White 139 vs Black 304

The two setups

White: setup #139 N R Q N B K R B

King on the f-file, rooks on b, g, queen on the c-file; one 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 139 gives White +0.28 (Morozov Balance Index, 400M nodes).

Black: setup #304 B B N Q R K R N

King on the f-file, rooks on e, g, queen on the d-file; one 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 304 gives White +0.29 (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 65.

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 -18 and +12 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 139 gives White +0.28 and setup 304 gives White +0.29: 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 g3; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (11 moves) the evaluation stayed within ±9 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.

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 +102. 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: -1
• Lc0 0.32.1: +9

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 +21, Black +138, difference -117. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 160 games, 0 White wins, 160 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.

Main-line play-out

11 moves, 5 000 000 nodes per half-move. Largest |evaluation| 9 cp, mean 0.4 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 41.0 moves.

1. g3 e5 2. d4 exd4 3. Nb3 Qe7 4. Qd2 c5 5. c3 dxc3 6. Qc2 cxb2 7. Nxc5 O-O 8. Bb4 Bd6 9. Ne3 b6 10. Nf5 Qd8 11. Bxa8 bxc5 12. Bc3 Be5 13. f4 Bxc3 14. Qxc3 Qf6 15. Qxf6 gxf6 16. Nh6+ Kg7 17. Nf5+ Kg8 18. Bb7 Ng6 19. Bxc8 Rxc8 20. Rxb2 Rfd8 21. Kf2 Kf8 22. Nd6 Rc6 23. Rd1 Ne7 24. Ke1 h5 25. Kf2 Ra8 26. Ke1 h4 27. gxh4 c4 28. Rc2 Rb8 29. Rxc4 Rxc4 30. Nxc4 Rb4 31. Ne3 d5 32. h5 Rxf4 33. Rb1 Rh4 34. Rb8+ Kg7 35. Rb7 d4 36. Nf1 Nf5 37. Rxa7 Rxh5 38. Ra3 Kg6 39. Kd2 Rh8 40. Kd1 Re8

1. g3 e5 2. d4 exd4 3. Nb3 Qe7 4. Qd2 c5 5. c3 dxc3 6. Qc2 cxb2 7. Nxc5 O-O 8. Bb4 Bd6 9. Ne3 b6 10. Nf5 Qd8 11. Bxa8 bxc5 12. Bc3 Be5 13. f4 Bxc3 14. Qxc3 Qf6 15. Qxf6 gxf6 16. Nh6+ Kg7 17. Nf5+ Kg8 18. Bb7 Ng6 19. Bxc8 Rxc8 20. Rxb2 Rfd8 21. Kf2 Kf8 22. Nd6 Rc6 23. Rd1 Ne7 24. Ke1 h5 25. Kf2 Ra8 26. Ke1 h4 27. gxh4 c4 28. Rc2 Rb8 29. Rxc4 Rxc4 30. Nxc4 Rb4 31. Ne3 d5 32. h5 Rxf4 33. Rb1 Rh4 34. Rb8+ Kg7 35. Rb7 d4 36. Nf1 Nf5 37. Rxa7 Rxh5 38. Ra3 Kg6 39. Kd2 Rh8 40. Kd1 Re8

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 139 / 304 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): bbnqrkrn/pppppppp/8/8/8/8/PPPPPPPP/NRQNBKRB w BGeg - 0 1

Mirror twin: White 817 vs Black 367 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 29.