White 415 vs Black 309

The two setups

White: 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).

Black: setup #309 N Q B B R K R N

King on the f-file, rooks on e, g, 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 309 gives White +0.15 (Morozov Balance Index, 400M nodes).

Why the pair is balanced

At the deepest rungs (400M, 800M, 1.6B, 3.2B nodes) the evaluation is exactly 0.00 each time, reaching search depth 63.

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 -23 and +5 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 415 gives White +0.27 and setup 309 gives White +0.15: 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 f4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (30 moves) the largest swing was 32 cp (around move 21), 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.

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.

This pair stays within the ±5 cp corridor up to 16 000 000 000 nodes.

Swap the two setups, giving White the black back rank and Black the white one, and the evaluation jumps to +104. The same two armies dealt the other way round are no longer balanced at all: that is how precisely this pair pays for the first move.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: +15

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 +30, Black +69, difference -39. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 6 White wins, 144 draws, 10 Black wins, White scored 48.8%.

Best first moves

The 3 best first moves for White, searched together at 400 000 000 nodes.

Main-line play-out

30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 32 cp, mean 7.8 cp, final 0 cp.

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 33.8 moves.

1. f4 d6 2. Ne3 O-O 3. c4 c6 4. Qc2 Ng6 5. f5 Ne5 6. Nd3 Nxd3+ 7. Qxd3 Nb6 8. O-O-O d5 9. cxd5 cxd5 10. g3 e6 11. Kb1 exf5 12. Nxf5 g6 13. Nh6+ Kg7 14. Ng4 Bxg4 15. Qd4+ Qe5 16. Qxg4 Qxe2 17. Qxe2 Rxe2 18. Bf3 Re6 19. a4 Nxa4 20. Bxd5 Re7 21. Bb3 Re4 22. Rc1 b6 23. Bd5 Re7 24. d4 b5 25. Bc6 Bc7 26. Rfe1 Rxe1 27. Rxe1 Rd8 28. Kc2 Nb6 29. Bxb5 h5 30. Kd3 Nd5 31. Re8 Rxe8 32. Bxe8 Nb6 33. Bb5 Bd6 34. Bc6 Kf6 35. Bf3 Kf5 36. Kc3 Ke6 37. Kd3 f5 38. b3 Kd7 39. Kc3 Be7 40. Kd3 Bd6

1. f4 O-O 2. g3 c6 3. c4 d6 4. Qc2 Bh3 5. Rf3 Qc8 6. Ra3 e5 7. fxe5 Rxe5 8. Rxa7 Rf5 9. Bf3 Ng6 10. Nd3 Rxf3 11. exf3 Bg2 12. Kf2 Bh3 13. Ne3 h5 14. Rc1 Bb6 15. Ra4 Bd4 16. c5 dxc5 17. Nxc5 Rd8 18. Nb3 Bf6 19. Ra5 h4 20. Nd5 Bg5 21. Nc3 Bf6 22. Ne4 Be7 23. Ke1 Nc7 24. Bb6 Re8 25. Kd1 Be6 26. Bxc7 Qxc7 27. Qc3 Rd8 28. Nbc5 Bc8 29. Ra8 Kh7 30. Qb3 f5 31. Rxc8 Qxc8 32. Nxb7 fxe4 33. Nxd8 Qxd8 34. f4 Qd4 35. Rc4 Qg1+ 36. Kc2 Bf6 37. Qe3 Qa1 38. Rb4 Qxa2 39. g4 Qd5 40. Rxe4 Kg8 41. g5 Be7 42. Rd4 Qf7 43. Qe4 Bf8 44. Kc1 Ne7 45. Rd6 Qb3 46. g6 Qb5 47. Kd1 Qh5+ 48. Qe2 Qxe2+ 49. Kxe2 Nf5 50. Rd8 Ne7 51. Rd6 Nf5 52. Rd8 Ne7

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 415 / 309 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): nqbbrkrn/pppppppp/8/8/8/8/PPPPPPPP/RQNNKRBB w AFeg - 0 1

Mirror twin: White 736 vs Black 362 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 63.