White 126 vs Black 150
White starts from setup 126 (NQRNKBBR), Black from setup 150 (NRBNQBKR). In the encyclopedia since 2026-10-15: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #126 N Q R N K B B R
King on the e-file, rooks on c, h, queen on the b-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 126 gives White +0.27 (Morozov Balance Index, 400M nodes).
Black: 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).
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 54.
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 ±15 cp.
For comparison, in symmetric play setup 126 gives White +0.27 and setup 150 gives White +0.30: 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 evaluation stayed within ±20 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 9, Black won 1 (White scored 45.0%).
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 | -10 | 1. f4 Nc6 2. c4 d6 3. b4 e5 4. b5 Nd4 |
| S1 | 500 000 | 19 | +3 | 1. c4 b6 2. h4 e5 3. h5 c5 4. Nc3 d6 |
| S2 | 2 000 000 | 23 | -15 | 1. c4 d6 2. Nc3 c5 3. h3 g6 4. Bh2 Nc6 |
| S3 | 8 000 000 | 28 | -8 | 1. c4 c5 2. h3 d6 3. e3 b6 4. Bh2 g6 |
| S4 | 32 000 000 | 34 | +1 | 1. c4 e5 2. Nc3 b6 3. f3 c6 4. e4 Nc7 |
| S5 | 128 000 000 | 43 | 0 | 1. c4 c5 2. f3 e5 3. b4 b6 4. bxc5 Nc6 |
| S6 | 400 000 000 | 51 | 0 | 1. c4 c5 2. Nb3 b6 3. d4 cxd4 4. Nxd4 e5 |
| S7 | 800 000 000 | 54 | 0 | 1. c4 c5 2. Nb3 b6 3. d4 cxd4 4. Nxd4 e5 |
| S8 | 1 600 000 000 | 54 | 0 | 1. c4 c5 2. Nb3 b6 3. d4 cxd4 4. Nxd4 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 | 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: -2
- Lc0 0.32.1: -3
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 +9, Black +42, difference -33. 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, 9 draws, 1 Black wins, White scored 45.0%.
Best first moves
The 3 best first moves for White, searched together at 400 000 000 nodes.
| # | Eval, cp | Depth | Main line |
|---|---|---|---|
| 1 | 0 | 42 | 1. c4 c5 2. f3 e5 3. b4 b6 4. bxc5 Nc6 5. cxb6 Nxb6 |
| 2 | -12 | 41 | 1. f3 Nb6 2. c4 e5 3. c5 Nd5 4. e4 Nf6 5. Nc3 c6 |
| 3 | -20 | 41 | 1. e4 e5 2. f3 c5 3. b4 d6 4. c3 Ne6 5. Nb3 Nb6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 20 cp, mean 3.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c4 | -13 | e5 | -12 |
| 2 | Nc3 | -3 | b6 | +3 |
| 3 | Nc2 | +18 | a6 | +10 |
| 4 | e3 | +20 | h5 | +17 |
| 5 | h3 | +5 | Rh6 | 0 |
| 6 | Bh2 | 0 | Bb7 | 0 |
| 7 | b4 | 0 | c5 | 0 |
| 8 | e4 | +17 | cxb4 | +14 |
| 9 | Nd5 | +6 | Nc6 | +5 |
| 10 | Be2 | +7 | Bc5 | 0 |
| 11 | O-O | +11 | d6 | +10 |
| 12 | Kh1 | +4 | Rc8 | 0 |
| 13 | f4 | -6 | Nc7 | -6 |
| 14 | fxe5 | -6 | dxe5 | -1 |
| 15 | Rf5 | 0 | f6 | 0 |
| 16 | Rcf1 | 0 | Ne6 | +4 |
| 17 | Qd1 | 0 | Ng5 | 0 |
| 18 | d3 | 0 | h4 | 0 |
| 19 | Nce3 | 0 | Bxe3 | 0 |
| 20 | Nxe3 | 0 | Rd8 | 0 |
| 21 | Ng4 | 0 | Rg6 | 0 |
| 22 | Qe1 | 0 | Nd4 | 0 |
| 23 | Rxf6 | 0 | gxf6 | 0 |
| 24 | Nxf6+ | 0 | Rxf6 | 0 |
| 25 | Rxf6 | 0 | Qe7 | 0 |
| 26 | Rg6+ | 0 | Kh7 | 0 |
| 27 | Rxb6 | 0 | Nf7 | 0 |
| 28 | Bh5 | 0 | Rf8 | 0 |
| 29 | Bxf7 | 0 | Rxf7 | 0 |
| 30 | Rxb7 | 0 | Qxb7 | 0 |
Engine self-play
10 games at 500 000 nodes per move: White won 0, drawn 9, Black won 1 — White scored 45.0%. Average length 45.0 moves.
Sample game 1 (1/2-1/2)
1. c4 e5 2. f4 b5 3. Bxa7 Rb7 4. Bf2 bxc4 5. e4 exf4 6. Bxc4 h5 7. O-O h4 8. Nb3 h3 9. g3 fxg3 10. hxg3 Nb6 11. Ba6 Nc6 12. Be3 d5 13. Kh1 Rh5 14. Nc3 Ne5 15. Rf4 Nbc4 16. Nxd5 Nxe3 17. dxe3 Ng6 18. Bxb7 Bxb7 19. Re1 Re5 20. Nc3 Bb4 21. Nd2 Re6 22. Kh2 Ne5 23. Qc2 g5 24. Rf5 Rg6 25. Re2 Bxc3 26. Qxc3 Ng4+ 27. Kg1 Bxe4 28. Rc5 h2+ 29. Rxh2 Nxh2 30. Kxh2 Qa4 31. Qb3 Rh6+ 32. Kg1 Rh1+ 33. Kf2 Rh2+ 34. Ke1 Rh1+ 35. Kf2 Rh2+ 36. Ke1 Rh1+
Sample game 2 (1/2-1/2)
1. c4 c5 2. f4 e6 3. Nb3 b6 4. d4 d5 5. dxc5 h5 6. e4 Rh6 7. Be3 bxc5 8. f5 Rf6 9. Bg5 Be7 10. Bxf6 Bxf6 11. fxe6 dxe4 12. exf7+ Nxf7 13. Be2 Bh4+ 14. g3 Bg5 15. Rc3 Nb6 16. Nxc5 Qe5 17. h4 Bh6 18. Qxe4 Qxc5 19. Qe8+ Qf8 20. Qxf8+ Kxf8 21. Bxh5 Ne5 22. Ne3 Kg8 23. Bd1 Be6 24. b3 Rd8 25. Be2 Nc8 26. c5 Ne7 27. O-O Rd2 28. Rf2 Rxa2 29. Bc4 Nxc4 30. Nxc4 Ra6 31. Re2 Nd5 32. Rd3 Nf6 33. Rd4 Ra1+ 34. Kg2 Bd5+ 35. Kf2 Rh1 36. Rxd5 Nxd5 37. Re8+ Kf7 38. Rd8 Ne7 39. Rd6 Nf5 40. Rd3 Ne7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 126 / 150 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): nrbnqbkr/pppppppp/8/8/8/8/PPPPPPPP/NQRNKBBR w CHbh - 0 1
Mirror twin: White 836 vs Black 806 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 371.