White 33 vs Black 38
White starts from setup 33 (BNNBQRKR), Black from setup 38 (NNBQRBKR). In the encyclopedia since 2026-10-10: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #33 B N N B Q R K R
King on the g-file, rooks on f, h, queen on the e-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 33 gives White +0.39 (Morozov Balance Index, 400M nodes).
Black: setup #38 N N B Q R B K R
King on the g-file, rooks on e, h, queen on the d-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 38 gives White +0.11 (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 57.
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 -20 and +3 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 33 gives White +0.39 and setup 38 gives White +0.11: 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 b3, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the largest swing was 35 cp (around move 23), ending at 0 cp — the position stays playable for both sides.
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 | 16 | -12 | 1. f4 d5 2. b3 h5 3. h3 c5 4. Qf2 d4 |
| S1 | 500 000 | 20 | +3 | 1. f4 d5 2. Rf2 h5 3. O-O c5 4. b3 e6 |
| S2 | 2 000 000 | 23 | -15 | 1. f4 d5 2. b3 h5 3. Rf2 c5 4. O-O Nc7 |
| S3 | 8 000 000 | 28 | -20 | 1. f4 d5 2. e3 h5 3. Rf2 c5 4. Nd3 e6 |
| S4 | 32 000 000 | 34 | -17 | 1. f4 c5 2. b3 d5 3. e3 h5 4. Rf2 Rh6 |
| S5 | 128 000 000 | 44 | 0 | 1. f4 d5 2. b3 h5 3. e3 Nc6 4. Rf2 e5 |
| S6 | 400 000 000 | 50 | 0 | 1. f4 h5 2. b3 d5 3. e3 Nc6 4. Rf2 e5 |
| S7 | 800 000 000 | 53 | 0 | 1. f4 d5 2. b3 h5 3. e3 Nc6 4. Rf2 e5 |
| S8 | 1 600 000 000 | 57 | 0 | 1. f4 d5 2. b3 h5 3. e3 Nc6 4. Rf2 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: 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 +100, Black +88, difference +12. 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 | 43 | 1. b3 d5 2. f4 h5 3. e3 Nc6 4. Rf2 e5 5. fxe5 Nxe5 |
| 2 | 0 | 43 | 1. f4 d5 2. b3 h5 3. e3 Nc6 4. Rf2 e5 5. fxe5 Nxe5 |
| 3 | -16 | 42 | 1. Nd3 d5 2. f4 Nb6 3. b3 Bf5 4. Nc3 Bxd3 5. cxd3 e6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 35 cp, mean 18.4 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | f4 | -28 | d5 | -18 |
| 2 | b3 | -13 | h5 | +2 |
| 3 | e3 | +11 | c5 | -11 |
| 4 | Nd3 | -11 | Bf5 | -1 |
| 5 | Ne5 | -1 | Nb6 | -21 |
| 6 | d3 | +11 | N6d7 | -7 |
| 7 | Nxd7 | -12 | Bxd7 | -14 |
| 8 | Qf2 | -19 | h4 | -11 |
| 9 | Re1 | -11 | h3 | -15 |
| 10 | g3 | -15 | b5 | -21 |
| 11 | O-O | -20 | Nc6 | -19 |
| 12 | Nd2 | -26 | e6 | -27 |
| 13 | Nf3 | -26 | Be7 | -20 |
| 14 | Bb2 | -27 | a5 | -24 |
| 15 | a3 | -27 | Qc7 | -24 |
| 16 | c4 | -24 | Rb8 | -21 |
| 17 | Qe2 | -33 | Qa7 | -23 |
| 18 | Rf2 | -29 | a4 | -21 |
| 19 | cxb5 | -22 | Rxb5 | -18 |
| 20 | bxa4 | -25 | Rb7 | -28 |
| 21 | Ref1 | -29 | c4 | -16 |
| 22 | Ne5 | -18 | Be8 | -11 |
| 23 | Bc3 | -21 | Nxe5 | -35 |
| 24 | fxe5 | -32 | Bxa3 | -23 |
| 25 | Qa2 | -18 | Be7 | -30 |
| 26 | Bd4 | -20 | Qa6 | -22 |
| 27 | dxc4 | -19 | dxc4 | -29 |
| 28 | a5 | -15 | Rb8 | -14 |
| 29 | Bf3 | -11 | O-O | -3 |
| 30 | Qe2 | 0 | Bc6 | 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 39.0 moves.
Sample game 1 (1/2-1/2)
1. h4 e5 2. f4 e4 3. h5 h6 4. e3 Nb6 5. b3 d5 6. d3 Bc5 7. b4 Be7 8. dxe4 dxe4 9. a3 Bf6 10. Bxf6 Qxf6 11. Nb3 O-O 12. g4 Qb2 13. Be2 Qxc2 14. Nd4 Qa2 15. Rh2 Nc6 16. Bb5 Qd5 17. Nc3 Qd6 18. Bxc6 bxc6 19. Rg2 a5 20. bxa5 Nc4 21. Qc1 Rd8 22. Nxe4 Qe7 23. Qxc4 Qxe4 24. Rg3 Rd5 25. Rc1 Bxg4 26. Nxc6 Rd1+ 27. Kf2 Rd2+ 28. Kg1 Rd1+ 29. Kf2 Rd2+ 30. Kg1
Sample game 2 (0-1)
1. b3 e5 2. f4 e4 3. e3 h5 4. d3 d5 5. dxe4 dxe4 6. Rf2 b5 7. Rd2 Nd7 8. Ne2 c6 9. O-O Nab6 10. Qf2 h4 11. Kh1 Bb4 12. c3 Bf8 13. Nd4 Qc7 14. h3 Nc5 15. Be2 Nbd7 16. c4 b4 17. a3 bxa3 18. Nxa3 Nd3 19. Bxd3 exd3 20. Nb1 Nc5 21. Nc3 a5 22. Re1 Rh6 23. Rdd1 Qb6 24. Rd2 Qb4 25. Red1 Rd6 26. Qf3 Rg6 27. Nxc6 Qxb3 28. Ne5 Bb7 29. e4 Rxe5 30. fxe5 Qxc4 31. Rxd3 Nxd3 32. Qxd3 Qxd3 33. Rxd3 Re6 34. Rd8 Rxe5 35. Bb2 Bc6 36. Rc8 Be8 37. g3 hxg3 38. Kg2 Bd6 39. Kf3 g2 40. Kxg2 Kh7 41. Bc1 Re6 42. Kf3 Rf6+ 43. Ke2 Bd7 44. Ra8 Bb4 45. Nd5 Bb5+ 46. Ke3 Bc5+ 47. Kd2 Ra6 48. Rc8 Bd6 49. Rc3 Rc6 50. Rf3 f6 51. Ba3 Be5 52. Rb3 Bf1 53. Rb7 Bg2 54. Ra7 Bxe4 55. Rxa5 Rc2+ 56. Ke3 Bxd5 57. Rxd5 Rh2 58. Ke4 Rxh3 59. Bf8 Kg6 60. Rd7 Rh4+ 61. Kf3 f5 62. Rd5 Rf4+ 63. Kg2 Re4 64. Ra5 Kf7 65. Ba3 g5 66. Ra8 Rc4 67. Kf1 g4 68. Bf8 f4 69. Ke2 Ke6 70. Kd3 Rc3+ 71. Kd2 Rb3 72. Bc5 g3 73. Ra4 Kf5 74. Ba7 f3 75. Rh4 Rb1 76. Ke3 f2 77. Rh5+ Ke6 78. Bd4 Re1+ 79. Kd2
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 33 / 38 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): nnbqrbkr/pppppppp/8/8/8/8/PPPPPPPP/BNNBQRKR w FHeh - 0 1
Mirror twin: White 923 vs Black 918 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 144.