Homeworlds - Monopoly

Question

Lee wins in 5 turns (click the image for a bigger version)

This puzzle is inspired by the other Homeworlds puzzles introduced by @Destructible Lemon. You should explain how Lee (the player on the left side) can beat Ray (the player on the right side) in 5 turns. Ray will of course try to prevent this if he can.

• The Homeworlds rules can be found here.
• Pieces pointing from left to right are Lees ships.
• Pieces pointing from right to left are Rays ships.
• Pieces pointing upwards are stars.

Text version:

System name     Stars    Lees ships     Rays ships

Lee             Y1B2     Y2Y1B2B1
DS1             B2       Y3Y1B1
DS2             Y2       Y3Y2B3B1
DS3             G2                      G1
DS4             R2                      R2G3
DS5             G2                      G1
DS6             R3                      R1G3
DS7             R2                      R1G3
Ray             R1                      R3

I have uploaded an Inkscape template in case you would like to create similar puzzles yourself. The background for the puzzle is from here.

Answer 1

sorry it took so long. :p

i made a diagram, which has moves which don't need specific spaces (i think?) have specific spaces.

(the yellow blue ship is because it doesn't matter which of blue or yellow is captured and either could be but like i guess i didn't need to do that)

turn 1: transmute a large to red (ray builds a small green)
turn 2: transmute a medium to green (ray sacrifices and builds a small green)
turn 3: sacrifice medium green, build two larges (careful not to catastrophe anything) (ray builds medium green)
turn 4: sacrifice a yellow large, move 3 nonred larges to rays homeworld, ray sacrifices medium red to capture 2 of these larges
turn 5: sacrifice red large to capture all of rays ships at his homeworld, winning.

Answer 2

Turn 1: sacrifice yellow large at homeworld, move blue large and yellow large (remaining one) to DS4 and DS3 respectively. also move a yellow small to DS3

if ray chooses to catastrophise either of DS4 and DS3, we will be able to change some of our pieces to reds next turn, and explode his homeworld on turn 3. if he does not do something, we are able to catastrophise with our large blue changing the large yellow to green or red, and using the remaining two changes to change some pieces on DS 1 and 2 to red before exploding the homeworld on turn 3. in fact, if he does not get rid of the large red, something will be catastrophised. so he builds it on his homeworld, by sacrificing a green on DS3 (small) to build, so it cannot be catastrophised in one turn.

turn 2: we would like to attack and capture a red, but Ray would just capture back. we will instead sacrifice a blue large to change the two yellows to greens, and catastrophise the system. we now have 3 reds in the bank. use the remaining change to swap a the small in DS1 to a red.

Ray's response. Ray currently can't do anything except sacrifice pieces for no goal, or catastophise something. the best such one would be sacrificing a red at his homeworld

Turn 3: swap the medium yellow at DS2 to a red.

Ray's response. he has none. he can't build to help himself, a catastrophe at this point is pointless for him.

turn 4 sacrifice a yellow medium to move both the reds at Ray's homeworld, regardless of his last move. catastrophise.

What'd I miss? how come it worked so quickly? oh wait i know. he could have sacrificed his medium and... nope, that doesn't save him. capturing the yellow allows the system to be catastrophed the next turn, and setup to ray losing next turn. Oh i see... I think it's because he could've prevented the use of the smalls by... wait nvm if he kept a small with him to prevent it from being built, it would have been a liability in the end anyway. actually, it might have slowed Lee down... let me see...

---

Turn 1: sacrifice yellow large at homeworld, move blue large and yellow large (remaining one) to DS4 and DS3 respectively. also move a yellow small to DS3

Ray responds by sacrificing a green 2 in DS3, building red in DS3, overpopulation, and building the red small at his homeworld

turn 2: sacrifice medium blue, catastrophe DS4, change small blue to red.

ray: can't do anything but remove a red, or build a green, or steal a yellow. stealing yellow means instant loss (red catastrophe).

turn 3: change something else to red: yellow at DS2. ray: build or nothing. either way he's doomed

turn 4: move red pieces to Ray's homeworld, catastrophe, win.

---

still not five...

please point out what i did wrong?

---

Monopoly is because both players have a monopoly on at least one colour at at least one point in the game (Ray monopolises red).

Answer 3

The position, in my notation, is this:

Lee (0, y1b2) y1y2b1b2-
DS1 (b2) y1y3b1-
DS2 (y2) y2y3b1b3-
DS3 (g2) -g1
DS4 (r2) -r2g3
DS5 (g2) -g1
DS6 (r3) -r1g3
DS7 (r2) -r1g3
Ray (1, r1) -r3

The stash contains r3y3g1g2b3b3.

Notice that Ray has no yellow (so he can't move to new systems), and no blue (so he can't get new colors of ship). So he can't do anything except build red and green at the systems he already controls. (And of course sac red to do nothing, and sac green to teleport it around.)

For Lee to win, he'd have to do one of the following:

1. Catastrophe red at Ray. This requires moving in two red, which he can't get unless Ray cooperates.
2. Capture Ray's r3. This requires moving in enough big ships that Ray can't capture them all at once. Ray has an r2 to sac at DS4, but Ray doesn't yet have an r3 to sacrifice, and Lee can deny him the remaining r3 from the stash.

So Lee's overall strategy seems to be "build r3 to keep Ray from getting it; then build three big ships within one hop of Ray; then sac y3 to move them all in; Ray captures two of them; sac r3 to capture all of Ray's ships and win."

The final step could be "trade for red to blow up Ray's star"; but in that case Lee would have to have wrested some red from Ray's hands — either into Lee's ships or back into the stash. I don't see how that could happen.

Lee currently has three big ships, but he needs two more. So Lee's top priority is to keep the r3 out of Ray's hands... and also to get some green so Lee can build more ships.

Here is Lee's line assuming that Ray doesn't do anything to interfere (e.g. if Ray just does pass every turn). This is Destructible Lemon's solution, modulo a bugfix: Lemon forgot that Lee's second move returned a b2, so building b3 on the third move is impossible.

1. trade y3 r3 at DS1 - pass
2. trade b2 g2 Lee - pass
3. sac g2; build y3y3 at DS1 - pass
4. sac y3 at DS1; move y3 from DS1 to Ray; move y3b3 to Ray (checkmate)

However, Ray can interfere right on turn number 1!

1. trade y3 r3 at DS1 - sac g3 DS7; build g1 DS6; build g2 DS3; build g3 DS5! Now Ray has a green monopoly, and Lee is stymied:
2. sac y2 Lee; move r3 from DS1 to DS6; move r3 from DS6 to DS3 - sac g2 DS3
3. capture g1 - ...I don't think this line works at all.

Or, Lee could try to soak up the r3 by placing it as a star. Lee might also gain access to green at the same time (by discovering a g1 star, or by invading DS5); but either way, Lee won't gain a saccable g2, which means he won't be able to get the two additional big ships he needs in order to checkmate in four. (Lee can't even use a blue ship to discover a g2 star and then sac the blue to trade for the g2 — a variant of the "investment" strategy — because Lee can't reach a g2 star in only one hop, and if he sacs a y3 to reach it in two hops, that leaves him even further from his goal of five big ships.)

Or, Lee's line could start with getting that g2; but then the whole thing goes right off the rails immediately:

1. trade b2 g2 Lee - sac g3 DS6; build g1 DS4; build g3 DS7; build r3 Ray
2. move b3 to DS6 (?) - sac r1 at DS6

Or, better, Lee's line could start with getting both green and r3 in one fell swoop:

1. sac b3 at DS2; trade y3 r3 at DS2; trade y2 g2 at DS2 - pass
2. build b3 - pass
3. sac g2; build b3 at DS1; build b3 at DS2 - pass
4. sac y3 at DS1; move b3b3 from DS2 to Ray; move b3 from DS1 to Ray (checkmate)

Can Ray screw up this plan? Well, Ray is limited to shuffling around reds and greens, and after Lee's first move, Lee doesn't care about the distribution of reds and greens. Lee's ships never share a system with Ray's, so Ray can't interfere by capturing or catastropheing. But, Ray could still gain that second r3, like this:

1. sac b3 at DS2; trade y3 r3 at DS2; trade y2 g2 at DS2 - sac r1 at DS6
2. build b3 - sacrifice g3 at DS6; build r1 at DS4; build g1r3 at DS7! At this point, Ray has gotten his second r3 and his homeworld is impregnable.
3. sac g2; build b3 at DS1; build b3 at DS2 - pass
4. sac y3 at DS1; move b3b3 from DS2 to Ray; move b3 from DS1 to Ray (check) - sac r3 at DS7; capture b3b3b3 at Ray!

I don't think Lee can do anything to stop Ray from doing that.

So, I think this puzzle is still flawed, and Lee cannot force a win in 5.