White 112 vs Black 385
White starts from setup 112 (BBNQRNKR), Black from setup 385 (BQRBNNKR). 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 #112 B B N Q R N K R
King on the g-file, rooks on e, h, queen on the d-file; one 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 112 gives White +0.36 (Morozov Balance Index, 400M nodes).
Black: setup #385 B Q R B N N K R
King on the g-file, rooks on c, h, queen on the b-file; one 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 385 gives White +0.14 (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 61.
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 ±13 cp.
For comparison, in symmetric play setup 112 gives White +0.36 and setup 385 gives White +0.14: 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 c4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the largest swing was 35 cp (around move 12), 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 | 16 | -10 | 1. b4 h5 2. h4 b6 3. c4 c5 4. bxc5 Rxc5 |
| S1 | 500 000 | 20 | +3 | 1. h4 h5 2. c4 c5 3. b3 b5 4. Nd3 Nf6 |
| S2 | 2 000 000 | 25 | -1 | 1. h4 h5 2. c4 c5 3. b3 b5 4. Nd3 Nf6 |
| S3 | 8 000 000 | 30 | +9 | 1. c4 c5 2. e4 h5 3. b3 e6 4. h4 b5 |
| S4 | 32 000 000 | 39 | +13 | 1. c4 c5 2. b3 h5 3. e4 e6 4. h4 b5 |
| S5 | 128 000 000 | 43 | 0 | 1. c4 c5 2. e4 e6 3. h4 h5 4. b3 b5 |
| S6 | 400 000 000 | 49 | 0 | 1. c4 c5 2. e4 e6 3. h4 h5 4. b3 b5 |
| S7 | 800 000 000 | 54 | 0 | 1. c4 c5 2. e4 e6 3. h4 h5 4. b3 b5 |
| S8 | 1 600 000 000 | 61 | 0 | 1. c4 c5 2. e4 e6 3. h4 h5 4. b3 b5 |
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: -15
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 +177, Black +163, difference +14. 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 | 0 | 41 | 1. c4 c5 2. e4 h5 3. b3 e6 4. h4 b5 5. Nd3 bxc4 |
| 2 | -12 | 41 | 1. h4 c5 2. c4 h5 3. b3 b5 4. Nd3 bxc4 5. bxc4 Nd6 |
| 3 | -26 | 41 | 1. e4 b5 2. b4 d6 3. d4 c5 4. bxc5 dxc5 5. c3 h5 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 35 cp, mean 12.5 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | +2 | c5 | +10 |
| 2 | b3 | +10 | h5 | +19 |
| 3 | e4 | +9 | e6 | +12 |
| 4 | h4 | +21 | b5 | +8 |
| 5 | Nd3 | +6 | Ng6 | 0 |
| 6 | Ng3 | 0 | Nf6 | 0 |
| 7 | Rh3 | 0 | bxc4 | 0 |
| 8 | bxc4 | -5 | d6 | -8 |
| 9 | Bc2 | -4 | Qb6 | -11 |
| 10 | Bc3 | -7 | Qa6 | -25 |
| 11 | e5 | -25 | Qc6 | -23 |
| 12 | f3 | -35 | Nd7 | -33 |
| 13 | Ba4 | -31 | Qc7 | -29 |
| 14 | f4 | -29 | dxe5 | -30 |
| 15 | Bxd7 | -31 | Qxd7 | -34 |
| 16 | Nxe5 | -28 | Nxe5 | -33 |
| 17 | Bxe5 | -22 | Bf6 | -23 |
| 18 | Nxh5 | -16 | Bxe5 | -10 |
| 19 | Rxe5 | -9 | Qd4+ | -15 |
| 20 | Kh2 | -14 | O-O-O | -13 |
| 21 | d3 | -7 | Kb8 | -10 |
| 22 | Qg1 | -14 | g6 | -12 |
| 23 | Qxd4 | -11 | Rxd4 | -10 |
| 24 | Nf6 | -11 | Rxf4 | -10 |
| 25 | Ne4 | -2 | Rhxh4 | -7 |
| 26 | Rxh4 | -4 | Rxh4+ | 0 |
| 27 | Kg3 | 0 | Rh1 | -2 |
| 28 | Nd6 | 0 | Rd1 | -11 |
| 29 | Nxf7 | 0 | Rxd3+ | 0 |
| 30 | Kh2 | 0 | Rd2 | 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 37.8 moves.
Sample game 1 (1/2-1/2)
1. c4 h5 2. h4 c5 3. b3 b5 4. Nd3 Nf6 5. Ng3 Ng6 6. e4 bxc4 7. bxc4 e5 8. Nf5 d6 9. f3 Ne7 10. Rh3 Bc6 11. f4 Ng4 12. Nf2 Nxf2 13. Kxf2 Ng6 14. Rd3 Nxh4 15. fxe5 Nxf5 16. exf5 Bh4+ 17. g3 Bg5 18. Rxd6 h4 19. Be4 hxg3+ 20. Kg1 Bxe4 21. Rxe4 Rh2 22. Qb3 Rd8 23. Rg4 Qa8 24. Rxd8+ Qxd8 25. Qxg3 Rxd2 26. Rxg5 Rd1+ 27. Kh2 Qd2+ 28. Qg2 Qf4+ 29. Kh3 Rd3+ 30. Rg3 Qxf5+ 31. Kh2 Qf4 32. Kh3 Rxg3+ 33. Qxg3 Qf1+ 34. Qg2 Qxa1 35. Qa8+ Kh7 36. Qe4+ Kg8 37. Qa8+ Kh7 38. Qe4+ Kh8 39. Qa8+
Sample game 2 (1/2-1/2)
1. c4 h5 2. h4 c5 3. b3 b5 4. Nd3 Nf6 5. Ng3 Ng6 6. e4 bxc4 7. bxc4 e5 8. Nf5 d6 9. f3 Ne7 10. Rh3 Bc6 11. f4 Ng4 12. Nf2 Nxf2 13. Kxf2 Ng6 14. Rd3 Nxh4 15. fxe5 Nxf5 16. exf5 Bh4+ 17. g3 Bg5 18. Rxd6 h4 19. Be4 hxg3+ 20. Kg1 Bxe4 21. Rxe4 Rh2 22. Qb3 Rd8 23. Rg4 Qa8 24. Rxd8+ Qxd8 25. Qxg3 Rxd2 26. Rxg5 Rd1+ 27. Kh2 Qd2+ 28. Qg2 Qf4+ 29. Kh3 Rd3+ 30. Rg3 Qxf5+ 31. Kh2 Qf4 32. Kh3 Rxg3+ 33. Qxg3 Qf1+ 34. Qg2 Qxa1 35. Qa8+ Kh7 36. Qe4+ Kg8 37. Qa8+ Kh7 38. Qe4+ Kh8 39. Qa8+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 112 / 385 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): bqrbnnkr/pppppppp/8/8/8/8/PPPPPPPP/BBNQRNKR w EHch - 0 1
Mirror twin (the same position mirrored): White 847 vs Black 763.
Current place in the live balance rating: 119.