White 20 vs Black 846

The two setups

White: setup #20 N B B Q N R K R

King on the g-file, rooks on f, 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 20 gives White +0.21 (Morozov Balance Index, 400M nodes).

Black: setup #846 R K N R Q B B N

King on the b-file, rooks on a, d, queen on the e-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 846 gives White +0.22 (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 same corridor is required at every deeper budget (8 G, 16 G) at which the pair has been evaluated.

The shallow rungs wandered between -11 and +18 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.

For comparison, in symmetric play setup 20 gives White +0.21 and setup 846 gives White +0.22: 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 e4; the alternatives are slightly weaker but keep the game level.

Along the engine's main line (14 moves) the evaluation stayed within ±21 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 4 000 000 000 nodes.

Independent engines, run on the same position:

• Berserk 14: +1
• Lc0 0.32.1: 0

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 +60, Black +94, difference -34. 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.

Main-line play-out

14 moves, 5 000 000 nodes per half-move. Largest |evaluation| 21 cp, mean 2.8 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 38.8 moves.

1. e4 f6 2. b3 d5 3. exd5 Bxd5 4. c4 Bg8 5. d4 e5 6. Nac2 exd4 7. Nxd4 a6 8. Qg4 h5 9. Qf4 Ng6 10. Qg3 Rxd4 11. Bxg6 Bf7 12. Nc2 Rd7 13. Re1 Re7 14. Rxe7 Nxe7 15. Bxf7 Qxf7 16. Qh3 Qg6 17. Nd4 Qe4 18. Qe3 Qxe3 19. Bxe3 O-O-O 20. g3 Kd7 21. Kg2 Nc6 22. Ne2 Ke8 23. Nf4 Kf7 24. Nxh5 Nb4 25. Nf4 Nxa2 26. h4 Nb4 27. Rc1 Nd3 28. Rb1 Nb4 29. Kf3 Nc2 30. g4 a5 31. h5 b6 32. Nd5 Nxe3 33. fxe3 Bd6 34. Rf1 Ke6 35. Ke4 Re8 36. Kd3 Rd8 37. Ke4 Re8 38. Kd3 Rd8

1. e4 f6 2. d4 Nb6 3. Nf3 e5 4. c3 a5 5. Re1 d5 6. exd5 Bxd5 7. h4 a4 8. Nc2 Bf7 9. Qe2 Ng6 10. dxe5 Nxe5 11. Nxe5 Qxe5 12. Qxe5 fxe5 13. Rxe5 Nc4 14. Re2 Bh5 15. f3 Bg6 16. Kh2 Bd6+ 17. g3 Ne5 18. f4 Ng4+ 19. Kh3 Bf5 20. Rhe1 g6 21. Kg2 Bc5 22. b4 axb3 23. axb3 Bf8 24. Bd2 Bg7 25. c4 c5 26. h5 Kc8 27. Ne3 Bxb1 28. Rxb1 Rxd2 29. Rxd2 Nxe3+ 30. Kf3 Nf5 31. Rd5 Bf8 32. Rbd1 Nd4+ 33. Kg4 Kc7 34. b4 b6 35. hxg6 hxg6 36. Rh1 Nf5 37. Rh7+ Be7 38. Kf3 Ra3+ 39. Kf2 Ra2+ 40. Kf3 Ra3+

Play it in the CH960 app

Open this page on a phone with the CH960 app installed, or find pair 20 / 846 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): rknrqbbn/pppppppp/8/8/8/8/PPPPPPPP/NBBQNRKR w FHad - 0 1

Mirror twin: White 942 vs Black 116 — a different position (castling squares are fixed), not evaluated by the search.

Current place in the live balance rating: 134.