An atomic study

[Reminder: in atomic chess, kings can be adjacent, and are immune to check when adjacent (but can be killed by an adjacent explosion; killing your own king in the process is not allowed though.) Exploding a king takes precedence over mate. Captures trigger explosions, removing the capturing unit, the captured unit and all adjacent non-pawn units.]

Maybe half a year ago I made a little atomic chess endgame study. It's very tricky, it completely confuses computer engines, and probably most people too. This is the chess.com version since adjacent kings refuse to display correctly, so I shuffled some things around. White wins.

[Hints: K+Q+P v K+P is a win if you can somehow promote. Bishops are restricted to their own colour squares, so black can use that fact as a defensive weapon.]

I'm putting this up just in case the problemists are interested, since I doubt there're many atomic players on the site (and if any, they would probably have already seen me post it elsewhere before.)

I play on lichess, for almost 2 years now. As for easier problems... the field isn't rich in problems. Tactic puzzles yes, on Chess Variants Training, but not problems proper as of yet. Endgame technique (and therefore some study-like material) is fairly well-developed though, look for tipau's videos on Youtube and his analyses on lichess for instance.

The key idea to the study is breaking what's called "pawnitisation" - it's not terribly hard once you understand what the winning plan must be, just takes some care.

As a newcomer to atomic chess, I'd hoped I could ease into this by starting with the simplest and most naive try (namely, BxR), determining why it fails, and gaining a bit of insight into atomic chess endgames in the process (maybe even enough insight to eventually get the real solution ). But it turns out I may need a little help figuring out how to draw with Black after the presumably silly BxR move. Here is the limited amount that I can see, at the moment:

1. Bxb6 Kg8 [if bK escapes via h7, I think it's drawn; if 1...a3, then just bxa3; if 1...Ke8 (looking to escape via c8), then 2. d5 Kd8 (2...Kd7? loses to 3. d6) 3. Bg4 Ke8  4. Kh7 Kf8 (4...Kd8?  5. Bd7 with zz) 5. Be6 transposes to the main line; finally, 1...e5? loses to 2. d5 and 1...e6? loses to 2. Bg4 e5  3. d5, because White can sac his b-pawn and bishop for the a- and e-pawns, while Black has only his king to block the d-pawn and will soon face zz] 2. Kh7 Kh8  3. d5 Kg8  4. Bg4 Kf8  5. Be6 Ke8  6. Kh8 Kf8  7. Bf7 Kg8  8. Kh7 Kf8 (or 8...Kh8  9. Bg8 with a similar zz) 9. Kg8  looks like a win for White to me, but I'm clearly missing something. 

You have a good idea and one of the important insights already, but indeed a misevaluation in your line: 1. Bxb6 Ke8 2. d5 Kd8 3. Bg4 Ke8 4. Kh7 Kd8 5. Bd7 is not zz; 5...a3! 6. bxa3 Kc7! draws.

Ah, that's very clever - I missed that after 7. d6 Kb6, the center pawns will both explode on the next move regardless of how White continues. I have an outlandish scheme which attempts to work around the issue, but of course I'll have overlooked something else.

Here's a rough sketch of the plan I currently have in mind:

After the 1st 4 moves in the above post, I'm looking at a crazy maneuver with 5. Kg8 Ke8  6. Kf7 Kf8  (6...Kd8?  7. Ke8 looks like zz, but what do I know? ) 7. Ke6!? Kf7 (appears to escape, but...) 8. Kf6!? Kf8 (Who's protecting who, now?? If 8...Ke6, I think 9. d6 wins) 9. Ke5 Ke8  10. Be6 Kd8  11. Kd4 Ke8  12. Kc5 Kd8  13. Kb6 Ke8  14. Kb7 Kd8  15. Kc8 Ke8  16. Bg8 Kd8 (or 16...Kf8  17. Bf7 with a similar zz) 17. Bf7 Kc7  18. d6 Kb6  19. d7 etc.

So yeah, that's the idea, although I doubt it works. Even if it does work, I still need to verify that Black's king can be forced to d8 (or else Kg8 is never possible due to Kf7, followed by Kf6 with a draw), and that other lines from my previous post aren't compromised.

Verify away, then. For black's absolute best defence though, do note that the a4 pawn is on a light square and is vulnerable.

Okay, let's try this:

1. Bxb6 Ke8 (1...Kg8  2. Kh7 Kf8  3. d5 Ke8  4. Bg4 Kd8  5. Kg8, etc.) 2. d5 Kd8 (2...Kd7?  3. d6) 3. Bg4 a3 (3...Ke8?  4. Bd7+) 4. bxa3 Ke8 (4...Kc7?  5. d6+) 5. Bf5 Kd8 (5...Kf8?  6. Bd7 Kg8  7. Kh7 Kf8  8. Be8 Kg8  9. Bf7+ Kf8  10. Kg8, with zz) 6. Kg8 Ke8  7. Kf7 Kf8  8. Ke6! Kf7  9. Kf6! Kf8+ (9...Ke6?  10. d6) 10. Ke5 Ke8  11. Be6 Kd8  12. Kd4 Ke8  13. Kc5 Kd8  14. Kb6 Ke8  15. Kb7 Kd8  16. Kc8 Ke8  17. Bg8 Kd8 (or 17...Kf8  18. Bf7 with a similar zz) 18. Bf7, zz and 1-0

Almost correct. 5. Bf5 isn't most optimal, 5. Bh4 is better - the reason is that in your main line, 8. Ke6? Kf7 9. Kf6 (else 9...Kf6) e6! threatens exf5#, so ...exd5 is next with a draw. Other than that, great solution.

I underestimated problemists once again. You've had the right main idea for a long while, which is not easy to see - and without a stipulation, most atomic players would probably misevaluate the position. Congratulations.

Not surprised I missed 9...e6 there, since by then I was "analyzing" without a board.  

I definitely wouldn't say you underestimated problemists, though - the only problemist (besides yourself) to comment on the study so far has been anselan, and he made no attempt to solve it!  Plus, I was fooled by this problem multiple times, despite being on the right track, so I think I should be congratulating you on your terrific composition... not the other way around. Bravo! 

and this is a variation of what you showed me before, it seems