White 138 vs Black 58

The two setups

White: setup #138 N R Q N B B K R

King on the g-file, rooks on b, h, queen on the c-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 138 gives White +0.45 (Morozov Balance Index, 400M nodes).

Black: setup #58 N N R Q B B K R

King on the g-file, rooks on c, 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 58 gives White +0.19 (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 55.

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 -16 and +10 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 138 gives White +0.45 and setup 58 gives White +0.19: 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 b4, and 2 first moves are within 10 cp of it.

Along the engine's main line (30 moves) the largest swing was 38 cp (around move 21), ending at 0 cp — the position stays playable for both sides.

Engine self-play agrees: 10 games, White won 1, drawn 9, Black won 0 (White scored 55.0%).

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 4 000 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: 0
• Lc0 0.32.1: +5

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 +38, Black +33, difference +5. A balanced pair needs White's setup to be weaker by about the price of the first move.

Extended self-play: 10 games, 1 White wins, 9 draws, 0 Black wins, White scored 55.0%.

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| 38 cp, mean 8.9 cp, final 0 cp.

Engine self-play

10 games at 500 000 nodes per move: White won 1, drawn 9, Black won 0 — White scored 55.0%. Average length 44.8 moves.

1. d4 d5 2. h4 h5 3. Nb3 e6 4. e4 b6 5. exd5 exd5 6. c4 dxc4 7. Qxc4 c5 8. dxc5 bxc5 9. Ne3 Nb6 10. Qf4 Rh6 11. Bc3 Nc6 12. Re1 Bd7 13. Rd1 Qc7 14. Qxc7 Rxc7 15. Be2 Na4 16. O-O Nxc3 17. bxc3 Ne5 18. Na5 Ng4 19. Nd5 Rc8 20. Rd2 Re8 21. g3 Rd6 22. Bf3 Bb5 23. c4 Bd7 24. Rfd1 Bf5 25. Kg2 Rb8 26. Nb3 g6 27. Ne7+ Bxe7 28. Rxd6 Bxd6 29. Rxd6 Rb4 30. Be2 Ne5 31. Ra6 Bd3 32. Bxd3 Nxd3 33. Nd2 Rb2 34. Ne4 f5 35. Ng5 Rxf2+ 36. Kg1 Rc2 37. Rxg6+ Kf8 38. Rd6 Rc3 39. Rd5 Ke7 40. Rxf5 Rxc4

1. b4 h5 2. d4 Nc6 3. e3 d5 4. h4 Nb6 5. Nb3 a6 6. Nc5 Rb8 7. Bc3 e6 8. Nb2 Ne7 9. g3 Nf5 10. Bg2 Bc6 11. Qe1 Qe8 12. Nbd3 Nc4 13. Ne5 Nxe5 14. dxe5 b6 15. Nb3 Rc8 16. Qd2 Bb5 17. Nd4 Nxd4 18. exd4 c5 19. Kh2 Qc6 20. Rhc1 g6 21. Rb2 Bh6 22. f4 Bf8 23. bxc5 bxc5 24. Rcb1 Kh7 25. a4 cxd4 26. Bxd4 Bxa4 27. Rb7 Rc7 28. Rxc7 Qxc7 29. c4 Qxc4 30. Rb7 Be8 31. Qc3 Qxc3 32. Bxc3 Kg8 33. Ba5 Bb5 34. Bd8 Bg7 35. Bf6 d4 36. Bf3 d3 37. Bd1 Bxf6 38. exf6 Bc4 39. Rc7 Ba2 40. Rd7 Bc4 41. Kg2 Kh7 42. Rxf7+ Kh6 43. Rc7 Bb5 44. Rf7 Re8 45. Kf2 Bc4 46. Rc7 Bb5 47. Rf7 Rd8 48. Ke3 d2 49. Rc7 Bd3 50. Kxd2 Bf5+ 51. Ke1 Rf8 52. Ra7 Rxf6 53. Rxa6

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 138 / 58 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): nnrqbbkr/pppppppp/8/8/8/8/PPPPPPPP/NRQNBBKR w BHch - 0 1

Mirror twin: White 821 vs Black 901 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 393.