Dominion Strategy Forum
Dominion => Dominion General Discussion => Topic started by: Carline on April 22, 2020, 07:43:20 pm
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Which are all the cards and landscapes in Dominion that are essential to make infinite loops? I mean, the ones that if you remove them from the game no infinite loop would be possible.
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There is no definite answer to this, because some cards only cause infinite loops in a combination with others (Forum + Trader is a simple example). We can come up with some smallest set, but it won't be unique.
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Well partly we need to define how simple an infinite loop is allowed to be. Simply having Moat (http://wiki.dominionstrategy.com/index.php/Moat) along with any attack card can create an infinite loop of revealing Moat forever. Though you could also be slightly more creating by revealing Secret Chamber (http://wiki.dominionstrategy.com/index.php/Secret_Chamber) and changing around your hand forever.
If you mean an infinite loop in which you gain at least some value out of performing the action forever, then you have a pretty simply one with Forum (http://wiki.dominionstrategy.com/index.php/Forum), Highway (http://wiki.dominionstrategy.com/index.php/Highway) (or any cost reduction), Trader (http://wiki.dominionstrategy.com/index.php/Trader), and Goons (http://wiki.dominionstrategy.com/index.php/Goons) (or Merchant Guild (http://wiki.dominionstrategy.com/index.php/Merchant_Guild)).
Other than that, most infinite loops involve King's Court; removing that eliminates a lot of possibilities. The most recent version of "Empty the Supply on Turn 1 (http://forum.dominionstrategy.com/index.php?topic=17800.0)" that we had relied on several different specific cards; although doesn't work with the new Band of Misfits (http://wiki.dominionstrategy.com/index.php/Band_of_Misfits) errata.
So basically, there's no simple answer to this question; you would have to remove a lot of different cards in order to have no infinite loops left.
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Well partly we need to define how simple an infinite loop is allowed to be. Simply having Moat (http://wiki.dominionstrategy.com/index.php/Moat) along with any attack card can create an infinite loop of revealing Moat forever. Though you could also be slightly more creating by revealing Secret Chamber (http://wiki.dominionstrategy.com/index.php/Secret_Chamber) and changing around your hand forever.
If you mean an infinite loop in which you gain at least some value out of performing the action forever, then you have a pretty simply one with Forum (http://wiki.dominionstrategy.com/index.php/Forum), Highway (http://wiki.dominionstrategy.com/index.php/Highway) (or any cost reduction), Trader (http://wiki.dominionstrategy.com/index.php/Trader), and Goons (http://wiki.dominionstrategy.com/index.php/Goons) (or Merchant Guild (http://wiki.dominionstrategy.com/index.php/Merchant_Guild)).
Other than that, most infinite loops involve King's Court; removing that eliminates a lot of possibilities. The most recent version of "Empty the Supply on Turn 1 (http://forum.dominionstrategy.com/index.php?topic=17800.0)" that we had relied on several different specific cards; although doesn't work with the new Band of Misfits (http://wiki.dominionstrategy.com/index.php/Band_of_Misfits) errata.
So basically, there's no simple answer to this question; you would have to remove a lot of different cards in order to have no infinite loops left.
There is no definite answer to this, because some cards only cause infinite loops in a combination with others (Forum + Trader is a simple example). We can come up with some smallest set, but it won't be unique.
Thank you.
Maybe I can make the question in a different way. Which are the features of the cards that make possible to them create an infinite loop?
For instance, all the cards in the loop Forum – Trader – Highway – Goons have an under the line effect. In general, I think no infinite loop would be possible without cards or landscapes with effects that break the vanilla rules of the game for targeted cards and a trigger condition. It’s right?
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In the Forum – Trader – Highway – Goons loop the element that create infinity is in Forum, the +buy on buy, like in some events like Delve. This feature is what allows infinite acts of the player. Trader and Goons react to these infinite acts and Highway only enable them removing money constraints.
Maybe the three elements are necessary to an infinite loop, create infinite acts, react to them and remove constraints, but the essential feature seems to be the first.
So, maybe we can list the cards that change the game this way, allowing infinite acts. Of course, excluding the case of unproductive repetitive acts, like Moat do.
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In fact, the elements of an infinite loop seem to be four:
- Something that allow repetitions of acts, like +buy on buy of Forum
- Something that remove the costs (in $, actions, cards or buys) of each repetition, like Highway in this case, or something that produces the payload for it at each iteration
- Something that prevents the repetitions from stop, like Trader effect of giving a silver or an inexistent silver, keeping intact Forum pile.
- Something that make each iteration productive, like Goons effect in cards buy.
(edited to change "Goons effect in cards gain" to "Goons effect in cards buy")
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It seems uncontroversial to consider that an infinite loop is a sequence of steps which can be repeated indefinitely to give unbounded benefit.
The trickier part is determining which aspects of the game are infinite-loop "enablers". How about reckoning chronologically? The feature which, when added by an expansion, makes the infinite loop possible is the enabler; the components which already existed are not. A feature which creates an infinite loop in conjunction with an existing enabler is not a new enabler.
This could go wrong when two things are introduced by the same expansion which combine to create a loop, but hey...
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For a lot of loops, the key is being able to remove things from play, such as with Mandarin or Bonfire, so that they can be played again.
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For a lot of loops, the key is being able to remove things from play, such as with Mandarin or Bonfire, so that they can be played again.
Yeah! Unless I’m mistaken, the only two voluntary acts a player can do for herself, without specific command from cards or situation, are “play” and “buy”. These two acts are the driving force of the game. So maybe the loop enablers in a strict sense are just the cards which establish a game state in which infinite plays or infinite buys are possible.
Mandarin and Bonfire are examples of the first case, Forum and Delve of the second.
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For a lot of loops, the key is being able to remove things from play, such as with Mandarin or Bonfire, so that they can be played again.
Yeah! Unless I’m mistaken, the only two voluntary acts a player can do for herself, without specific command from cards or situation, are “play” and “buy”. These two acts are the driving force of the game. So maybe the loop enablers in a strict sense are just the cards which establish a game state in which infinite plays or infinite buys are possible.
I will try to list the features of infinite-loop enablers and the cards that have these features. I think these are the features that make possible infinite plays or infinite buys of the same copy of a card. If it’s right, we wouldn’t be able to make an infinite loop without one of these cards.
I'm not sure if the list is complete, please tell me if I forgot some card with a certain feature or some other feature that enables infinite plays or buys.
Cards that return phases
Villa
Cavalry
Cards that allow play actions in buy phase
Capitalism
Gamble
Toil
March
Scepter
Cards that remove cards from play
Mint
Horn of Plenty
Mandarin
Urchin
Pillage
Procession
Death Cart
Counterfeit
Madman
Spoils
Raze
Bonfire
Engineer
Small Castle
Pixie
Wish
Acting Troupe
Magic Lamp
Experiment
Stockpile
Horse
Way of the Butterfly
Way of the Horse
Obs:
- Cards that go to Tavern Mat remove themselves from play, but only when played, not when called, so they can’t be played repeatedly
- Knights can be removed from play, but it depends on the opponent deck
- Encampment also can leaves play area, but returns to the game only in clean-up phase
- Monastery, Changeling, Vampire and Bat remove cards from play, but only in the night phase
- Improve remove cards from play, but already in the clean-up phase
Cards that remove cards from the trash
Lurker
Fortress
Graverobber
Rogue
Treasurer
Cards that return cards to pile
Ambassador
Madman
Spoils
Wish
Experiment
Horse
Way of the Butterfly
Way of the Horse
Obs: Encampment also do it, but only in clean-up phase
Cards that make at least one action play that doesn’t put a card in play area
Throne Room
King’s Court
Procession
Band of Misfits
Disciple
Inheritance (Inherited Estates do it)
Overlord
Crown
Scepter
Citadel
Captain
Way of the Mouse
Obs:
- Innovation can do it, but only once per turn
- Royal Carriage can do it, but only once per turn for each copy of it
- Necromancer can do it, but only once per turn for each card in the trash
- Mastermind and Ghost do it, but only in your next turn
Cards that make at least one treasure play that doesn’t put a card in play area
Counterfeit
Crown
Cards that can be bought repeatedly
Forum
Scouting Party
Travelling Fair
Delve
Gamble
Pursue
Toil
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For a lot of loops, the key is being able to remove things from play, such as with Mandarin or Bonfire, so that they can be played again.
Yeah! Unless I’m mistaken, the only two voluntary acts a player can do for herself, without specific command from cards or situation, are “play” and “buy”. These two acts are the driving force of the game. So maybe the loop enablers in a strict sense are just the cards which establish a game state in which infinite plays or infinite buys are possible.
Mandarin and Bonfire are examples of the first case, Forum and Delve of the second.
Another voluntary act is to "react" to something you caused yourself (e.g. with Sheepdog, Patron and others). But almost all Reactions are specifically designed so that you can either react only once (like Sheepdog), or reacting several times makes no difference (like Moat), so they shouldn't be a problem (Exception: Diplomat, but it can still only be used a finite amount of times, and usually only on an opponent's turn.)
Therefore I also think that infinite loops "that accomplish something" are only possible with infinite plays or infinite buys. So you need either one of the "Cards that remove cards from play" (together with a way to get the removed cards back to play again) or one of the "Cards that can be bought repeatedly" (together with a cost decrease to $0 or a way to also get the infinite money required) for any infinite loop.
By the way, has someone compiled a list of all known infinite combos? What is the lowest number of kingdom cards/landscapes you need to go infinite? heron found two similar ways (pun intended) to play an infinite number of Actions with only 3 card-shaped things - though to get something "productive" out of it ($, VP, or permanent card gain), you'd need a fourth card (e.g. putting an adventures token on King's Court):
Can do 1 kingdom card a 2 landscapes:
KC-KC (way of the rat, way of the horse to draw new KC + treasure, play new KC, repeat)
Donald says we should avoid using 2 Ways. But sounds nice.
You can replace way of the rat with inventor.
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Therefore I also think that infinite loops "that accomplish something" are only possible with infinite plays or infinite buys. So you need either one of the "Cards that remove cards from play" (together with a way to get the removed cards back to play again) or one of the "Cards that can be bought repeatedly" (together with a cost decrease to $0 or a way to also get the infinite money required) for any infinite loop.
I Think you’re right about not all the features I’ve listed make possible infinite plays or buys . Return phases, play actions in buy phase, remove cards from trash or return to pile can’t do the trick by itself, you still need to remove cards from play when played.
However, make an action play or a treasure play that doesn’t put a card in play area is similar to play a card and remove it from play, so I think it works.
Considering this, the list of features of infinite-loop enablers and respective cards (including Mining Village that I forgot in the first list) would be:
Cards that remove cards from play
Mining Village
Mint
Horn of Plenty
Mandarin
Urchin
Pillage
Procession
Death Cart
Counterfeit
Madman
Spoils
Raze
Bonfire
Engineer
Small Castle
Pixie
Wish
Acting Troupe
Magic Lamp
Experiment
Stockpile
Horse
Way of the Butterfly
Way of the Horse
Cards that make at least one action play that doesn’t put a card in play area
Throne Room
King’s Court
Procession
Band of Misfits
Disciple
Inheritance (Inherited Estates do it)
Overlord
Crown
Scepter
Citadel
Captain
Way of the Mouse
Cards that make at least one treasure play that doesn’t put a card in play area
Counterfeit
Crown
Cards that can be bought repeatedly
Forum
Scouting Party
Travelling Fair
Delve
Gamble
Pursue
Toil
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Consolidating alphabetically, these are the 42 cards that we can’t do an infinite loop without one of them:
1. Acting Troupe
2. Band of Misfits
3. Bonfire
4. Captain
5. Citadel
6. Counterfeit
7. Crown
8. Death Cart
9. Delve
10. Disciple
11. Engineer
12. Experiment
13. Forum
14. Gamble
15. Horn of Plenty
16. Horse
17. Inheritance
18. King’s Court
19. Madman
20. Magic Lamp
21. Mandarin
22. Mining Village
23. Mint
24. Overlord
25. Pillage
26. Pixie
27. Procession
28. Pursue
29. Raze
30. Scepter
31. Scouting Party
32. Small Castle
33. Spoils
34. Stockpile
35. Throne Room
36. Toil
37. Travelling Fair
38. Urchin
39. Way of the Butterfly
40. Way of the Horse
41. Way of the Mouse
42. Wish
Of course, if someone find a single infinite loop without these cards this theory would be ruinned, but at first I think it’s impossible.
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34. Stockpile
On second thought, I think Stockpile doesn't work, since there's no way to play it again when all of them are in the exile. You can have a total of 55 plays from 10 Stockpiles, but not infinite.
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34. Stockpile
On second thought, I think Stockpile doesn't work, since there's no way to play it again when all of them are in the exile. You can have a total of 55 plays from 10 Stockpiles, but not infinite.
You can trash Stockpiles and gain them from the trash to move them out of Exile. I admit I haven't read the entire discussion, so I'm not certain this is relevant in context.
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You can trash Stockpiles and gain them from the trash to move them out of Exile. I admit I haven't read the entire discussion, so I'm not certain this is relevant in context.
Yes, it's relevant, thank you! This way it can work as an infinite-loop enabler.
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I'm not sure if the list is complete, please tell me if I forgot some card with a certain feature or some other feature that enables infinite plays or buys.
[...]
Cards that remove cards from play
Mint
Horn of Plenty
Mandarin
Urchin
Pillage
Procession
Death Cart
Counterfeit
Madman
Spoils
Raze
Bonfire
Engineer
Small Castle
Pixie
Wish
Acting Troupe
Magic Lamp
Experiment
Stockpile
Horse
Way of the Butterfly
Way of the Horse
[...]
You're missing some other self-trashers like Embargo and Treasure Map (and Feast, if you want to include removed cards). However, trashing a card from play can only ever lead to an infinite turn when there's a way to return cards from the trash. So if we want a list of minimal size, I'd restrict this category to "Cards that remove cards from play without trashing them", and instead add the far fewer cards that return cards from the trash. Thus your list is reduced to:
Cards that remove cards from play without trashing them
Mandarin
Madman
Spoils
Wish
Experiment
Stockpile
Horse
Way of the Butterfly
Way of the Horse,
i.e. 9 cards, plus the 5 cards that remove cards from the trash and the 7 cards that can be bought repeatedly, for a total of only 21 cards that enable infinite loops.
I don't think that "Cards that make at least one action/treasure play that doesn’t put a card in play area" can create an infinite loop on their own since they still require to put themselves (and usually their target) in play: at best you get e.g. three plays out of one Action card in play with King's Court, but never infinitely many since the King's Court and its target card remain in play, reducing the finite number of cards that can still be played (in the absence of cards that do remove cards from play).
Edit: We can also remove Stockpile from the list since it is always exiled when played, so you can only play them a finite number of times. (There's no card that can remove it back from the Exile mat when the pile is gone -Transport only works on Actions.)
2nd Edit: Since there's no way to reduce the costs of Events (AFAIK), the only card that can actually be bought repeatedly an umlimited number of times (without having already achieved infinite $) is Forum (with cost reduction and Trader). So I think we're down to 14 cards total.
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You're missing some other self-trashers like Embargo and Treasure Map (and Feast, if you want to include removed cards). However, trashing a card from play can only ever lead to an infinite turn when there's a way to return cards from the trash. So if we want a list of minimal size, I'd restrict this category to "Cards that remove cards from play without trashing them", and instead add the far fewer cards that return cards from the trash. Thus your list is reduced to:
Cards that remove cards from play without trashing them
Mandarin
Madman
Spoils
Wish
Experiment
Stockpile
Horse
Way of the Butterfly
Way of the Horse,
i.e. 9 cards, plus the 5 cards that remove cards from the trash and the 7 cards that can be bought repeatedly, for a total of only 21 cards that enable infinite loops.
I don't think that "Cards that make at least one action/treasure play that doesn’t put a card in play area" can create an infinite loop on their own since they still require to put themselves (and usually their target) in play: at best you get e.g. three plays out of one Action card in play with King's Court, but never infinitely many since the King's Court and its target card remain in play, reducing the finite number of cards that can still be played (in the absence of cards that do remove cards from play).
Edit: We can also remove Stockpile from the list since it is always exiled when played, so you can only play them a finite number of times. (There's no card that can remove it back from the Exile mat when the pile is gone -Transport only works on Actions.)
2nd Edit: Since there's no way to reduce the costs of Events (AFAIK), the only card that can actually be bought repeatedly an umlimited number of times (without having already achieved infinite $) is Forum (with cost reduction and Trader). So I think we're down to 14 cards total.
Thank you! I think you’re right. I was mistaken in many thoughts in this reasoning.
Considering what you said, the cards that remove cards from trash also don´t work, since they have to be removed from play when played too. The exception seems to be Fortress, which can be trashed by Advance (an event with cost $0) and removed from trash without playing any card. Of course, in the loop you have to produce the +buys for new Advances.
About Stockpile, Treasurer can remove it from trash, enabling the other Stockpiles to leave exile. However, in this case, the problem would be the same above, Treasurer has to be removed from play itself. So, it doesn’t work.
About the cards that remove cards from play to trash, I think you’re right, but Bonfire seems to be an exception. Since it can trash any type of played card, maybe it could enable a loop with the aid of a card that allow play actions in buy phase, loop in which you can trash and recover from trash the cards needed and also produce the payload for a new Bonfire.
Finally, I don’t know if exists nowadays a card that can pin your opponent if she isn’t a bot. If exists such a card, it can be an enabler of an infinite loop in infinite turns, doing in each of these turns the same thing that give you VPs without reduce the piles, like playing a Monument.
Besides this last case, if I’m not wrong again at some point, the list of infinite-loop enablers seems to be reduced to these 11 cards:
Mandarin
Madman
Spoils
Wish
Experiment
Horse
Way of the Butterfly
Way of the Horse
Fortress
Bonfire
Forum
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Of the 11 cards listed there, I am pretty sure that most of them can't actually form infinite loops, since I don't think a card that just returns itself is sufficient; it needs to get the other combo pieces out of play.
In particular, I don't see any way in which Madman, Spoils, Wish, Experiment, Horse, or Fortress would suffice.
Actually Fortress is involved in the Priest + Travelling Fair + Advance + Fortress combo, so maybe Fortress is needed. This combo actually doesn't involve removing cards from play ever; Fortress is needed for the reason of triggering "when you trash" an infinite number of times.
Another thing: Buying a Mint trashes treasures in play, which probably can be used to set up infinite combos. So we need to add Mint to the list.
Thus, I would guess that the list is just:
Mandarin
Mint
Way of the Butterfly
Way of the Horse
Fortress
Bonfire
Forum
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Another thing: Buying a Mint trashes treasures in play, which probably can be used to set up infinite combos. So we need to add Mint to the list.
I thought it before, but now I don´t think it works, since you have to remove the treasures from trash. You can do it with Treasurer, but in this case you will need another of these enablers to remove Treasurer from play.
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Of the 11 cards listed there, I am pretty sure that most of them can't actually form infinite loops, since I don't think a card that just returns itself is sufficient; it needs to get the other combo pieces out of play.
In particular, I don't see any way in which Madman, Spoils, Wish, Experiment, Horse, or Fortress would suffice.
Thus, I would guess that the list is just:
Mandarin
Mint
Way of the Butterfly
Way of the Horse
Fortress
Bonfire
Forum
With Way of the Horse, any action becomes a Horse, so if it works Horse itself has to work. And so, also Experiment.
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Another thing: Buying a Mint trashes treasures in play, which probably can be used to set up infinite combos. So we need to add Mint to the list.
I thought it before, but now I don´t think it works, since you have to remove the treasures from trash. You can do it with Treasurer, but in this case you will need another of these enablers to remove Treasurer from play.
Mint can be your enabler for removing treasurer, since it is a treasure with capitalism.
Of the 11 cards listed there, I am pretty sure that most of them can't actually form infinite loops, since I don't think a card that just returns itself is sufficient; it needs to get the other combo pieces out of play.
In particular, I don't see any way in which Madman, Spoils, Wish, Experiment, Horse, or Fortress would suffice.
Thus, I would guess that the list is just:
Mandarin
Mint
Way of the Butterfly
Way of the Horse
Fortress
Bonfire
Forum
With Way of the Horse, any action becomes a Horse, so if it works Horse itself has to work. And so, also Experiment.
Way of the Horse definitely works but horses and experiments don't. The key is Way of the Horse can return a card that was throned, and thus can allow you to play any action and return that action to the supply. Horse and Experiment just let you return themselves to the supply, they can't cause other actions to get returned.
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Way of the Horse definitely works but horses and experiments don't. The key is Way of the Horse can return a card that was throned, and thus can allow you to play any action and return that action to the supply. Horse and Experiment just let you return themselves to the supply, they can't cause other actions to get returned.
If it is the only way that Way of the Horse could be an infinite-loop enabler, it also doesn't work, since you still have to remove Throne Room from play.
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Way of the Horse definitely works but horses and experiments don't. The key is Way of the Horse can return a card that was throned, and thus can allow you to play any action and return that action to the supply. Horse and Experiment just let you return themselves to the supply, they can't cause other actions to get returned.
If it is the only way that Way of the Horse could be an infinite-loop enabler, it also doesn't work, since you still have to remove Throne Room from play.
It is still possible with just Way of the Horse, since it can in fact remove the throne itself. Consider the following position:
3x cost reduction from bridge/highway.
king's court is in play, and just played another king's court.
deck and discard are empty. hand contains only a single ironworks.
first play of kc: way of the horse, returning it
second play of kc: ironworks
first play of ironworks: gain ironworks
second play of ironworks: gain kc
third play of ironworks: way of the horse, returning it and drawing ironworks and kc.
third play of kc: kc
end position is exactly identical to the start, except you have more +actions.
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Way of the Horse definitely works but horses and experiments don't.
I created an infinite loop that works with Experiment:
Hand: 3 Highways, Goons
Empty deck and empty discard pile
Way: Way of the Chameleon
Events: Seaway, Gamble
Seaway +1 Buy token in Experiment pile
1 – Play the 3 Highways
2 – Play Goons – now you have $2 and 2 buys
3 – Buy Experiment at Cost 0 – gain 1 VP from Goons – receive another Experiment
4 – Buy Gamble
5 – Play Experiment as Chameleon – gain $2 and +1 buy (by Seaway token) - Experiment returns to its pile
6 – Buy Gamble
7 – Play Experiment as Chameleon – gain $2 and +1 buy - Experiment returns to its pile
Repeat steps 3 to 7 indefinitely for infinite VPs
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Way of the Horse definitely works but horses and experiments don't. The key is Way of the Horse can return a card that was throned, and thus can allow you to play any action and return that action to the supply. Horse and Experiment just let you return themselves to the supply, they can't cause other actions to get returned.
I've found an infinite loop with Way of the Horse without a throne card:
Way of the Horse, Seaway and Villa in the setup
Hand: 4 Merchant Guilds and a Goons
4 Villagers in Villagers Mat
Seaway +1 buy token in Villa pile
1 – Play the 4 Merchant Guilds
2 – Play Goons
3 – Buy Villa – Gain 1 VP from Goons – Gain 4 Coffers from Merchant Guilds
On gain Villa goes to hand, give + 1 action and returns game to action phase
4 – Play Villa as Way of the Horse – gain +1 Buy - Villa returns to its pile
5 – Play 4 Coffers
Repeat steps 3 to 5 indefinitely for infinite VPs
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Way of the Horse definitely works but horses and experiments don't. The key is Way of the Horse can return a card that was throned, and thus can allow you to play any action and return that action to the supply. Horse and Experiment just let you return themselves to the supply, they can't cause other actions to get returned.
I've found an infinite loop with Way of the Horse without a throne card:
Way of the Horse, Seaway and Villa in the setup
Hand: 4 Merchant Guilds and a Goons
4 Villagers in Villagers Mat
Seaway +1 buy token in Villa pile
1 – Play the 4 Merchant Guilds
2 – Play Goons
3 – Buy Villa – Gain 1 VP from Goons – Gain 4 Coffers from Merchant Guilds
On gain Villa goes to hand, give + 1 action and returns game to action phase
4 – Play Villa as Way of the Horse – gain +1 Buy - Villa returns to its pile
5 – Play 4 Coffers
Repeat steps 3 to 5 indefinitely for infinite VPs
Nice. Also works with four Highways, or any other means of getting the cost of Villa to $0.
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Events: Toil, Bonfire
Project: Canal – player cube already there
Trash: 2 King’s Courts, 2 Rogues, Silk Merchant, Monument
Hand: 2 King’s Courts, 2 Rogues, Silk Merchant
Empty deck and empty discard pile
1 – Play King’s Court
2 – King’s a King’s Court
3 – King’s a Rogue – gain 3 cards from trash – gain $6
4 – King’s a Rogue – gain 3 cards from trash – gain $6
5 – King’s a Silk Merchant – draws 6 cards – gain 3 buys
6 – Play Monument – gain $2 and 1 VP
7 – Buy 3 Bonfires – trash all cards in play
8 – Buy Toil
9 – Play King’s Court
10 – King’s a King’s Court
11 – King’s a Rogue – gain 3 cards from trash – gain $6
12 – King’s a Rogue – gain 3 cards from trash – gain $6
13 – King’s a Silk Merchant – draws 6 cards – gain 3 buys
14 – Buy Toil
15 – Play Monument – gain $2 and 1 VP
Repeat steps 7 to 15 indefinitely for infinite VPs
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Maybe I can make the question in a different way. Which are the features of the cards that make possible to them create an infinite loop?
For a lot of loops, the key is being able to remove things from play, such as with Mandarin or Bonfire, so that they can be played again.
Your categorized lists earlier in this thread are very nice, I'll have to bookmark this thread. Even so, I feel like answering your original question in my own words, in the hope it's helpful to someone (who might be me, if I invite corrections).
There are a lot of quantities in Dominion which typically only move in one direction:
- Number of actions
- Amount of money you have to spend
- Your number of buys
- The number of cards in play
- The number of cards in the trash
- The number of cards in the supply
- How far you have progressed along the phase trajectory (action -> buy -> night -> cleanup)
- I'm sure you can think of more quantities here
The most interesting quantities are those tied into your ability to change the game state—most often by playing a card, but sometimes by triggering on-buy, on-gain and on-trash abilities (and triggering reactions, but they're typically not powerful enough to be useful).
There are many effects which give you +2 actions, +(1-5) cards, +$1, etc.; those are not so interesting. Effects that take cards out of play, or out of the trash, or return them to the supply, and so on, are rare; much rarer than vanilla bonuses. It makes good sense to make an inventory of those effects, as you have done, since if you can use one of them to overcome a limitation, you can usually think of vanilla cards that fill in whatever the gaps are. The rarest effects are, in some sense, those that are most responsible for enabling loops. [For example, give each card a point for every valid kingdom with a loop it occurs in; your lists will likely contain all the high-scoring cards: the more substitutes a card has, the less of the point mass will be dedicated exclusively to it.]
There are some other effects that may sometimes be useful, such as repeatably stealing a card from your opponent's hand via Masquerade (http://wiki.dominionstrategy.com/index.php/Masquerade), Cutpurse (http://wiki.dominionstrategy.com/index.php/Cutpurse), Pirate Ship (http://wiki.dominionstrategy.com/index.php/Pirate_Ship) and Treasurer (http://wiki.dominionstrategy.com/index.php/Treasurer) (or Thief (http://wiki.dominionstrategy.com/index.php/Thief)), as I did here: http://forum.dominionstrategy.com/index.php?topic=15366.msg697190#msg697190 (http://forum.dominionstrategy.com/index.php?topic=15366.msg697190#msg697190). This was necessary as a side effect of using Ambassador (http://wiki.dominionstrategy.com/index.php/Ambassador) to return Villa (http://wiki.dominionstrategy.com/index.php/Villa) to the supply; these days, with Way of the Horse (http://wiki.dominionstrategy.com/index.php/Way_of_the_Horse), those shenanigans are likely not necessary, but it may be useful to know techniques and combinations for achieving various tasks such as this. All of these are unique (IIRC) tools for taking a card out an opponent's hand without making them discard, repeatably forcing a discard (without gaining treasures to your discard pile), trashing a Copper in your opponent's discard pile and gaining Copper from the trash. None of them are obvious loop enablers, and maybe Pillage (http://wiki.dominionstrategy.com/index.php/Pillage) is better, but they do work around a limitation of Ambassador which is a (more obvious) loop component.
The tokens from Peasant (http://wiki.dominionstrategy.com/index.php/Peasant)/Teacher (http://wiki.dominionstrategy.com/index.php/Teacher) are also often helpful, see e.g. http://forum.dominionstrategy.com/index.php?topic=20927.0 (http://forum.dominionstrategy.com/index.php?topic=20927.0). They don't circumvent any of the unidirectionalities I outlined above, but they often help a loop be net neutral or positive on some resource, such as buys in the linked example (or money, if you use Highway (http://wiki.dominionstrategy.com/index.php/Highway) instead of Merchant Guild (http://wiki.dominionstrategy.com/index.php/Merchant_Guild)). Resource conversions are also useful to know about: money into buys via Travelling Fair (http://wiki.dominionstrategy.com/index.php/Travelling_Fair), trashes into money with previously played Priest (http://wiki.dominionstrategy.com/index.php/Priest)s, and buys into trashes via Advance (http://wiki.dominionstrategy.com/index.php/Advance), for example.