White 461 vs Black 268
White starts from setup 461 (RNNBKQBR), Black from setup 268 (NBRKNQBR). In the encyclopedia since 2026-10-09: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #461 R N N B K Q B R
King on the e-file, rooks on a, h, queen on the f-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 461 gives White +0.47 (Morozov Balance Index, 400M nodes).
Black: setup #268 N B R K N Q B R
King on the d-file, rooks on c, h, queen on the f-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 268 gives White +0.58 (Morozov Balance Index, 400M nodes).
Why the pair is balanced
At the deepest rungs (400M, 800M, 1.6B nodes) the evaluation never left ±2 centipawns of equality, reaching search depth 54.
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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±7 cp.
For comparison, in symmetric play setup 461 gives White +0.47 and setup 268 gives White +0.58: 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 (30 moves) the evaluation stayed within ±19 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 | 15 | +4 | 1. e4 f5 2. e5 f4 3. d4 c5 4. f3 Nb6 |
| S1 | 500 000 | 20 | +2 | 1. e4 f5 2. e5 f4 3. d4 c5 4. f3 cxd4 |
| S2 | 2 000 000 | 25 | +7 | 1. e4 f5 2. e5 f4 3. Bf3 Qf5 4. Qe2 Qxc2 |
| S3 | 8 000 000 | 28 | -4 | 1. f4 f5 2. c3 c5 3. d3 h6 4. Nb3 b6 |
| S4 | 32 000 000 | 38 | 0 | 1. e4 f5 2. e5 f4 3. d4 c5 4. f3 Qf5 |
| S5 | 128 000 000 | 42 | 0 | 1. e4 f5 2. e5 f4 3. Qe2 c5 4. f3 d6 |
| S6 | 400 000 000 | 46 | 0 | 1. e4 f5 2. e5 f4 3. d4 c5 4. f3 Qf5 |
| S7 | 800 000 000 | 50 | 0 | 1. e4 f5 2. e5 f4 3. d4 c5 4. f3 cxd4 |
| S8 | 1 600 000 000 | 54 | +2 | 1. f4 f5 2. Nb3 c6 3. d3 O-O-O 4. N1d2 h5 |
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 | 0 |
| 8 000 000 000 | not checked |
| 16 000 000 000 | not checked |
This pair stays within the ±5 cp corridor up to 4 000 000 000 nodes.
Independent engines, run on the same position:
- Berserk 14: +9
- 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 +32, Black +46, difference -14. 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 | +18 | 41 | 1. e4 f5 2. e5 f4 3. Qe2 c5 4. f3 d6 5. Na3 Qf5 |
| 2 | +7 | 40 | 1. Nb3 f5 2. f4 Nb6 3. d3 c6 4. N1d2 Nf6 5. c4 d5 |
| 3 | +4 | 40 | 1. f4 f5 2. Nb3 c6 3. d3 O-O-O 4. N1d2 h5 5. c3 h4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 19 cp, mean 3.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | e4 | -8 | f5 | -3 |
| 2 | e5 | 0 | f4 | -11 |
| 3 | d4 | 0 | c5 | 0 |
| 4 | f3 | +2 | cxd4 | +11 |
| 5 | Bxd4 | +19 | Qf5 | +9 |
| 6 | Qe2 | +10 | Nec7 | +4 |
| 7 | c3 | +7 | Ne6 | +10 |
| 8 | Bf2 | +7 | b6 | +6 |
| 9 | O-O | +8 | Qxe5 | +7 |
| 10 | a4 | +4 | Bf7 | +6 |
| 11 | Re1 | +10 | Qxe2 | +8 |
| 12 | Bxe2 | +5 | O-O | +8 |
| 13 | Nd3 | +4 | Nd8 | +7 |
| 14 | a5 | +9 | Nc6 | +7 |
| 15 | axb6 | +8 | Nxb6 | 0 |
| 16 | b4 | 0 | h6 | 0 |
| 17 | h4 | 0 | Nc4 | +1 |
| 18 | Nc5 | 0 | N6e5 | 0 |
| 19 | Na3 | +8 | Nxa3 | 0 |
| 20 | Rxa3 | 0 | Bc4 | 0 |
| 21 | Bxc4+ | +3 | Nxc4 | +4 |
| 22 | Ra2 | 0 | Ne5 | 0 |
| 23 | Rxe5 | +8 | Bxe5 | 0 |
| 24 | Nxd7 | +6 | Bxc3 | +3 |
| 25 | Nxf8 | 0 | Rxf8 | +1 |
| 26 | Bc5 | 0 | Bf6 | 0 |
| 27 | Kf1 | 0 | Bxh4 | 0 |
| 28 | Rxa7 | 0 | Kf7 | 0 |
| 29 | Ke2 | 0 | Ke6 | 0 |
| 30 | Kd3 | 0 | Rd8+ | 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 41.7 moves.
Sample game 1 (1/2-1/2)
1. Nd3 c6 2. Nc3 Nb6 3. e4 f5 4. e5 f4 5. Be2 Qf5 6. g4 Qf7 7. f3 d6 8. h4 h6 9. h5 Bh7 10. O-O-O O-O-O 11. e6 Qxe6 12. Nxf4 Qf7 13. Ng6 Bxg6 14. hxg6 Qxg6 15. Bd3 Qf7 16. g5 Nd7 17. g6 Qf6 18. Bf2 Qxf3 19. Re1 d5 20. Bh4 Qxf1 21. Rhxf1 Bd6 22. Bxe7 Bxe7 23. Rxe7 Rg8 24. Bf5 Nf6 25. Rfe1 Kc7 26. Kd1 Rde8 27. Rf7 Rxe1+ 28. Kxe1 Kd6 29. Ne2 Ne5 30. Rxb7 Nf3+ 31. Kf2 Nxd2 32. Rxa7 Ke5 33. Bh3 Nfe4+ 34. Kg2 Kf6 35. Nf4 Kg5 36. Rf7 Nd6 37. Ne6+ Kxg6 38. Rc7 Kf6 39. Rxc6 Ke5 40. Nc5 N6e4
Sample game 2 (1/2-1/2)
1. Nd3 f5 2. f4 Nf6 3. Nc3 c6 4. a4 d6 5. Qf3 Nc7 6. a5 Bc4 7. Bf2 Qf7 8. O-O Ncd5 9. Nxd5 Bxd5 10. Qh3 O-O 11. c3 c5 12. Bc2 Ne4 13. Be3 Bb3 14. Bxb3 Qxb3 15. Qf3 d5 16. Rfc1 e6 17. Ne1 Qb5 18. d3 Nf6 19. Bf2 h6 20. g3 Ng4 21. h3 Nxf2 22. Kxf2 Kh7 23. d4 cxd4 24. cxd4 Rxc1 25. Rxc1 Qxb2 26. Qe3 Re8 27. a6 Re7 28. axb7 Qxb7 29. Qa3 Rc7 30. Ra1 Qb6 31. Nf3 Rc2 32. Qe7 a5 33. Qe8 Ba7 34. Re1 Rc7 35. g4 Qc6 36. Qf8 Rc8 37. Qf7 Rc7 38. Qf8 Rc8 39. Qf7 Rc7
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 461 / 268 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): nbrknqbr/pppppppp/8/8/8/8/PPPPPPPP/RNNBKQBR w AHch - 0 1
Mirror twin: White 696 vs Black 604 — a different position (castling squares are fixed), not evaluated by the search.