I think it is more productive to list loops that use only one distinct card from our current short list of cards required for inifinite loops, since there are a lot of similar loops using the same card.
Trying to see by another angle the question about which cards are essential to infinite loops and so refine the list of them:
- When you restart the loop, all copies of all cards in the game must be again in the same place they were in the beginning of the loop.
- The game has to be in the same phase of the beggining of the loop when you restart the loop.
- In the restart of the loop you have to get back the resources (actions, buys, coins) you spent during the loop
- You can’t go back to the same situation in clean-up phase.
- There’s no way to remove cards from play and put them back where they were in night phase.
So, the loops can only occur:
- In both, action phase and buy phase
- Within buy phase only
- Within action phase only
If the loops occur in both action and buy phases you need
Villa or
Cavalry to go back to same situation.
If the loop occurs within buy phase you can’t go back to the same situation only buying things (you have to restore your buy power) or playing treasure type cards that don’t play actions (they can't remove cards from play and put them back where they were). You need actions to be played. So you need one or more of the cards that allow play actions in buy phase:
Scepter,
Capitalism,
Gamble,
Toil or
March.
If the loop occurs within action phase, you need to be able to remove cards from play and put them back where they were in this phase only.
Cards when removed from play only can be recovered if they went to:
- Pile
- Trash or
- Deck, by gaining Mandarin
In all this cases, you need to gain a card from pile or trash to go back to initial position. In action phase you can’t do it by buying (Black Market doesn’t buy from supply piles).
So, you need a gainer. Gainers don’t remove themselves from play. So, you have to be able to remove cards from play, play a gainer and remove gainer from play, all in action phase.
There are only two known ways to do that:
- Gaining Mandarin with cube on Capitalism, so you will be able to topdeck the gainer.
- Playing two King’s Court and using the third slot of second King's Court to play a King’s Court again and restart the cycle. In meanwhile, you have six actions plays, four of them that don’t put a card in play, so you can remove and gain back both King's Court and the gainer.
All loops I saw that occur only in action phase use one of these two mechanisms.
Since you can’t do the Mandarin trick without Capitalism and Capitalism is an enabler also in buy phase, the real enablers in action phase are
King’s Court and
Capitalism.
Finally, we have the case of the only act you can do that changes nothing in the game (cards place, game phase and your amount of actions, buys and coins): react to a gain with a
Trader when silver pile is out.
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
