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Ydobon

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Infinite loops
« on: December 19, 2022, 01:20:05 pm »
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It seems, like even after all the errata, there are still loopholes out there with Command cards. [I have posted the first loop using Reckless in http://forum.dominionstrategy.com/index.php?topic=21560.msg898780#msg898780]

Necromancer+Reckless Band of Misfits+Lich: Necromancer playing a Reckless Band of Misfits playing a Sentinel, trashing a BoM and a Lich to take a face down BoM from trash and put a face up BoM back in. Then we follow Reckless Band of Misfits’ instructions again and play a Necromancer from the supply to start all over.

It seems like Reckless was written so, that one cannot once play a card normally and then via a Way. Anyway, thinking about it way longer, I came up with a Way of the Horse loop [Edit: yes that is old news. Anyway look into the next post for newer work.]

Way of the Horse: King’s Court an Inventor and draw your entire deck head start. King’s Court a King’s Court, then triple an Inventor to get a new Inventor, get a new King’s Court and Way of the Horse the Inventor back to draw the newly gained cards and get it back to the supply. Also Way of the Horse the King’s Court back to the supply on its second play. Now, playing the King’s Court the third time, we can triple the King’s Court we have just drawn to triple the Inventor and start all over.
« Last Edit: December 20, 2022, 06:27:17 pm by Ydobon »
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Ydobon

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Re: Infinite loops
« Reply #1 on: December 20, 2022, 06:19:44 pm »
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Building on Carline’s and mad4math’s work partly quoted below, I compiled a new list of cards necessary for infinite loops. It seems, like many arguments from two years past, do not work as well any more, so my result ends up somewhat differently:

The list of 9 card shaped things (for two of them we may choose among three) (8 if you do not count Mandarin) I got up with:
  • Lich
  • Fortress/Priest/Traveling Fair
  • Mandarin (removed)
  • Mint
  • Improve/Reckless/King’s Court
  • Way of the Horse
  • Way of the Butterfly
  • Experiment
  • Horse

For a proof by case analysis see below. Anyway, quite likely I missed something in the proof (I added some question marks, where this seemed to be most likely to me.) So I am happy to be corrected.

I give examples containing only one of the listed cards in the post above and at the end of this post. So, no single card can be removed from the list, but perhaps there exists a list with several cards removed and less added that would also work. Any ideas anyone? Searching for more examples using different sets of cards out of this list (besides those from the list) could help.

Proof by case analysis

During the loop …
  • … never play cards, only buy …
    • … cards without moving cards: Trader (the revised version exchanges and thus stops working, when the Silver runs out). I see no other way to make this work. (?)
    • … cards and later put them back to their pile: without playing any cards, I do not see, how to put cards back to their pile. (?)
    • … events with gaining cards and later putting them back to their pile: see the point above
    • … events with gaining cards but not from their pile: Lich allows to gain from the trash using any trashing event, trashing two cards (via some Events or Sewers) allows to use the other card’s on gain and on trash effect (e.g. Nearby Cultist or from Galleria or Guildmaster). Besides Lich, I see no other option here. (?)
    • … events without gaining cards: to get back the economy needed to buy the event we trigger …
      • … trashing: Fortress+Priest+Traveling Fair with any trashing event. (With empty trash trashing Lich may also fall in this category, but there is no event for drawing cards or trashing them from the deck.)
      • … revealing: Patron: was revised to only work in action phase → not helpful
      • … discarding: all discard reactions either play themselves (not helpful), set themselves asides until end of turn (not helpful) or gain something (not helpful). Besides that, discarding may trigger shuffling, see there.
      • … shuffling: Fated reveals (see there), all other shuffle triggers only reorder or discard the shuffled cards and thus do not help
    • … play cards …
      • … without putting them into play by …
        • … playing a Necromancer: needs to regain cards from trash to turn them around. Right? See further below. → not helpful
        • … playing a Scepter: there is no way to play a non-Action without putting it into play. Right? → not helpful
        • … moving a Royal Carriage from the Reserve into play: putting in play is not helpful
        • … playing a Command card. To that end …
          • … put that Command card into play: not helpful
          • … play that Command card without putting it into play: needs Necromancer, Scepter, or Royal Carriage. Right? → not helpful
      • … and remove them from play by …
        • … getting arbitrary cards out of play:
          • Mandarin: this is known to remove arbitrary enough cards (namely treasures) out of play to enable loops, keep it. (**)
          • Mint: like Mint. Somewhat weaker. (***)
          • Improve: this is tough, but it works, perhaps it only works with Reckless King’s Court? See example below.
          • Procession: Procession chains sadly cannot trash themselves entirely. Right? (With Flagship this would work, but Procession cannot play durations.) So we either need a way to trash the Procession from play or play it without putting it into play. The first option does not help in our problem and the second is covered below. → not helpful
          • Counterfeit: works the same as Procession, so Counterfeit chains are likewise unable to trash themselves. → not helpful
          • Bonfire: the revised version does not help anymore.
        • … playing cards that trash themselves from play: we need to regain the cards from trash via …
          • … trashing a Lich: already listed
          • … playing one of the other out of trash gainers (Lurker, Graverobber, Rogue, Treasurer): this means playing cards, that do do not remove themselves from play → not helpful, but see (***)
        • … playing cards that remove themselves from play to somewhere else than the trash before clean-up (****):
          • Way of the Horse
          • Way of the Butterfly
          • Experiment
          • Horse: can be obtained via Events, needs a way to get money for those events, this is solvable.
          • Student: needs to trash a treasure, which needs to get cards out of the trash. → not helpful
          • Spoils: can only be obtained by playing a card that either (if played normally) remains in play (not helpful) or trashes itself (Pillage). So Spoils need some other ingredient to either play cards non-normally or get them out of play/trash. → not helpful
          • Wish: can only be obtained by Secret Lamp, which trashes itself or playing a Leprechaun. So, essentially the same as with Spoils. → not helpful
          • Hermit: needs to exchange itself. To that end it needs to gain Cavalry or Villa to end the buy phase. So we need a way to gain cards arbitrarily often. Gaining from trash would not allow for any new combo, so we need gaining from supply and hence a way to put cards from deck back to the supply without any of the listed cards. Only Ambassador and Swap do that trick, but they need to get played, resulting in the problem above. → not helpful
          • Madman: needs to exchange Hermit. → not helpful as just argued
          • Stockpile: needs to get the Stockpiles back from exile. We can only get cards from exile via Transport (but Stockpile is no Action) or by gaining those cards.
        • … playing cards that remove themselves from play to somewhere else at the start of clean-up: we would need to trigger some reaction to play those cards during start of clean-up, then trigger their remove reaction, then repeat. Besides moving cards, the triggers during start of clean-up come from:
          • Friendly: can be used only once per turn → not helpful
          • Improve: needs to be played as part of the loop. Actually useful for its ability to trash cards from play. See above.

    (**) When we gain the Mandarin we either need to trash Mandarin and gain it from trash (see the note below) or put it back to the supply using Trader (old one or new but then we must put the Silver back to its supply), Changeling (same problem as with new Trader), Swap or Ambassador (e.g. with Scepter).
    (***) When using Mints on gain trashing, we need to get the cards back from trash. So we can either add four cards for gaining from trash or three cards: Mint, Mandarin and Improve.

    (****) There are numerous possibilities to play and gain those self removing cards over and over: Possibilitites include Rush, City State+Guildmaster, fun with King’s Court or King’s Cache+Scepter. The necessary buys may come from the adventure token or Nearby among others. So, I am confident, it is more efficient to list those two Ways and two cards, than finding a bottleneck among enablers to gain and play them.

    In the following, I use Nearby to get buys. Adventure tokens work just as nice.

    Using Guildmaster+City State we get the following loops:
    Experiment: play two Guildmasters and enough cost reduction head start. Buy Nearby Experiment, play both gained Experiments with City State. Repeat.
    Way of the Horse/Butterfly: play two Guildmasters and enough cost reduction head start. Buy Nearby card and play it with City State applying the Way. Repeat.
    Horse: play two Guildmasters and a Galleria head start. Buy Ride and play the Horse you get with City State and Way of the Chameleon. Repeat.

    With Berserker and the Ways we get another loop:
    Way of the Horse/Butterfly: play enough cost reduction head start. Buy Nearby Berserker and play it as the Way. Repeat.

    With Fortress and trashing Events, there are several loops, I assume. One well known works with Advance and Traveling Fair+Priest. Costlyer Events will work with more Priests.
    Fortress: Play Priest head start. Buy Advance, trash Fortress from hand, gain any card you like (if there are any left), buy Traveling Fair. Repeat.

    mad4math built loops with Mandarin and Mint.
    Mandarin only loop

    play scepter playing lurker. gain mandarin from the trash, reveal watchtower to trash it. two scepters and your favorite treasure are topdecked.
    play your favorite treasure
    play scepter playing smithy, drawing the two scepters and your favorite treasure.
    With Trader not working anymore as before, I had to rewrite the Mint loop, now using King’s Cache for mostly useless repetitions (only a surplus of one for the Lurker was really needed) based on mad4math’s work.
    Mint: buy toil, playing King’s Cache
      play King’s Cache thrice
        play Scepter playing Treasurer thrice, gaining 2 King’s Courts to your hand and taking the Key
        play Scepter playing Treasurer thrice, gaining 3 Scepters to your hand
        play Scepter playing Lurker, gaining Mint from the trash
          trash 2 King’s Courts and 3 Scepters from play
        play Scepter again, playing a Worker’s Village or the like for +1buy and drawing the Mint from discard
        play Scepter again, playing a Chapel or anything for trashing the Mint

    The Improve example is tough. I assume an Improve loop without the other listed cards relies on Reckless King’s Court. So I add this as alternative to the list. In the example the Inspiring can probably be exchanged by 1 cost reduction, Graverobber topdecking a King’s Court and Sheepdog playing Way of the Mouse Vassal. I guess, it is possible to get rid of the Sheepdog as well. Though, I currently do not know how.
    Improve: During start of clean-up: Resolve an Improve trigger, gain a card, react to the gain and play an Inspiring Sheepdog followed by 3 Reckless King’s Courts tripling 5Lurkers+2Rogues (gain 4 King’s Courts, 7 Improves, 5 Lurkers + 2 Rogues, 1 Scrying Pool, 1 Sheepdog, and 1 Necropolis), a Scrying Pool (draw your deck), and 1 more Reckless King’s Court (17 tripling in total, 8 of them already used, 9 more will be used), triple 1 Necropolis, 1 Encampment, and 7 Improves; resolve the Encampment returning to Supply, resolve the Improves (trash 4 King’s Courts, 7 Improve, 5 Lurkers + 2 Rogues, 1 Scrying Pool, 1 Sheepdog, and 1 Necropolis gaining 1 Encampment). React to the gain with the Inspiring Sheepdog and repeat.


    For reference, here are the lists of cards necessary for infinite loops, that mad4math and Carline compiled before.
    Thus, I would guess that the list is just:
    Mandarin
    Mint
    Way of the Butterfly
    Way of the Horse
    Fortress
    Bonfire
    Forum
    This list (with credits also due to Carline) is similar to mine, although Forum seems unnecessary, Bonfire does not work anymore. Lich and the revised Patron are new and Experiment, Horse, and Improve are missing.
    That said, you can’t do an infinite loop without one of these cards:

    - Villa
    - Cavalry
    - Scepter
    - Capitalism
    - Gamble
    - Toil
    - March
    - King’s Court
    - Trader
    This list is rather different due to an approach that with today’s cards would result in a list quite longer (I think).

    Well, that is it. Any thoughts about my list? Corrections?
« Last Edit: December 21, 2022, 06:23:31 am by Ydobon »
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Ydobon

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Re: Infinite loops
« Reply #2 on: December 21, 2022, 03:51:05 am »
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Patron+Pursue: buy Pursue, reveal 4 Patrons for +4 Coffers, spend 2 Coffers. Repeat.

I missed this one for the item of only buying events without gaining and playing cards. With the new Coffers ruling, Patron seems to be pretty useful for loops. Here are some more Patron examples with Fated:

Buy Scouting Party, shuffle 3 Fated Patrons revealing them for +3 Coffers, draw and discard them, spend 2 Coffers. Repeat.
Buy Gamble, shuffle 1 Fated Patron revealing it for +1 Coffer, revealing it with Gamble for +1 Coffer, spend 2 Coffers. Repeat. [Probably useless time waster]

I guess, using the Fated trait moves the card and so Avoid cannot move it as it is not among the to-be-shuffled cards where expected, right? Otherwise, every Avoid bought would yield +$1 on the next shuffle by discarding 3 uselessly revealed Fated Patrons which could make the Gamble loop above productive.

In the Fortress case, it seems, that Priest is the only way to produce any useful economy on trashing cards. So without ever gaining or playing or using Patron, we need Priest in the Fortress loop as well as Traveling Fair to produce the +buy we need. For the trashing events we can choose among Advance, Enhance, Maelstrom, Peril and Trade.

I will update the previous post accordingly.
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grrgrrgrr

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Re: Infinite loops
« Reply #3 on: December 21, 2022, 03:55:19 am »
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Patron+Pursue: buy Pursue, reveal 4 Patrons for +4 Coffers, spend 2 Coffers. Repeat.

I missed this one for the item of only buying events without gaining and playing cards. With the new Coffers ruling, Patron seems to be pretty useful for loops. Here are some more Patron examples with Fated:

Buy Scouting Party, shuffle 3 Fated Patrons revealing them for +3 Coffers, draw and discard them, spend 2 Coffers. Repeat.
Buy Gamble, shuffle 1 Fated Patron revealing it for +1 Coffer, revealing it with Gamble for +1 Coffer, spend 2 Coffers. Repeat. [Probably useless time waster]

I guess, using the Fated trait moves the card and so Avoid cannot move it as it is not among the to-be-shuffled cards where expected, right? Otherwise, every Avoid bought would yield +$1 on the next shuffle by discarding 3 uselessly revealed Fated Patrons which could make the Gamble loop above productive.

In the Fortress case, it seems, that Priest is the only way to produce any useful economy on trashing cards. So without ever gaining or playing or using Patron, we need Priest in the Fortress loop as well as Traveling Fair to produce the +buy we need. For the trashing events we can choose among Advance, Enhance, Maelstrom, Peril and Trade.

I will update the previous post accordingly.

The Gamble Patron loop has already been addressed through errata. (Namely by restricting Patron's reaction to the Action phase)
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Ydobon

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Re: Infinite loops
« Reply #4 on: December 21, 2022, 06:24:59 am »
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The Gamble Patron loop has already been addressed through errata. (Namely by restricting Patron's reaction to the Action phase)
Thanks, updated my post accordingly.

Also added a new loop with Improve. I would be glad about any help getting rid of the Sheepdog in that loop, if anyone wants to puzzle.
« Last Edit: December 21, 2022, 06:29:38 am by Ydobon »
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Donald X.

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Re: Infinite loops
« Reply #5 on: December 23, 2022, 01:04:03 am »
+4

It's possible that Necromancer will become a Command card after all, whenever Nocturne next gets reprinted.
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