Dominion > Puzzles and Challenges
The Challenge #1 Most Coins in a Turn
jakav:
There just aren't many puzzles or challenges going on or getting started right now, so I thought it would be fun to do a slower challenge, but on focused on puzzles.
This challenge would last about 2 weeks each, and there would be a new topic for each challenge so that discussion could be continued. Topics for the challenge would basically include anything that is not going on in the current two challenges.
Should we do it?
Either way, this challenge is to make a board in which the highest amount of coins in one turn is possible, but they are still limited (so no coffers). You do not have to post your solution, just how many coins you got, until the contest ends, on March 14th. Have fun!
More Specific Rules
The solution can assume perfect shuffle luck, but should be possible on Dominion Online (given an infinite amount of tries). It can have any number of buildup-turns, just like the How High Can You Go puzzle. The board cannot go infinite.
ephesos:
Lich is a fancy new card, so I kind of want to try using it. Normally, I'd Priest chain with King's Court to trash N Fortresses and gain O(N^2) money. With Lich, you can trash it to gain cheaper cards back from the trash, so you can instead Procession the Priests. The limiting factor is then instead how many Procession plays you can do; because the first Procession you play cannot be played with Procession, you eventually end up with all the Processions in play, and all the Priests shortly afterwards, so you can't go infinite.
Let's say you play the first Procession ("Procession 1"). Each time Procession 1 is played, it plays Procession 2 twice, so that's 2 plays of Procession 2, 4 plays of Procession 3, etc. for 2^(N-1) plays of Procession and thus 2^N plays of Priest. With Inheritance on Procession, we can increase N by the number of Estates in the game. Supposing a 4 player game where every Estate was passed to you by Ambassador/Masquerade/etc., you can get 24 more Processions. Band of Misfits gets you 10 more, though you have to keep 1 Procession in the Supply. So that's 43 Processions total.
I think Captain can go infinite with this setup, so I won't risk it. I think you can stack up Duration plays of Procession to play more and more Captains each turn. Necromancer might work for 10 more Processions, but I can't figure out how to keep a Procession in the trash since Lich is mandatory, so I'll skip it.
Overlord can't be gained back by Lich, but you can use it to start the chain. Each Overlord can play Procession 1 twice, and you can play Overlord 30 times with King's Court, so that's 60 * 2^43 Priest plays.
To handle card draw issues, you can use Band of Nomads (along with some infinite buildup of Favors from previous turns using Student) and put a +1 Card token on Priest. You only need to draw back Lich and the card you fetch from the trash (if any), so that should be enough draw by itself.
N Priest plays gives O(N^2) money, so overall that's 3600 * 2^86 coins. Add in a Fortune to double it again for 2600*2^87, which, since I like seeing big numbers spelled out, is 402,330,512,767,748,589,342,215,372,800 coins.
I think you can optimize a bit further probably, there's still more room for extra cards. I'm only using Procession, Band of Misfits, King's Court, Overlord, Priest, Lich, Ambassador/Masquerade, and Fortune. I only need one copy each of the last 3, so those can be from a Black Market (depending on your feelings about split plies like Wizards and Gladiator/Fortune). So I only use 6 Kingdom cards. For events, there's Inheritance, and since Teacher can't be in the Black Market deck, we need to include Pathfinding or add another Kingdom pile. But that's still only 1-2 sideways cards.
As to whether this is doable on Dominion Online or not, it relies on having around 60 * 2^43 Favors from Student. If you click really quickly, you might be able to play like 10 Students a second, at which point it will take you about 1.67 million years to finish collecting the required Favors. So I probably won't be playing it out anytime soon.
Holger:
--- Quote from: ephesos on March 04, 2022, 07:14:53 pm ---Let's say you play the first Procession ("Procession 1"). Each time Procession 1 is played, it plays Procession 2 twice, so that's 2 plays of Procession 2, 4 plays of Procession 3, etc. for 2^(N-1) plays of Procession and thus 2^N plays of Priest. With Inheritance on Procession, we can increase N by the number of Estates in the game. Supposing a 4 player game where every Estate was passed to you by Ambassador/Masquerade/etc., you can get 24 more Processions. Band of Misfits gets you 10 more, though you have to keep 1 Procession in the Supply. So that's 43 Processions total.
--- End quote ---
That's a great idea to get lots of Priests into play. But it assumes that you can re-play each Procession immediately after it has been trashed, which is not possible since Priest is not played and thus Lich is not triggered inbetween two Procession plays.
But I think you can salvage the idea by playing only N/2 Processions and keeping the others in your hand, for 2^(N/2) Priest plays. Then you can use those Processions from your hand to continue the chain, while some of the next Priest plays gives you back the Processions from the trash for later use.
On the positive side, since this process trashes 1+2+4+...+2^(N/2-1)=2^(N/2) - 1 cards and retrieves at most 2^(N/2) cards from the trash, you can easily keep one Procession in the trash and add Necromancer to increase N by 9 to 52, to get 2^(N/2)=2^26. (Letting Lich always gain turned-over Processions when possible, so that Necromancer doesn't run out of Processions it can use.) So with Overlord and King's Court you'd get 60*2^26 Priest plays.
Holger:
Actually, we only have N=7+24+10+10=51 "copies" of Procession as there's 3 Procession cards that we cannot play (one in the supply for BoM, one in the trash for Necromancer, and one set aside for Inheritance). For odd N, we can alternate between a chain with (N+1)/2 Processions and a chain with (N-1)/2 processions between two consecutive Overlord plays.
Without cost reduction, I think Captain can't lead to infinity since it cannot be recovered from the trash. So playing 10 Captains on the previous turn, Masterminded for good measure, lets you play 30 more "Procession chains" for 90*(2^26+2^25)/2=270*2^24 Priest plays in one turn, with the following "full" kingdom (10 kingdom cards, 2 landscapes):
Non-supply cards used:
ephesos:
--- Quote from: Holger on March 07, 2022, 12:43:01 pm ---
--- Quote from: ephesos on March 04, 2022, 07:14:53 pm ---Let's say you play the first Procession ("Procession 1"). Each time Procession 1 is played, it plays Procession 2 twice, so that's 2 plays of Procession 2, 4 plays of Procession 3, etc. for 2^(N-1) plays of Procession and thus 2^N plays of Priest. With Inheritance on Procession, we can increase N by the number of Estates in the game. Supposing a 4 player game where every Estate was passed to you by Ambassador/Masquerade/etc., you can get 24 more Processions. Band of Misfits gets you 10 more, though you have to keep 1 Procession in the Supply. So that's 43 Processions total.
--- End quote ---
That's a great idea to get lots of Priests into play. But it assumes that you can re-play each Procession immediately after it has been trashed, which is not possible since Priest is not played and thus Lich is not triggered inbetween two Procession plays.
But I think you can salvage the idea by playing only N/2 Processions and keeping the others in your hand, for 2^(N/2) Priest plays. Then you can use those Processions from your hand to continue the chain, while some of the next Priest plays gives you back the Processions from the trash for later use.
On the positive side, since this process trashes 1+2+4+...+2^(N/2-1)=2^(N/2) - 1 cards and retrieves at most 2^(N/2) cards from the trash, you can easily keep one Procession in the trash and add Necromancer to increase N by 9 to 52, to get 2^(N/2)=2^26. (Letting Lich always gain turned-over Processions when possible, so that Necromancer doesn't run out of Processions it can use.) So with Overlord and King's Court you'd get 60*2^26 Priest plays.
--- End quote ---
Yeah, that might be an issue. I think you can optimize it a little by only keeping Processions around when they're needed. Essentially, you can swap a Procession play for a Priest play at any time, so if you're out of Processions at step k of the tree, you can get 2 Processions back by sacrificing 2^(N-k) - 2 Priest plays. So it's somewhere in between 2^(N/2) and 2^N.
e.g. for N=6:
play P1
play P2
play P3
play P4
play P5
play Priest twice, then trash it
play P5 again
play Priest twice, gaining the trashed Priest
trash P5
play P4 again
play P6
play Priest twice, gaining P5
play P6 again
play Priest twice, gaining Priest
trash P6
trash P4
play P3 again
play P5
play Priest twice, gaining P4 and P6
play P5 again
play P4
play Priest twice
play P4 again
play Priest twice
trash P4
trash P5
trash P3
play P2 again
play P6
play Priest twice, gaining P4 and P5
play P6 again
play P4
play P5
play Priest twice, gaining P3
play Priest twice
play P4 again
play P3
play Priest twice, gaining P5
play P5
play Priest twice
play P5 again
play Priest twice
trash P5
trash P3
trash P4
trash P6
trash P2
Not sure if that's completely optimal, but it's somewhere between 2^(N/2) and 2^N. Possibly a linear factor times 2^(N/2)?
The trashing calculation is a little off since the last N cards are trashed after all gains have been made, but you can just start with N Coppers in the trash if you need to. That said, I think with Necromancer you might be able to cheat the 1 Procession in the trash requirement by starting your chain with Necromancers, then gaining back the trashed Procession at the end. Since you end a Procession chain before you have to replay Necromancer, you'll always have a freshly trashed set of Processions available to use. Though it might get tricky when you factor in having to shuffle in a Procession somewhere because all your Necromancers are still in the trash.
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