps to +34. The same two armies dealt the other way round are no longer balanced at all: that is how precisely this pair pays for the first move.
Independent engines, run on the same position:
- Berserk 14: +3
- Lc0 0.32.1: 0
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 +11, Black +58, difference -47. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 160 games, 11 White wins, 149 draws, 0 Black wins, White scored 53.4%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | -3 | 44 | 1. g4 d6 2. e3 g5 3. Ne2 Nb6 4. d4 e5 5. Nb3 exd4 |
| 2 | -7 | 44 | 1. e3 d6 2. g4 g5 3. Ne2 Nb6 4. d4 e5 5. Nb3 exd4 |
| 3 | -8 | 44 | 1. Nab3 d6 2. d4 Nb6 3. g4 g5 4. e3 e5 5. Ne2 exd4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 22 cp, mean 7.6 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g4 | +19 | c5 | +5 |
| 2 | f4 | +4 | Nc7 | 0 |
| 3 | c3 | +2 | g6 | -5 |
| 4 | Nc2 | +14 | d6 | +7 |
| 5 | Bf2 | +11 | b6 | 0 |
| 6 | Bg2 | 0 | Bxg4 | 0 |
| 7 | b4 | 0 | Bf5 | 0 |
| 8 | Nd3 | 0 | Nd7 | -6 |
| 9 | Bc6 | -7 | c4 | -5 |
| 10 | Nb2 | 0 | d5 | 0 |
| 11 | Bxd5 | -8 | Nxd5 | -19 |
| 12 | Qxd5 | -17 | Be6 | -20 |
| 13 | Qf3 | -9 | Nf6 | -11 |
| 14 | Ne3 | -10 | Rc8 | -11 |
| 15 | Nexc4 | -13 | Bxc4 | -18 |
| 16 | Nxc4 | -17 | Qa4+ | -15 |
| 17 | Ke1 | -9 | O-O | -11 |
| 18 | Ne5 | -16 | Qxa2 | -15 |
| 19 | Rd1 | -22 | e6 | -19 |
| 20 | Bd4 | -10 | Rc7 | -10 |
| 21 | Kf2 | -4 | Bg7 | -3 |
| 22 | Kg2 | -13 | Qd5 | -11 |
| 23 | Qxd5 | 0 | Nxd5 | +5 |
| 24 | Rgf1 | +12 | f6 | +5 |
| 25 | Nd3 | +6 | Rd7 | +2 |
| 26 | Ra1 | +8 | h6 | +6 |
| 27 | Ra2 | +6 | g5 | +4 |
| 28 | Bg1 | +3 | Rc8 | -1 |
| 29 | h4 | 0 | gxf4 | 0 |
| 30 | Nxf4 | 0 | Nxf4+ | 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 36.1 moves.
Sample game 1 (1/2-1/2)
1. g4 g5 2. Nab3 Nb6 3. e3 d6 4. d4 e5 5. dxe5 Qxe5 6. Nd3 Qe7 7. O-O-O Bd7 8. Na5 c6 9. Kb1 Kc7 10. h3 Ng6 11. Qh2 Na4 12. f4 b6 13. Nb3 gxf4 14. exf4 f5 15. g5 Rge8 16. h4 Bxb2 17. Nxb2 Qxe1 18. Rxe1 Rxe1+ 19. Nd1 Rxd1+ 20. Nc1 Nc3+ 21. Kb2 Na4+ 22. Kb1 Nc3+ 23. Kb2 Na4+
Sample game 2 (1/2-1/2)
1. Nab3 g5 2. h4 g4 3. d4 d6 4. g3 Nb6 5. Bg2 Ne6 6. Bc3 Na4 7. O-O Qb5 8. Nd3 Nxc3 9. bxc3 O-O 10. Nbc5 Qa5 11. Nxe6 Bxe6 12. Bxb7 Qxc3 13. e3 Bg7 14. Nf4 Bxa2 15. Ra1 e5 16. dxe5 dxe5 17. Nd5 Qa3 18. h5 Rxb7 19. Rxa2 Qxa2 20. Ne7+ Kh8 21. Qxb7 Qxc2 22. Ra1 f5 23. Rxa7 f4 24. Qxc7 Qd1+ 25. Kg2 Qf3+ 26. Kg1 Qd1+ 27. Kg2 Qf3+ 28. Kf1 Qh1+ 29. Ke2 Qf3+ 30. Ke1 Qh1+ 31. Ke2 Qxh5 32. Nf5 Bf6 33. Qc5 f3+ 34. Kd2 Rd8+ 35. Nd6 Qh2 36. Kc3 Qxf2 37. Nf7+ Kg8 38. Nh6+ Kh8 39. Nf7+ Kg8 40. Nh6+ Kh8
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 186 / 247 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): nrbkqnrb/pppppppp/8/8/8/8/PPPPPPPP/NRNKBBRQ w BGbg - 0 1
Mirror twin: White 773 vs Black 610 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 42.