White 159 vs Black 546
White starts from setup 159 (NRNQKRBB), Black from setup 546 (BRNKNBQR). In the encyclopedia since 2026-10-15: neither side starts better.
|cp| ≤ 5 at 400M · 800M · 1.6B · 4B nodes, two independent engines agree
The two setups
White: setup #159 N R N Q K R B B
King on the e-file, rooks on b, f, 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 159 gives White +0.26 (Morozov Balance Index, 400M nodes).
Black: setup #546 B R N K N B Q R
King on the d-file, rooks on b, h, queen on the g-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 546 gives White +0.26 (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 -17 and +5 cp before settling — a reminder that quick engine checks overstate imbalances, and why the ladder goes deep.
For comparison, in symmetric play setup 159 gives White +0.26 and setup 546 gives White +0.26: 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 (30 moves) the largest swing was 38 cp (around move 6), ending at 0 cp — the position stays playable for both sides.
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 | -17 | 1. g3 Ned6 2. c3 h5 3. Nd3 b6 4. Bxa8 Rxa8 |
| S1 | 500 000 | 20 | -3 | 1. g3 Ned6 2. d3 f5 3. c4 b6 4. Bxa8 Rxa8 |
| S2 | 2 000 000 | 25 | -8 | 1. g3 Ned6 2. d3 f5 3. c4 b6 4. Bxa8 Rxa8 |
| S3 | 8 000 000 | 28 | +5 | 1. g3 f5 2. Nd3 g6 3. c3 Bg7 4. f4 b6 |
| S4 | 32 000 000 | 38 | -1 | 1. g3 f5 2. f4 g6 3. c3 b6 4. Bxa8 Rxa8 |
| S5 | 128 000 000 | 43 | -1 | 1. g3 f5 2. f4 g6 3. c3 Bg7 4. Nd3 d6 |
| S6 | 400 000 000 | 55 | 0 | 1. g3 f5 2. f4 g6 3. c3 Bg7 4. Nd3 d6 |
| S7 | 800 000 000 | 57 | 0 | 1. g3 f5 2. f4 g6 3. c3 Bg7 4. Nd3 d6 |
| S8 | 1 600 000 000 | 60 | 0 | 1. g3 f5 2. f4 g6 3. c3 Bg7 4. Nd3 d6 |
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: +1
- Lc0 0.32.1: +4
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 +7, Black +62, difference -55. 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 | +11 | 40 | 1. g3 f5 2. f4 g6 3. d3 Nf6 4. Nab3 Bg7 5. Nd2 d6 |
| 2 | -14 | 39 | 1. f3 b6 2. g3 f5 3. e4 e5 4. Ne2 Ncd6 5. d3 h5 |
| 3 | -18 | 39 | 1. e4 b6 2. f3 f5 3. g3 e5 4. Ne2 h5 5. d4 exd4 |
Main-line play-out
30 moves, 5 000 000 nodes per half-move. Largest |evaluation| 38 cp, mean 13.9 cp, final 0 cp.
| # | White | cp | Black | cp |
|---|---|---|---|---|
| 1 | g3 | +24 | f5 | +8 |
| 2 | f4 | -5 | b6 | -6 |
| 3 | Bxa8 | -6 | Rxa8 | +19 |
| 4 | d3 | +22 | Nf6 | +13 |
| 5 | Ncb3 | +27 | h5 | +28 |
| 6 | Nd2 | +23 | Qxa2 | +38 |
| 7 | c4 | +29 | h4 | +24 |
| 8 | Nc2 | +27 | Qa6 | +27 |
| 9 | e4 | +29 | hxg3 | +22 |
| 10 | hxg3 | +23 | e6 | +26 |
| 11 | Qf3 | +25 | Qb7 | +20 |
| 12 | Bd4 | +26 | c5 | +24 |
| 13 | exf5 | +20 | Qxf3 | +33 |
| 14 | Bxf6+ | +23 | gxf6 | +23 |
| 15 | Nxf3 | +23 | Ke8 | +20 |
| 16 | Ne3 | +17 | Ne7 | +17 |
| 17 | Kf2 | +14 | Kf7 | +12 |
| 18 | d4 | +12 | a5 | +21 |
| 19 | dxc5 | +7 | Nxf5 | 0 |
| 20 | Nxf5 | +7 | exf5 | +7 |
| 21 | cxb6 | +6 | Bc5+ | +5 |
| 22 | Kg2 | +8 | Rhb8 | +6 |
| 23 | Nh4 | +8 | Rxb6 | +8 |
| 24 | Rfd1 | +4 | d6 | +5 |
| 25 | Nxf5 | +8 | Rab8 | 0 |
| 26 | Kh3 | 0 | a4 | 0 |
| 27 | Ra1 | 0 | Rh8+ | 0 |
| 28 | Nh4 | 0 | Rb4 | 0 |
| 29 | Rd3 | 0 | Rg8 | 0 |
| 30 | Re1 | 0 | Rxb2 | 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. g3 Ncd6 2. d3 f5 3. c4 Nf6 4. c5 Nc8 5. Nc2 b6 6. Bxa8 Rxa8 7. d4 g6 8. f3 Bg7 9. Nd3 Qf7 10. a4 O-O 11. Bf2 d6 12. O-O Re8 13. Rc1 dxc5 14. b4 cxd4 15. Nxd4 e5 16. Nc6 Nd7 17. b5 a6 18. bxa6 Rxa6 19. Ndb4 Ra8 20. e4 h6 21. g4 Nd6 22. Nd5 Nf6 23. Ncb4 Rac8 24. Rc6 Nxd5 25. Qxd5 fxe4 26. fxe4 Ra8 27. Bxb6 Qxd5 28. Nxd5 cxb6 29. Rxd6 Rxa4 30. Rxb6 Rea8 31. g5 Kh7 32. Rb7 hxg5 33. Rff7 Ra1+ 34. Kf2 R8a2+ 35. Ke3 Ra3+ 36. Ke2 Kh6 37. Rxg7 R1a2+ 38. Kf1 Ra1+ 39. Ke2 R1a2+ 40. Kf1 Ra1+
Sample game 2 (1/2-1/2)
1. g3 Ned6 2. d3 e5 3. f4 exf4 4. gxf4 f5 5. c4 Be7 6. Bd4 Qf7 7. Nc2 b6 8. Bxa8 Rxa8 9. e3 O-O 10. Qf3 Bh4+ 11. Kd2 Ne7 12. Rg1 Bf6 13. Bxf6 Qxf6 14. Ne2 c6 15. Qg2 Ne8 16. Ncd4 Rd8 17. Nf3 d5 18. cxd5 Nxd5 19. Ne5 c5 20. Nc3 Nxc3 21. bxc3 Nd6 22. Kc2 Nf7 23. d4 Nxe5 24. fxe5 Qe7 25. e6 cxd4 26. exd4 g6 27. d5 Qa3 28. Rb2 Rc8 29. Qd2 Rfd8 30. Rd1 Rc5 31. e7 Qa4+ 32. Kc1 Rdxd5 33. Qxd5+ Rxd5 34. Rxd5 Qf4+ 35. Rbd2 Kf7 36. Rd7 Qc4 37. Kb2 Qb5+ 38. Kc2 Qa4+ 39. Kc1 Qc4 40. Kd1 Qa4+
Play it in the CH960 app
Open this page on a phone with the CH960 app installed, or find pair 159 / 546 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): brnknbqr/pppppppp/8/8/8/8/PPPPPPPP/NRNQKRBB w BFbh - 0 1
Mirror twin: White 800 vs Black 503 — a different position (castling squares are fixed), not evaluated by the search.
Current place in the live balance rating: 453.