Homeworlds: War Games

Here's my second Homeworlds problem! (My first was Homeworlds: Mini Doomsday Machine.)

Lee (0,g3b2) y2g1-
Ray (1,r2) r2-y3y3y3
DS1 (y1) -y1g3
Y (y2) r1-y1
G (g2) r2-g2
R (r3) g1-r1
B (b3) r1-b1


The stash contains r3r3 y2 g3g2g1 b3b3b2b2b1b1.

So... it is down to me, and it is down to you.

If you capture my red ship, you threaten to invade with r1r1.

If you capture my yellow ship, you threaten to invade with y1.

If you capture my green ship, you threaten to build r3r3.

If you capture my blue ship, you threaten to trade r2 for y2.

The battle of wits has begun. It ends when you decide and we both move, and we find out who is right... and who is dead.

Lee to play and mate in 1. (That is, you must find the unique move which Lee can make, such that no matter what Ray replies, Lee will win on the very next turn.)

• @melfnt Why that edit? Homeworlds isn't a video game, and we have enough puzzles about it that it makes sense for it to have its own tag. – Joseph Sible-Reinstate Monica May 31 '20 at 19:30
• (I've rolled the edit back.) It'd be nice for someone to tag the other Homeworlds puzzles with [homeworlds], btw. I tried doing that myself but got shot down. – Quuxplusone May 31 '20 at 20:09
• @JosephSible-ReinstateMonica there are only two puzzles tagged [homeworlds] and that tag does not even have description nor excerpt. My bad I didn't know it is not a videogame – melfnt May 31 '20 at 20:42
• @melfnt: If you look at the related items in the right sidebar (especially the ones explicitly linked from "Mini Doomsday Machine"), you'll find 4 more Homeworlds puzzles without the [homeworlds] tag. – Quuxplusone May 31 '20 at 20:45
• @Quuxplusone I added the tags just now :) – melfnt May 31 '20 at 20:46

Homeworlds is new to me, so please forgive any misunderstandings or mistakes :)

Proposed solution:

Sacrifice g1 at R to build r3 at Ray.

This creates a powerful threat of sacrifice y2 at Lee to move one of several red ships (r1 at Y, r1 at B or r2 at G) to Ray which wins by a red catastrophe.

Ray can't remove the red ships already at Ray. (Catastrophe is clearly not an option, and capturing the ships will leave them in place.)

Ray has only an r1 red ship, so can't capture all three of Lee's red ships that threaten to invade Ray. It is also impossible to eliminate all the attackers by catastrophe.

The only way Ray can cause trouble at Lee is by catastrophe. This is possible by sacrificing y3 at Ray to move g3 at DS1 and g2 at G into Lee. This catastrophe leaves the y2 as the last defender of the homeworld which can't be sacrificed on the following turn[*]. This seems to be the only defense. (Conveniently, this also defends the alternate threat of sacrifice g1 at Lee to build r3 at Ray.)

However, Lee can now win with a sacrifice of r2 at G to capture both remaining defenders of Ray.

[*] If I understand the rules correctly, this sacrifice would be allowed if Lee used it to move another ship back to Lee by the end of the turn, but there is no ship close enough to do this and also press the attack.

Refutations of some alternatives:

Sacrificing g1 at Lee to build r3 at Ray doesn't work as above, as sacrificing y2 is no longer possible and thus not a threat. There is another threat to cause catastrophe at Ray by sacrificing g1 at R to build the last r3, but this can be refuted by capturing g1, building r3, or exploring r3.

Simply capturing at R or Y can be refuted by the catastrophe line pinning y2 at Lee (as there is no capture threat at Ray).

Simply capturing at B or G is refuted by capturing at Ray.

Sacrificing r2 at G for a double threat is more convincing, but the catastrophe line defends them all simultaneously. (It defends the trade threat by sacrificing y3.)

Sacrificing y2 at Lee actually loses to the catastrophe.

• Correct! FWIW, I didn't understand what you meant by "all three attackers" at first. You might clarify that by "attackers" you mean the three red ships mentioned 2 paragraphs earlier. Saying "potential attackers" or "threatening ships" would be an improvement, too; colloquially I would call a ship "attacking" only if it were already in a contested system, threatening a capture action on its next turn. (Of course there's no formal definition of "attacking" in Homeworlds, but that's how I'd informally interpret the word.) Other than that wording nit, this looks like a perfect analysis! – Quuxplusone Sep 1 '20 at 18:34
• I showed the problem to one of my game buddies this Monday; we solved it together in less than 20 minutes, after I refuted some of his answers. If no answer had been formulated today, I would've entered it. Despite the number of hours I spent, it was definitely worth it. And @tehtmi, you are certainly on your way to get better at this game! – Cuc Sep 3 '20 at 6:39

Am I the first with a good idea? Here is my second attempt:

Lee: S G1 Lee / B R3 Ray
Lee threatens to build another Red with a sac of his G1 at R. So, Ray will capture the G1. Ray: C G1 R, however,
Lee: C G2 G -- Lee has now potentially two builds. Can Ray build the last Red to prevent Lee from building Red? Well, Ray has only Red in R and in his HW. So, he must build it at R.
Ray: B R3 R -- But now Lee can move his R1 from Y to R:
Lee: M R1 Y R / Cat R R -- and now the Bank contains 4 Reds. No matter what Ray does now, Lee will build 2 Reds at his next move.
Ray: C R3 Ray (this prevents a double capture)
Lee: S G2 G / B R Ray / B R Ray / Cat R Ray / GO.

Yes, this is an EXTREMELY difficult problem. But can Lee even win if Ray has an R3 as part of his HW and an R2 (instead of an R1) at R?

• Sadly, incorrect. After Lee's first move, Ray could prevent your continuation via "sac r1 at R; capture r2 at Ray"... oh wait, also, Lee does not have a g2 at G! The g2 at G is Ray's ship, not Lee's. – Quuxplusone Aug 25 '20 at 14:47
• @Quuxplusone How do you make an unscalable font? I couldn't align everything nice, like in your example. If I know how to, I will align the moves. – Cuc Aug 26 '20 at 9:42
• By "unscalable font" you mean monospace/teletype like this? Put backticks around it, or indent a whole paragraph four spaces. You can also "edit" my question to see its exact Markdown code (and then cancel or close your browser tab instead of submitting the edit, of course). Also, add 2 spaces at the end of a line to create a linebreak — or just use an HTML <br>. – Quuxplusone Aug 26 '20 at 17:12
• Second attempt: Better, but still incomplete. IIUC, you're describing a line of play that leads to GO (Game Over), but only on Lee's 4th move, whereas the puzzle asks for the play that inevitably leads to GO on Lee's 2nd move (plus a proof that it is inevitable; i.e., you should demonstrate that you've considered all of Ray's possible replies). Bonus nerdsnipe puzzle: You imply that Ray must reply to sac G1 Lee / build R3 Ray with capture G1 R or else lose immediately; but I believe I see at least one other possible reply! – Quuxplusone Aug 27 '20 at 22:29
• Btw, if you make a third attempt, I recommend doing it as a new answer, not an edit on this answer, because every edit you make to this answer invalidates my old comments. If you ever get it right, the "Sadly, incorrect" comment will be sadly incorrect! – Quuxplusone Aug 27 '20 at 22:30

I finally see it. It was a real challenge. Wow.

Lee S R1 Y / C G2 G
Now, I solved the problem of the Bank. Lee has a G2 to build 2 Red ships in Ray, unless Ray builds at least 2 Red ships. But to do that, Ray has to sac his G3. Can Ray build 3 ships? Well, yes, he could build all of them at R and not call catastrophe, but Lee will be able to at the start of his turn. So, perhaps he needs only to build 2 Red ships? Again only at R, otherwise Lee could build the last ship at Ray.
Ray S G3 DS1 / B R1 R / B R3 R
Lee Cat R R / S G2 G / B R Ray / B R Ray / GO

Comment.

I tried to prevent the Green invasion. If I don't, then Ray can invade Lee. In fact, Ray can always sac a Yellow, and Lee can not cause a Yellow Overpopulation in Ray. So, Lee must somehow get 2 Red ships to Ray.

Thanks for this one! Great, great, great.

• Thanks... but still not right. :) Let's say Lee does sac r1 Y; capture g2 G, intending to build two red ships at Ray on his next turn. You're right that Ray can't prevent that by building out the red stash; but Ray has another way to prevent Lee from building two red ships at Ray! – Quuxplusone Aug 28 '20 at 13:16
• @quuxplusone. I see. Ray C R2 Ray prevents the use of Lee's G2. I'm stumped. – Cuc Aug 29 '20 at 19:29