White 46 vs Black 147
White starts from setup 46 (NNQRKBBR), Black from setup 147 (BNRNQKRB). In the encyclopedia since 2026-10-10: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
How to play with different setups
White sets up the pieces by position No. 46, Black by position No. 147, mirrored on their own side; the pawns stand as usual.
Moves as usual: White starts; everything else follows the Chess960 rules.
The two setups
White: setup #46 N N Q R K B B R
King on the e-file, rooks on d, h, queen on the c-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 46 gives White +0.19 (Morozov Balance Index, 400M nodes).
Black: setup #147 B N R N Q K R B
King on the f-file, rooks on c, g, queen on the e-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 147 gives White +0.39 (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 agreed early: from 100 thousand to 128 million nodes the evaluation never left ±9 cp.
For comparison, in symmetric play setup 46 gives White +0.19 and setup 147 gives White +0.39: 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 f3, and 3 first moves are within 10 cp of it.
Along the engine's main line (30 moves) the evaluation stayed within ±13 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 | 16 | +1 | 1. d4 O-O 2. f3 b6 3. c4 e6 4. Nc3 d5 |
| S1 | 500 000 | 21 | -1 | 1. d4 d5 2. c4 dxc4 3. Qxc4 c5 4. f3 O-O |
| S2 | 2 000 000 | 26 | -4 | 1. d4 d5 2. c4 dxc4 3. Qxc4 c5 4. f3 g6 |
| S3 | 8 000 000 | 29 | +1 | 1. d4 d5 2. h3 b6 3. Bh2 g6 4. e3 e5 |
| S4 | 32 000 000 | 36 | -9 | 1. f3 e5 2. d4 exd4 3. c3 Ne6 4. cxd4 d5 |
| S5 | 128 000 000 | 48 | 0 | 1. d4 d5 2. Nc3 b6 3. h4 g6 4. f3 e5 |
| S6 | 400 000 000 | 54 | 0 | 1. d4 d5 2. Nc3 b6 3. h4 g6 4. f3 e5 |
| S7 | 800 000 000 | 56 | 0 | 1. d4 d5 2. Nc3 b6 3. h4 g6 4. f3 e5 |
| S8 | 1 600 000 000 | 60 | 0 | 1. d4 d5 2. Nc3 b6 3. h4 g6 4. f3 e5 |
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: 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 +39, Black +62, difference -23. 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 | +2 | 42 | 1. f3 b6 2. d4 d5 3. Nc3 e5 4. dxe5 Qxe5 5. Qe3 Qd6 |
| 2 | 0 | 42 | 1. d4 d5 2. c4 dxc4 3. Qxc4 O-O 4. f3 c5 5. e4 g6 |
| 3 | -8 | 42 | 1. Nb3 e5 2. d4 exd4 3. Nxd4 g6 4. h4 Ne6 5. f3 b6 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 13 cp, mean 2.3 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | d4 | -2 | d5 | -13 |
| 2 | c4 | 0 | dxc4 | -6 |
| 3 | Qxc4 | 0 | O-O | 0 |
| 4 | f3 | 0 | c5 | 0 |
| 5 | dxc5 | 0 | g6 | -4 |
| 6 | Nc3 | 0 | Ne6 | 0 |
| 7 | Nb3 | -3 | b6 | -8 |
| 8 | e4 | -8 | Nd7 | -11 |
| 9 | Be3 | +5 | Ndxc5 | -2 |
| 10 | Qb4 | 0 | Rd8 | 0 |
| 11 | Bc4 | +3 | Rxd1+ | 0 |
| 12 | Nxd1 | 0 | Qc6 | 0 |
| 13 | Nxc5 | +4 | Nxc5 | +8 |
| 14 | b3 | +8 | a5 | +6 |
| 15 | Qd2 | +8 | b5 | +5 |
| 16 | Be2 | +5 | b4 | +4 |
| 17 | O-O | 0 | Ne6 | 0 |
| 18 | Qc1 | +5 | h5 | +5 |
| 19 | Qxc6 | +8 | Bxc6 | 0 |
| 20 | Bc4 | 0 | Rd8 | 0 |
| 21 | Nf2 | +6 | Bd4 | 0 |
| 22 | Bxd4 | 0 | Nxd4 | 0 |
| 23 | Rd1 | 0 | Kg7 | 0 |
| 24 | Kf1 | 0 | h4 | 0 |
| 25 | Ng4 | 0 | f5 | 0 |
| 26 | exf5 | 0 | gxf5 | 0 |
| 27 | Ne5 | 0 | f4 | 0 |
| 28 | Nf7 | 0 | Rd7 | 0 |
| 29 | Ne5 | 0 | Rd6 | 0 |
| 30 | Nf7 | 0 | Rd7 | 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 40.2 moves.
Sample game 1 (1/2-1/2)
1. d4 d6 2. e4 c5 3. dxc5 dxc5 4. f3 b5 5. Nb3 Ne6 6. h4 g6 7. Be3 O-O 8. Nc3 c4 9. Nd4 Nxd4 10. Bxd4 Bxd4 11. Rxd4 e5 12. Rd1 b4 13. Nd5 Bxd5 14. Rxd5 Qe7 15. h5 Nd7 16. hxg6 fxg6 17. Rb5 Nb6 18. Qe3 Rfd8 19. c3 bxc3 20. bxc3 Rd6 21. Be2 Rdc6 22. O-O Rc5 23. Rfb1 Kg7 24. g3 R8c7 25. Kg2 h5 26. Rxc5 Qxc5 27. Qg5 Na4 28. Qd2 Nb6 29. Qg5 Na4 30. Qd2 Nb6
Sample game 2 (1/2-1/2)
1. f3 b6 2. Nb3 g6 3. d4 d5 4. Nc3 O-O 5. e4 dxe4 6. fxe4 c5 7. h4 h5 8. Bb5 Bc6 9. Be2 cxd4 10. Nxd4 Ne6 11. Nxe6 fxe6 12. Bd4 Bxd4 13. Rxd4 Qf7 14. Qe3 Nd7 15. Rf1 Qg7 16. Rxf8+ Rxf8 17. b4 Ne5 18. b5 Bb7 19. Kd2 Rc8 20. Ra4 Ra8 21. g3 Nf7 22. Nd1 Qf6 23. Nf2 Rd8+ 24. Bd3 Ne5 25. Ke2 Ra8 26. Bc4 Rf8 27. Nd3 a6 28. Nxe5 axb5 29. Nxg6 Qf1+ 30. Kd2 Rf2+ 31. Kc3 bxc4 32. Kb2 Re2 33. Qg5 Rxc2+ 34. Kxc2 Bxe4+ 35. Kb2 Qe2+ 36. Ka3 Qd3+ 37. Kb4 Qd6+ 38. Kb5 Qc6+ 39. Kb4 Qd6+ 40. Kc3 Qd3+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 46 / 147 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): bnrnqkrb/pppppppp/8/8/8/8/PPPPPPPP/NNQRKBBR w DHcg - 0 1
Mirror twin: White 916 vs Black 803 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 209.