White 414 vs Black 415
White starts from setup 414 (RQNNKBBR), Black from setup 415 (RQNNKRBB). 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 #414 R Q N N K B B R
King on the e-file, rooks on a, h, queen on the b-file; no bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 414 gives White +0.25 (Morozov Balance Index, 400M nodes).
Black: setup #415 R Q N N K R B B
King on the e-file, rooks on a, f, queen on the b-file; one bishop starts in a corner; the knights start on central files. Castling follows the Chess960 rule: king and rook end on the classical squares. In ordinary symmetric play setup 415 gives White +0.27 (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 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 shallow rungs wandered between -19 and +4 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 414 gives White +0.25 and setup 415 gives White +0.27: 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 e4, and 2 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±30 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 | 18 | -2 | 1. c3 f5 2. f3 Nd6 3. a4 g6 4. Bf2 b6 |
| S1 | 500 000 | 22 | +4 | 1. c3 f5 2. f3 g6 3. Bf2 Nd6 4. d4 e5 |
| S2 | 2 000 000 | 23 | +1 | 1. c3 f5 2. f3 g6 3. Bf2 d5 4. e4 dxe4 |
| S3 | 8 000 000 | 31 | -5 | 1. c3 g6 2. h4 e5 3. h5 Bg7 4. e4 f5 |
| S4 | 32 000 000 | 36 | -19 | 1. c3 f5 2. f3 g6 3. d4 e5 4. dxe5 Nc6 |
| S5 | 128 000 000 | 43 | 0 | 1. c3 f5 2. e4 fxe4 3. Qxe4 g6 4. h4 Nd6 |
| S6 | 400 000 000 | 53 | 0 | 1. e4 g6 2. c3 f5 3. exf5 gxf5 4. Bd3 Nd6 |
| S7 | 800 000 000 | 58 | 0 | 1. e4 g6 2. c3 f5 3. exf5 gxf5 4. Bd3 Nd6 |
| S8 | 1 600 000 000 | 60 | 0 | 1. e4 g6 2. c3 f5 3. exf5 gxf5 4. Bd3 Nd6 |
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: +3
- Lc0 0.32.1: 0
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 -8, Black +30, difference -38. 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 | +4 | 45 | 1. e4 g6 2. c3 f5 3. exf5 gxf5 4. Bd3 Nd6 5. f4 b6 |
| 2 | 0 | 45 | 1. c3 f5 2. e4 g6 3. exf5 gxf5 4. Bd3 Nd6 5. f4 b6 |
| 3 | -15 | 44 | 1. d4 f5 2. c3 g6 3. e3 e5 4. Be2 Nc6 5. f3 Bf7 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 30 cp, mean 9.2 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | c3 | -5 | f5 | -3 |
| 2 | h4 | +5 | g6 | -14 |
| 3 | e4 | -20 | e5 | -21 |
| 4 | h5 | -20 | Bg7 | -24 |
| 5 | Ne3 | -7 | Ne7 | -19 |
| 6 | f3 | -18 | Ne6 | -13 |
| 7 | Qc2 | -8 | c6 | -10 |
| 8 | Nb3 | -11 | Qc7 | -11 |
| 9 | O-O-O | -13 | a5 | -3 |
| 10 | Kb1 | 0 | a4 | -1 |
| 11 | Nc1 | -7 | a3 | -17 |
| 12 | b4 | -11 | d5 | -20 |
| 13 | Re1 | -30 | b6 | -20 |
| 14 | hxg6 | -9 | hxg6 | -4 |
| 15 | exf5 | 0 | gxf5 | 0 |
| 16 | g4 | +11 | Ng5 | 0 |
| 17 | Be2 | 0 | f4 | +16 |
| 18 | Nf5 | +10 | Nxf5 | +12 |
| 19 | gxf5 | +6 | O-O-O | +19 |
| 20 | Rh5 | +18 | Bf6 | +7 |
| 21 | Qa4 | +7 | Kb8 | +3 |
| 22 | Qxa3 | 0 | Bf7 | 0 |
| 23 | Rh6 | 0 | Bg7 | 0 |
| 24 | Rh2 | +8 | d4 | +13 |
| 25 | cxd4 | +9 | e4 | +9 |
| 26 | fxe4 | +28 | Bxd4 | +11 |
| 27 | b5 | +10 | Bxg1 | +10 |
| 28 | Rxg1 | +1 | Nxe4 | 0 |
| 29 | Bf3 | 0 | Bd5 | 0 |
| 30 | Re2 | 0 | Nd6 | 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 38.4 moves.
Sample game 1 (1/2-1/2)
1. a4 f5 2. f3 c6 3. c3 g6 4. e4 fxe4 5. fxe4 Qc7 6. Qc2 d5 7. exd5 Nd6 8. d4 a6 9. Bd3 cxd5 10. Ne3 e5 11. Nb3 Nc6 12. Bf2 exd4 13. cxd4 O-O-O 14. O-O Kb8 15. a5 Qc8 16. Ra4 Bg7 17. Re1 Ka8 18. h3 Rde8 19. Qd2 Bh6 20. Qc3 Bg5 21. Raa1 Rxf2 22. Kxf2 Qd8 23. Ng4 Ne4+ 24. Bxe4 dxe4 25. Nc5 h5 26. Ne3 Bh4+ 27. Kg1 Bxe1 28. Rxe1 Qxd4 29. Qxd4 Nxd4 30. b4 Nc6 31. Rd1 Nxb4 32. Rd7 Ba2 33. Nxb7 Re5 34. Rg7 g5 35. Rh7 Bg8 36. Rd7 Ba2 37. Rh7 h4 38. Nd6 Nd3 39. g3 hxg3 40. Kg2 Rxa5 41. Rh8+ Ka7 42. Rh7+ Kb8 43. Kxg3 Be6 44. Rb7+ Ka8 45. Re7 Re5 46. Re8+ Ka7 47. Re7+ Kb8 48. Rb7+ Ka8 49. Rg7 Kb8 50. Rb7+ Ka8 51. Rg7 a5 52. Nec4 Bxc4 53. Nxc4 Rb5 54. Nd6 Rd5 55. Nxe4
Sample game 2 (1/2-1/2)
1. a4 c5 2. c3 g6 3. g3 f5 4. Bg2 Qd6 5. Qd3 Qc7 6. f4 c4 7. Qc2 e5 8. fxe5 Bxe5 9. b3 f4 10. d4 cxd3 11. Nxd3 fxg3 12. Nxe5 Qxe5 13. Qd3 Nc6 14. Qxg3 Bxb3 15. Bxc6 Qxg3+ 16. hxg3 dxc6 17. Rxh7 Nd6 18. a5 O-O-O 19. Bxa7 Rf7 20. Rxf7 Bxf7 21. Nb2 Ne4 22. c4 Nxg3 23. Ra3 Ne4 24. Rh3 Re8 25. Na4 Kc7 26. Rh7 Ng5 27. Rh6 Bxc4 28. Bb6+ Kc8 29. e3 Bf7 30. Kf1 Ne4 31. Rh7 Ng5 32. Rh6 Re5 33. Rh8+ Re8
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 414 / 415 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): rqnnkrbb/pppppppp/8/8/8/8/PPPPPPPP/RQNNKBBR w AHaf - 0 1
Mirror twin (the same position mirrored): White 740 vs Black 736.