White 150 vs Black 104
White starts from setup 150 (NRBNQBKR), Black from setup 104 (QBNRBNKR). 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 #150 N R B N Q B K R
King on the g-file, rooks on b, h, queen on the e-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 150 gives White +0.30 (Morozov Balance Index, 400M nodes).
Black: setup #104 Q B N R B N K R
King on the g-file, rooks on d, 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 104 gives White +0.24 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±2 centipawns of equality, reaching search depth 56.
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 ±12 cp.
For comparison, in symmetric play setup 150 gives White +0.30 and setup 104 gives White +0.24: 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 e4; the alternatives are slightly weaker but keep the game level.
Along the engine's main line (30 moves) the largest swing was 71 cp (around move 10), ending at -19 cp — the position stays playable for both sides.
Engine self-play agrees: 10 games, White won 1, drawn 9, Black won 0 (White scored 55.0%).
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 | -12 | 1. h4 h5 2. e4 e5 3. Nb3 Ne7 4. Nc3 Ne6 |
| S1 | 500 000 | 20 | -3 | 1. e4 d5 2. exd5 h5 3. h4 c6 4. dxc6 Rh6 |
| S2 | 2 000 000 | 23 | 0 | 1. e4 d5 2. exd5 b6 3. b4 h5 4. h4 c6 |
| S3 | 8 000 000 | 30 | 0 | 1. e4 d5 2. exd5 h5 3. h4 c6 4. dxc6 Bxc6 |
| S4 | 32 000 000 | 40 | 0 | 1. e4 d5 2. exd5 h5 3. h4 c6 4. dxc6 Bxc6 |
| S5 | 128 000 000 | 45 | 0 | 1. e4 d5 2. exd5 e6 3. dxe6 Nxe6 4. b4 a5 |
| S6 | 400 000 000 | 48 | +2 | 1. e4 d5 2. exd5 e6 3. dxe6 Nxe6 4. b4 a5 |
| S7 | 800 000 000 | 50 | 0 | 1. e4 e5 2. b4 c6 3. d4 f6 4. dxe5 Bxe5 |
| S8 | 1 600 000 000 | 56 | 0 | 1. e4 e5 2. b4 c6 3. d4 f6 4. Nb3 Ng6 |
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: +2
- Lc0 0.32.1: +13
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 +42, Black +91, difference -49. A balanced pair needs White's setup to be weaker by about the price of the first move.
Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | +12 | 42 | 1. e4 d5 2. exd5 b6 3. c4 c6 4. Nc3 cxd5 5. Nxd5 Bc6 |
| 2 | -12 | 42 | 1. b4 d5 2. Nb3 b6 3. g3 e5 4. Bg2 c6 5. e4 Ne6 |
| 3 | -25 | 41 | 1. d3 e5 2. g3 Ne6 3. e4 c6 4. b4 d5 5. Bh3 Nd4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 71 cp, mean 42.6 cp, final -19 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | h4 | +1 | d5 | -39 |
| 2 | b4 | -45 | b6 | -50 |
| 3 | Bb2 | -36 | f6 | -41 |
| 4 | d3 | -38 | Nd6 | -44 |
| 5 | g3 | -42 | e5 | -45 |
| 6 | Nb3 | -52 | c6 | -39 |
| 7 | Ne3 | -43 | Qb7 | -46 |
| 8 | c4 | -46 | Qf7 | -45 |
| 9 | c5 | -47 | Nc8 | -54 |
| 10 | h5 | -64 | h6 | -71 |
| 11 | Ng2 | -57 | d4 | -54 |
| 12 | e4 | -63 | dxe3 | -49 |
| 13 | Nxe3 | -49 | Ne6 | -57 |
| 14 | d4 | -52 | Ng5 | -50 |
| 15 | Bc4 | -48 | Qxc4 | -45 |
| 16 | Nxc4 | -49 | Nf3+ | -58 |
| 17 | Kf1 | -48 | Nxe1 | -46 |
| 18 | Rxe1 | -43 | Bf7 | -43 |
| 19 | Ne3 | -43 | e4 | -40 |
| 20 | Nd2 | -37 | Bxa2 | -41 |
| 21 | Nxe4 | -34 | Ne7 | -34 |
| 22 | f3 | -37 | O-O | -37 |
| 23 | Kf2 | -38 | Bb3 | -35 |
| 24 | Nd2 | -34 | Bf7 | -40 |
| 25 | Ra1 | -46 | Nd5 | -54 |
| 26 | Nxd5 | -41 | Rxd5 | -32 |
| 27 | Ra6 | -35 | Rc8 | -41 |
| 28 | Bc3 | -31 | Bxh5 | -28 |
| 29 | cxb6 | -28 | axb6 | -27 |
| 30 | Rxb6 | -26 | Bf7 | -19 |
Engine self-play
10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 38.5 moves.
Sample game 1 (1/2-1/2)
1. b4 d5 2. g3 h5 3. h4 a5 4. bxa5 c5 5. d3 Bc7 6. Bd2 c4 7. Bg2 Bc6 8. O-O Nd6 9. Nc3 e6 10. a4 Bxa5 11. Nb5 Bxd2 12. Qxd2 Nf5 13. c3 cxd3 14. exd3 Rh6 15. Nc2 Qxa4 16. Rb4 Qa8 17. Ncd4 Rf6 18. Qe2 g6 19. Qb2 e5 20. Nxf5 gxf5 21. Qe2 Qb8 22. f4 e4 23. Nd4 Qc8 24. Rfb1 Ne6 25. Qxh5 Ng7 26. Qe2 Be8 27. R1b3 b5 28. Kh2 Rb6 29. Bf1 Kh7 30. Qe1 Ra6 31. Nxb5 Bxb5 32. Rxb5 Ra2+ 33. Rb2 Ra3 34. c4 dxc4 35. dxc4 Qd7 36. Rb7 Qd4 37. c5 Nh5 38. Be2 Ra1 39. Rb1 Ra2 40. Rxf7+ Kg8
Sample game 2 (1/2-1/2)
1. b4 d5 2. g3 b6 3. d3 c6 4. Nb3 e5 5. Bg2 h5 6. h4 Ne7 7. e4 Qb7 8. Ne3 Qc8 9. a4 Bd7 10. Nd2 Ne6 11. c3 O-O 12. Qd1 g6 13. b5 d4 14. cxd4 Nxd4 15. Nf3 Nxf3+ 16. Qxf3 Kg7 17. Kh2 Be6 18. Qe2 c5 19. a5 Qd7 20. Rd1 Bc7 21. Nc4 f6 22. Be3 Ng8 23. Qd2 Rf7 24. Bf1 Kh7 25. Bg2 Kg7 26. Bf1 Kh7 27. Bg2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 150 / 104 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): qbnrbnkr/pppppppp/8/8/8/8/PPPPPPPP/NRBNQBKR w BHdh - 0 1
Mirror twin (the same position mirrored): White 806 vs Black 861.
Current place in the live balance rating: 485.