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[NoMoreFun]

Infinite Room
Action - $10
You may reveal an action card from your hand. Play it until remaining plays have no effect on the rest of your turn.

Now questions:

1) Given the following conditions below, are there any cards where you will be stuck playing the card forever

• +Action=Unlimited actions
• +Buy=Unlimited buys
• +$=Unlimited Money
• +VP=You have infinite VP, and are guaranteed to win (although you can share your victory with other players who have played infinite room)
• Take a coin token=You have unlimited coin tokens (ie unlimited money for every remaining turn in the game)
  
• If a deck searcher (or even a card like Thief) will never find any more cards of the type it's searching for, then the end result is all the remaining cards in the discard pile (since that's where all the cards ultimately end up, and the shuffle it ends up as won't be determined by your playing of that card
• If nothing changes between decisions, then making additional decisions doesn't count (eg if you play it with chapel and have 2 cards left in your hand, neither of which you want to trash, that's not going to change no matter how many times you say no)

1b) If that isn't a comprehensive enough set of rules, then what need to be added so that it will work with every dominion card?

2) Without VP chip cards in the Kingdom, are there any cards that guarantee 1st place (shared or otherwise) when played with this card? There is at least one (I think).

3) Can you design a Kingdom where the card is worthwhile, but not broken?

[NoMoreFun]

My answer to 2)

Swindler, if you play it infinitely many times, can empty 3 piles with its gains (unless your opponents deck doesn't have sufficient different costs in his deck for the kingdom, but Copper and Estate are enough. Then their decks are trashed. It's then up to you to beat what they have left in their hand for total VP. You have infinite money.

Possible problem for 1)
Masquerade gets you into an oscillation, but you can escape it as long as you choose the trashing option to trash your deck (and then everyone else's hand)

[soulnet]

Infinite coin tokens cause problems with Possession. Can you spend your opponent's infinite coin tokens when possessing them? Can they spend them all before you possessed them?

In any case, with any card that gives money and buys, playing this is game over in almost every case. Spy is strange, you can basically see and then rearrange the entire deck/discard of each opponent to any configuration with probability 1.

Your limiting behavior for Thief is wrong. Playing Thief (or Pirate Ship) multiple times with an opponent with a treasureless deck with more than 2 cards in it will never lead to a limiting behavior, because it will continue to flip and reshuffle their deck. Each subsequent play leaves the game in a state different than what it was before the play.

[NoMoreFun]

Your limiting behavior for Thief is wrong. Playing Thief (or Pirate Ship) multiple times with an opponent with a treasureless deck with more than 2 cards in it will never lead to a limiting behavior, because it will continue to flip and reshuffle their deck. Each subsequent play leaves the game in a state different than what it was before the play.

Unless they have 2 or fewer cards in their deck

I put Thief in the same category as Adventurer etc. as a made up rule. It would also apply to draw and discards like Warehouse and Margrave's reaction. Is there one that would be more fitting so the card is playable?

[NoMoreFun]

Infinite coin tokens cause problems with Possession. Can you spend your opponent's infinite coin tokens when possessing them? Can they spend them all before you possessed them?

Your opponent has unlimited money for the rest of the game, but while you're possessing them it can be used to gain cards for you.

Also playing unlimited possessions means you can more than likely end the game (unless the remaining state of the kingdom and their deck means that you can never afford $2, which is extremely rare but possible), but you still might not win if they have too much of a lead. However if ambassador or masquerade is in the supply you can guarantee a win. You are in an oscillating game state but one that you can end by ending the game. It's not quite as good as playing it with Woodcutter.

[KingZog3]

For 1) Conspirator, unactivated makes infinite money. Cellar will go forever as long as you have a card in your hand. Monument for infinite VP. Goons is infinite $$ and buys, but not infinite VP. Plaza as long as you have 1 treasure card in hand it can be infinite. Possession gives infinite extra turns. Herbalist... the list is really long.

For 2) Monument is infinite points. Goons I think, because you just buy out the supply at the end of your turn.

3) This is hard

Counterfeit, Fools Gold, Philosopher's Stone, Warehouse, Treasure map, Quarry, Loan, Bank, Stash, Infinite Throne room. I would say it's useful to guarantee Treasure map collision with Warehouse.

[NoMoreFun]

For 2) Monument is infinite points. Goons I think, because you just buy out the supply at the end of your turn.

I specified without VP chip cards, but

Monument and Bishop guarantee a win. Goons almost certainly does but not necessarily (if your opponent has all of the Duchies, Estates and an Alt VP card, and all but one of every other card in the supply including Colony/Platinum, then even buying the rest of the supply won't help you, since Goons' VP chip gaining is a "while in play" effect

[NoMoreFun]

For 1) Conspirator, unactivated makes infinite money. Cellar will go forever as long as you have a card in your hand. Monument for infinite VP. Goons is infinite $$ and buys, but not infinite VP. Plaza as long as you have 1 treasure card in hand it can be infinite. Possession gives infinite extra turns. Herbalist... the list is really long.

Infinite money, infinite VP, infinite +buys and infinite coin tokens have been dealt with
With Cellar, you can make a decision that doesn't change the game state, which means it's fine under the Chapel rule. However Warehouse is problematic and therefore dealt with under the rule that covers Thief.

[KingZog3]

For 1) Conspirator, unactivated makes infinite money. Cellar will go forever as long as you have a card in your hand. Monument for infinite VP. Goons is infinite $$ and buys, but not infinite VP. Plaza as long as you have 1 treasure card in hand it can be infinite. Possession gives infinite extra turns. Herbalist... the list is really long.

Infinite money, infinite VP, infinite +buys and infinite coin tokens have been dealt with
With Cellar, you can make a decision that doesn't change the game state, which means it's fine under the Chapel rule. However Warehouse is problematic and therefore dealt with under the rule that covers Thief.

What about Mystic? It's infinite, but only if I don't name the card that I know is on top of my deck. So it can be, but only if you want it to be.

[Witherweaver]

For (2), couldn't you continually Masquerade to trash everything but one Victory card?  This may require you tracking their Victory cards.  Of course, it doesn't empty the supply, so you may not be able to end the game that turn.  On the other hand, all they could do the next turn is buy a Copper, so maybe you can eventually manage them to a point where they would be emptying the last supply pile by buying something.

Edit: Well, actually, that only gets rid of his current hand.  So you need something else to establish a pin, since you're not guaranteed his next draw can't end the game on a win...

[Awaclus]

Do the last two points deal with Sir Michael when your opponent has Fortresses in his deck? There could be a situation in which your opponent would actually want to trash a card only if his deck is in a specific order.

Also, Courtyard and putting a different card on top each time is pointless, but if you do that, then you'll end up playing it forever. Something changes between the decisions!

[Davio]

I don't really understand the question.

If you play a simple Village with this card, you can play it for an infinite amount of actions.
And if you're planning to play a Diadem, well, the amount of actions does matter (even if you're just going to buy 1 card).

But let's say you play this-Worker Village-Diadem then you can easily buy out the supply.

Simply this-Bridge will do it as well or any other card that just gives buys and some money, like Market, Woodcutter, Grand Market, Squire, Candlestick Maker, Merchant Guild and some others.

[Witherweaver]

I don't really understand the question.

If you play a simple Village with this card, you can play it for an infinite amount of actions.
And if you're planning to play a Diadem, well, the amount of actions does matter (even if you're just going to buy 1 card).

But let's say you play this-Worker Village-Diadem then you can easily buy out the supply.

Simply this-Bridge will do it as well or any other card that just gives buys and some money, like Market, Woodcutter, Grand Market, Squire, Candlestick Maker, Merchant Guild and some others.

But the opponent could have more than half the available VP cards before this point.  So you have to have a way to trash their deck to guarantee a win in general.

[NoMoreFun]

What about Mystic? It's infinite, but only if I don't name the card that I know is on top of my deck. So it can be, but only if you want it to be.

You can either draw your whole deck or deliberately misname when you've had enough of drawing; either way it will stop helping.

Wishing Well on the other hand will draw your whole deck whether you want it to or not.

[Witherweaver]

My answer to 2)

Swindler, if you play it infinitely many times, can empty 3 piles with its gains (unless your opponents deck doesn't have sufficient different costs in his deck for the kingdom, but Copper and Estate are enough. Then their decks are trashed. It's then up to you to beat what they have left in their hand for total VP. You have infinite money.

But what if they have 2 Provinces in their hand, and there is 1 Province left on the board, 0 Duchies, 0 Estates (no third pile empty and no alternate VP) when you start this?  Or even 2 Provinces left; you can only buy one with Swindler.  And you have no VP cards in your deck (because of various trashing attacks up to this point, say).

I think you need to trash their hand and deck together, and end the game on the same turn.

[Holger]

Also, Courtyard and putting a different card on top each time is pointless, but if you do that, then you'll end up playing it forever. Something changes between the decisions!

Nothing changes after Courtyard has drawn your entire deck for the first time. I think this is accounted for by the "Chapel rule".

[Awaclus]

Also, Courtyard and putting a different card on top each time is pointless, but if you do that, then you'll end up playing it forever. Something changes between the decisions!

Nothing changes after Courtyard has drawn your entire deck for the first time. I think this is accounted for by the "Chapel rule".

No, something changes. Say, you've drawn your entire deck for the first time and you topdeck a Smithy. Then you draw the Smithy and topdeck a Copper.

[Witherweaver]

Also, Courtyard and putting a different card on top each time is pointless, but if you do that, then you'll end up playing it forever. Something changes between the decisions!

Nothing changes after Courtyard has drawn your entire deck for the first time. I think this is accounted for by the "Chapel rule".

No, something changes. Say, you've drawn your entire deck for the first time and you topdeck a Smithy. Then you draw the Smithy and topdeck a Copper.

But ultimately you only have to make one choice: which card you want to leave on top of your deck, which you can consider to resolve the infinite Courtyard play.

[Holger]

2) Without VP chip cards in the Kingdom, are there any cards that guarantee 1st place (shared or otherwise) when played with this card? There is at least one (I think).

I don't think so, if you make no other assumptions on the kingdom or the game state. You'd need a trashing attack that can reliably trash almost all the opponents' green cards, and (if any remain) gain you enough points to equalize. But Swindler can't trash hand cards, Masq. can only trash hand cards, Saboteur can't trash Estates and can't gain you a VP card, Knights and Rogue can't trash Provinces without cost reducers. Rogue can always gain all Duchies and one Province, but that's not enough against an opponent having all the remaining Provinces (e.g. in 2p, you only get 30 points, out of 80 available points).

Actually, if your opponent (in 2p) has more than half the available VPs +10VP (to account for potential incoming curses) safe on his Island mat, he is unbeatable by any means, even infinite extra turns for you.

[Davio]

Yeah, the only way to win is if your opponent does not yet have the mathematical win (on his Island mat).
But if your opponent doesn't, it's trivial, you can just buy the remaining points.

[Holger]

Yeah, the only way to win is if your opponent does not yet have the mathematical win (on his Island mat).
But if your opponent doesn't, it's trivial, you can just buy the remaining points.

It's not quite trivial: the opponent may have more than half the VPs in his deck where the VP cards could still be trashed. In this case, you still have a chance to win, but can't guarantee a win by playing "Infinite Throne Room-X".

But even when you ignore the trivial case of an already decided game, and ban Island (and Native Village, Haven...), no card (other than Monument and Bishop) fulfills the "guaranteed win" condition, by my above post. (Unless I missed something...)

[achmed_sender]

I would play ITR-ITR-Burocrat-Rogue after 2 Highways or a Princess
Yeah, thats two cards throned, but the otherway I can't see any way.

Rogue trashes and gains the Duchies and Provinces of the opponents' deck, even all the alt VPs which costs $5 or more (problem aganist a Garden player, then you just don't play the cost reducer)
Burocrat is for removing VP cards from the opponents hands, not even Torturer can guarantee that.

[Asper]

3) Any combination of the following that has at least one of the "limited use" cards in it.

Limited use
Action cards that trash cards from your hand to work: Moneylender, Remodel, Expand, Remake, Treasure Map, Develop, Stonemason, Transmute, Trader, Taxman, Mine, Trading Post and Procession
Action cards that remove cards from you hand other ways: Island

No use
Actions that ITR has no effect on: Secret Chamber, Tactician, Outpost, Library, Watchtower, Chapel, Counting House
Non-Actions: All


Depends
Multipliers limited by your hand: Throne Room, King's Court
(Allow playing more than one different card in a turn, which is only relevant if you play with Shelters OR there is a card that does not require you to lower your handsize to do something. Those cards include "no use cards" that still don't get additional benefit from being played by ITR)


Honorable mention:
Rats (which gives actions and cards but doesn't make the card "broken" for obvious reasons)

Edit: Forgot that Procession is a tfb itself and should be in the "limited use" category rather than "no use". Probably the effect isn't really useful most of the time, but nonetheless.
Edit:Removed Forge, Salvager and Altar due to Holger's remark.
Edit: Made a category for TR and KC that can add flexibility (in some cases)

[NoMoreFun]

Infinite money may not necessarily be broken as long as there aren't easy +buys, and vice versa.

Infinite actions may not be a big deal, but most non terminals do something else that's broken if done infinitely.
Scout is an exception. Cellar is too. Shanty town may be as if you can set it up to draw your deck then you probably deserve to.

Rats (which gives actions and cards but doesn't make the card "broken" for obvious reasons)

Lookout will destroy your deck, but not your hand. Apprentice may very well destroy everything, but it may not. Junk Dealer will destroy everything, but you will have infinite money to show for it (hopefully some +buys too). Upgrade will destroy your deck and wreak havoc on the supply.

Spice Merchant is one of the more interesting cards, and while it will definitely have an "infinite" vibe, it probably isn't broken or even overpowered with this.

Advisor and Envoy are interesting because while they will draw your whole deck, the player to your left can still veto one card.

[florrat]

Most remodelers do not fall in the "limited use" category, because of Fortress   .

Also Procession does not fall in the "limited use" category, you can easily make infinite chains with Graverobber/Rogue, and do something useful. For example you can repeat X-X-X-Rogue-Rogue-Rogue-Rogue-Hunting Grounds (or 19*X-10*Rogue-10*Graverobber-Scrying Pool).

[Awaclus]

Most remodelers do not fall in the "limited use" category, because of Fortress   .

Also Procession does not fall in the "limited use" category, you can easily make infinite chains with Graverobber/Rogue, and do something useful. For example you can repeat X-X-X-Rogue-Rogue-Rogue-Rogue-Hunting Grounds (or 19*X-10*Rogue-10*Graverobber-Scrying Pool).

They do because you get to design the kingdom and exclude cards that make cards come back from the trash.

[Asper]

Also Procession does not fall in the "limited use" category, you can easily make infinite chains with Graverobber/Rogue, and do something useful. For example you can repeat X-X-X-Rogue-Rogue-Rogue-Rogue-Hunting Grounds (or 19*X-10*Rogue-10*Graverobber-Scrying Pool).

You cannot do infinite chains with those, unless you mean over several turns, which ITR isn't needed for and which isn't the point of the challenge.
As Procession is a tfb i admit that i made a mistake putting it in the "no use" category, though. Clearly it belongs in "limited use".

[Holger]

3) Any combination of the following that has at least one of the "limited use" cards in it.

Limited use
Action cards that trash cards from your hand to work: Moneylender, Remodel, Graverobber, Expand, Forge, Remake, Treasure Map, Develop, Stonemason, Transmute, Salvager, Trader, Taxman, Mine and Altar
Action cards that remove cards from you hand other ways: Island

No use
Actions that ITR has no effect on: Secret Chamber, Tactician, Outpost, Library, Watchtower
Multipliers limited by your hand: Procession, Throne Room, King's Court
Non-Actions: All


Honorable mention:
Rats (which gives actions and cards but doesn't make the card "broken" for obvious reasons)

Altar, Forge and Salvager (+1 buy) are unlimited by your hand size: Altar still gains a $5 card and Forge a Copper if you trash nothing. The multipliers are "limited use" instead of "no use", obviously.

Infinite money may not necessarily be broken as long as there aren't easy +buys, and vice versa.

Infinite actions may not be a big deal, [...]

Agreed; I think infinite draw might also be acceptable (though very strong; probably ITR should cost $15 or so then). Whether you draw all cards or all but one (with Advisor or Envoy) is usually no big difference.

With no cantrips, no Golem/Herald/BoM, no +$ and +buy on a single card, no unconditional gainers (Workshop etc.), no trashing attacks and no token-giving cards, ITR might be reasonable (if strong) at $10; you'd need multiple ITR's to do really crazy things...

[florrat]

They do because you get to design the kingdom and exclude cards that make cards come back from the trash.

Good point, I didn't read the question carefully enough.

You cannot do infinite chains with those, unless you mean over several turns, which ITR isn't needed for and which isn't the point of the challenge.
As Procession is a tfb i admit that i made a mistake putting it in the "no use" category, though. Clearly it belongs in "limited use".

You can (assuming the right kingdom). Suppose 1 Rogue and 1 Scrying Pool is already in the trash, and you have a deck consisting only of action cards.
Process X, play it twice and trash it.
Process Rogue, gain X and Rogue
Process Rogue, gain Scrying Pool and Rogue
Process Scrying Pool, draw deck
Then we've played X twice, and we are in the same initial position: 1 Rogue and 1 Scrying Pool in the trash. And you've played X twice.

[Asper]

Altar, Forge and Salvager (+1 buy) are unlimited by your hand size: Altar still gains a $5 card and Forge a Copper if you trash nothing. The multipliers are "limited use" instead of "no use", obviously.

Ah, i missed out that the gain of Altar was unconditional. Nur sure whether i see gaining the Copper pile as something that makes the card broken, at least when we are still designing the kingdom ourselves (so no Gardens). It still is not "limited" in the way i wanted it to, so good catch. Totally forgot about Salvager's buy, too, so i will remove those three just to have a correct list.

The multipliers are of no use, because when you can play an action as many times as you want with ITR, why would you use TR itself to play it two more times? I see that they might be useful to get to the 10$ that ITR costs, but the categories are about what a card does when played with ITR (nothing for multipliers). Otherwise Tactician and Secret Chamber would also be in the "limited use" list.

You can (assuming the right kingdom). Suppose 1 Rogue and 1 Scrying Pool is already in the trash, and you have a deck consisting only of action cards.
Process X, play it twice and trash it.
Process Rogue, gain X and Rogue
Process Rogue, gain Scrying Pool and Rogue
Process Scrying Pool, draw deck
Then we've played X twice, and we are in the same initial position: 1 Rogue and 1 Scrying Pool in the trash. And you've played X twice.

That's not unlimited. You can not play Procession unlimited times during one turn.

[florrat]

That's not unlimited. You can not play Procession unlimited times during one turn.

I do not understand. Why is it not unlimited? I can repeat the instructions I gave over and over, as much as I want. How is that not unlimited?

[Holger]

The multipliers are of no use, because when you can play an action as many times as you want with ITR, why would you use TR itself to play it two more times? I see that they might be useful to get to the 10$ that ITR costs, but the categories are about what a card does when played with ITR (nothing for multipliers).

Playing ITR-TR allows you to play arbitrarily many action cards twice; ITR itself only allows to play a single action card (even if infinitely often). It may be rare that you'd rather play e.g. 3 Action cards twice than one of them infinitely often, but it can happen: E.g. ITR-TR-Duchess+Militia+CountAltar can gain you a Province and two Duchies, but ITR played on either of Duchess, Militia, or CountAltar gives you less than 12 VP if there are <4 Duchies (and no other VP cards costing <=$5) left in the supply.

Edit: Fixed example.

[Awaclus]

The multipliers are of no use, because when you can play an action as many times as you want with ITR, why would you use TR itself to play it two more times? I see that they might be useful to get to the 10$ that ITR costs, but the categories are about what a card does when played with ITR (nothing for multipliers).

Playing ITR-TR allows you to play arbitrarily many action cards twice; ITR itself only allows to play a single action card (even if infinitely often). It may be rare that you'd rather play e.g. 3 Action cards twice than one of them infinitely often, but it can happen: E.g. ITR-TR-Duchess+Militia+Count can gain you a Province and two Duchies, but ITR played on either of Duchess, Militia, or Count gives you less than 12 VP if there are <4 Duchies left in the supply.

ITR-Count gains you as many Duchies as there are in the supply plus a Province. Though you might still want the discard attack from Militia rather than the extra Duchies in some cases.

[GeoLib]

That's not unlimited. You can not play Procession unlimited times during one turn.

You can if you ITR it...

More to the point, you can't gain scrying pool with Rogue

[Holger]

The multipliers are of no use, because when you can play an action as many times as you want with ITR, why would you use TR itself to play it two more times? I see that they might be useful to get to the 10$ that ITR costs, but the categories are about what a card does when played with ITR (nothing for multipliers).

Playing ITR-TR allows you to play arbitrarily many action cards twice; ITR itself only allows to play a single action card (even if infinitely often). It may be rare that you'd rather play e.g. 3 Action cards twice than one of them infinitely often, but it can happen: E.g. ITR-TR-Duchess+Militia+Count can gain you a Province and two Duchies, but ITR played on either of Duchess, Militia, or Count gives you less than 12 VP if there are <4 Duchies left in the supply.

ITR-Count gains you as many Duchies as there are in the supply plus a Province. Though you might still want the discard attack from Militia rather than the extra Duchies in some cases.

Thanks for noting, I missed Count's treasure option; I've replaced it by Altar to give an unambiguous example.

That's not unlimited. You can not play Procession unlimited times during one turn.

I do not understand. Why is it not unlimited? I can repeat the instructions I gave over and over, as much as I want. How is that not unlimited?

If your card X is fixed, playing Procession infinitely often like this doesn't do anything useful; you could just play ITR-X instead, giving the same end result of playing X infinitely often. But if there's e.g. one card of each kingdom pile in the trash, you can use this to recursively play all Rogue target infinitely often, which indeed makes ITR-Procession unlimited by your hand.

That's not unlimited. You can not play Procession unlimited times during one turn.

You can if you ITR it...

More to the point, you can't gain scrying pool with Rogue

Right; but you can just replace it by Smithy in the example (if the Rogue pile and your deck are empty otherwise)...

[dominator 123]

2) Woodcutter, Pawn, Bridge, Market etc. (Anything that gives you at least 1 buy and $1)

[Awaclus]

2) Woodcutter, Pawn, Bridge, Market etc. (Anything that gives you at least 1 buy and $1)

What if your opponent already has more than half of the available VP?

[Holger]

2) Woodcutter, Pawn, Bridge, Market etc. (Anything that gives you at least 1 buy and $1)

(Ninjaed)
That doesn't work, the opponent may already have more than half the available VPs . See http://forum.dominionstrategy.com/index.php?topic=10422.msg344475#msg344475 .

NoMoreFun, which card were you thinking about?

[NoMoreFun]

2) Woodcutter, Pawn, Bridge, Market etc. (Anything that gives you at least 1 buy and $1)

(Ninjaed)
That doesn't work, the opponent may already have more than half the available VPs . See http://forum.dominionstrategy.com/index.php?topic=10422.msg344475#msg344475 .

NoMoreFun, which card were you thinking about?

I was thinking Swindler, which is in the 2nd post, but there's a few caveats.

[NoMoreFun]

Thanks for noting, I missed Count's treasure option; I've replaced it by Altar to give an unambiguous example.

Altar's gain doesn't depend on you trashing a card, so it also lets you gain all the Duchies. In fact, you must gain all the cards in the supply costing 5 or less.

[Asper]

That's not unlimited. You can not play Procession unlimited times during one turn.

You can if you ITR it...

More to the point, you can't gain scrying pool with Rogue

Ah, i get the point...
Sure, that works, but only as long as you have a drawer. I never allowed one in my ITR kingdom though, which is why Procession can not be usefully played unlimited times in my kingdoms. The fact that it's broken comes from the drawer, not Procession.

The multipliers are of no use, because when you can play an action as many times as you want with ITR, why would you use TR itself to play it two more times? I see that they might be useful to get to the 10$ that ITR costs, but the categories are about what a card does when played with ITR (nothing for multipliers).

Playing ITR-TR allows you to play arbitrarily many action cards twice; ITR itself only allows to play a single action card (even if infinitely often). It may be rare that you'd rather play e.g. 3 Action cards twice than one of them infinitely often, but it can happen: E.g. ITR-TR-Duchess+Militia+CountAltar can gain you a Province and two Duchies, but ITR played on either of Duchess, Militia, or CountAltar gives you less than 12 VP if there are <4 Duchies (and no other VP cards costing <=$5) left in the supply.

Edit: Fixed example.

I admit you can use TR to become more flexible, which i didn't see before. As an example using the allowed cards for the kingdom, if you have Stonemason, Graverobber, TR, ITR and another action in hand, TR allows you to trash the action card with Stonemason and to get it back the same turn with Graverobber. So yes, you are right here.

[Awaclus]

Thanks for noting, I missed Count's treasure option; I've replaced it by Altar to give an unambiguous example.

Altar's gain doesn't depend on you trashing a card, so it also lets you gain all the Duchies. In fact, you must gain all the cards in the supply costing 5 or less.

But it doesn't let you gain a Province unlike Count.

[Holger]

Thanks for noting, I missed Count's treasure option; I've replaced it by Altar to give an unambiguous example.

Altar's gain doesn't depend on you trashing a card, so it also lets you gain all the Duchies. In fact, you must gain all the cards in the supply costing 5 or less.

But it doesn't let you gain a Province unlike Count.

Yes, that's the point. ITR-TR gives 12 VP in the example, ITR-Altar only gives all remaining Duchies, Estates and Curses, which can easily be <12 VP (possibly even <0 VP). If you're trailing by 7-11 VP and there's only 2 Duchies and no Estates left and another pile is empty, ITR-Altar would lose the game, while ITR-TR lets you win due to 3-piling.

[Holger]

3) Any combination of the following that has at least one of the "limited use" cards in it.

Limited use
Action cards that trash cards from your hand to work: Moneylender, Remodel, Graverobber, Expand, Remake, Treasure Map, Develop, Stonemason, Transmute, Trader, Taxman, Mine and Procession
Action cards that remove cards from you hand other ways: Island

No use
Actions that ITR has no effect on: Secret Chamber, Tactician, Outpost, Library, Watchtower
Non-Actions: All


Depends
Multipliers limited by your hand: Throne Room, King's Court
(Allow playing more than one different card in a turn, which is only relevant if there is a that card does something when played from an empty hand. Those cards include "no use cards" that still don't get additional benefit from being played by ITR)

Thanks for fixing this. Personally, I would just put TR and KC in the "Limited use" category: ITR-TR also does something with cards that don't do anything when played from an empty hand - e.g ITR-TR-Mine-Develop can gain you two Duchies if you have two Silvers in hand (by turning the Silvers into 2 Gold), but ITR-Develop can't. But it's your list, of course...

Also, I noticed that Graverobber is not really "limited to your hand" since you can gain the whole trash pile (in the $3-$6 price range) with it.
Trading Post and Chapel are missing from the "limited use" category (each "successful" play reduces your hand size at least by 1); and Counting House is another "No use" card.

[Asper]

3) Any combination of the following that has at least one of the "limited use" cards in it.

Limited use
Action cards that trash cards from your hand to work: Moneylender, Remodel, Graverobber, Expand, Remake, Treasure Map, Develop, Stonemason, Transmute, Trader, Taxman, Mine and Procession
Action cards that remove cards from you hand other ways: Island

No use
Actions that ITR has no effect on: Secret Chamber, Tactician, Outpost, Library, Watchtower
Non-Actions: All


Depends
Multipliers limited by your hand: Throne Room, King's Court
(Allow playing more than one different card in a turn, which is only relevant if there is a that card does something when played from an empty hand. Those cards include "no use cards" that still don't get additional benefit from being played by ITR)

Thanks for fixing this. Personally, I would just put TR and KC in the "Limited use" category: ITR-TR also does something with cards that don't do anything when played from an empty hand - e.g ITR-TR-Mine-Develop can gain you two Duchies if you have two Silvers in hand (by turning the Silvers into 2 Gold), but ITR-Develop can't. But it's your list, of course...

Also, I noticed that Graverobber is not really "limited to your hand" since you can gain the whole trash pile (in the $3-$6 price range) with it.
Trading Post and Chapel are missing from the "limited use" category (each "successful" play reduces your hand size at least by 1); and Counting House is another "No use" card.

Thank you, the list isn't perfect, i know...
You are right about Graverobber, it should be removed. Trading Post should be added.

Chapel is a "no use", as the kingdom still has no drawer, which means you will never have more than 4 cards in hand after playing Chapel.

You are right about the empty hand thing. It's more about not reducing your handsize to work, but it doesn't change that there are very few cards that work with it. As i defined the allowed kingdoms as any that include at least one "limited use", putting TR and KC there would seem wrong.
Also you can play with Shelters and trash an Overgrown Estate, which is still "depends" rather than "limited use".

[Holger]

Chapel is a "no use", as the kingdom still has no drawer, which means you will never have more than 4 cards in hand after playing Chapel.

Tactician, Library and Watchtower draw cards.

[NoMoreFun]

Trading Post becomes "trash your hand". A few silvers will disappear from the supply too.

[faust]

Answer for 1)

Possession, and Black Market if there are cards in the BM deck that you don't want to/can't buy (i.e. Potion cost cards). You will always have to reorder the Black Market deck.

Minion might also be a solution - while you're not exactly forced to play it forever, maybe you want a hand of four specific cards at the end, and it takes infinitely long to get there.

Possession might also be a solution for 2) - at least it guarantees you not to lose: You just possess your opponent infinite times, doing nothing every time, he will never be able to play again and thus cannot win.

[Grujah]

1) Oasis?

[Asper]

Chapel is a "no use", as the kingdom still has no drawer, which means you will never have more than 4 cards in hand after playing Chapel.

Tactician, Library and Watchtower draw cards.

Um... You are right... I think that means you actually can have endless turns. ITR, Procession, Library(or WT) and Graverobber are needed, so basically what Holger said... Man...

[Nevermind]

Hey guys!
     I know I'm new to this forum, but I thought I'd mention that there is a neat pin with this card. ITR-ITR-goons-goons-council room-x-y-z-MASQUERADE! As long as you don't play any more discard attacks, you can win by destroying their whole hand/deck. You win. GG. Any questions?

[SirPeebles]

Oh god, I just came across this thread.  I was really happy to see the OP's formulation of the question, but then it immediately devolved into a flurry of misuse of the word "infinite".  I feel physically ill from having been exposed to this.  Please, just stop even using the word "infinite".  It has little if any place in this discussion beyond the formal name of the proposed card.  Try using meaningful and accurate terms, such as "unlimited" or "arbitrarily many".  The word "infinite" means something, and you hurt it when you say things like "you have infinite VP".

[soulnet]

Oh god, I just came across this thread.  I was really happy to see the OP's formulation of the question, but then it immediately devolved into a flurry of misuse of the word "infinite".  I feel physically ill from having been exposed to this.  Please, just stop even using the word "infinite".  It has little if any place in this discussion beyond the formal name of the proposed card.  Try using meaningful and accurate terms, such as "unlimited" or "arbitrarily many".  The word "infinite" means something, and you hurt it when you say things like "you have infinite VP".

I haven't rechecked the entire thread for specific misuses, but I see no problem in saying something like "have infinite VP", at least if agree that by infinite we mean the "regular countable infinite" or "the only infinite" if you believe finitists. As far as board games go, non-finite is already strange enough, so assuming a finitist universe seems reasonable.

I certainly find having infinite VP less disturbing than transfinite induction.

[SirPeebles]

At no point does anyone ever have a VP total that is not a finite whole number.

[markusin]

At no point does anyone ever have a VP total that is not a finite whole number.

IANAM (I am not a mathematician), but I'm pretty sure Sir Peebles is correct. You can't have infinitely many of something, but you can be bounded by infinity, right?

[Witherweaver]

I don't see a problem.  You play "Infinite Throne Room" on something that gives +VP, and  you are awarded INF VP, where INF is an object that satisfies INF > x for all real x.  What's wrong with that?

[SirPeebles]

I don't see a problem.  You play "Infinite Throne Room" on something that gives +VP, and  you are awarded INF VP, where INF is an object that satisfies INF > x for all real x.  What's wrong with that?

Look at what Infinite Throne Room does.  You choose a card in your hand, let's say Monument, and then you play it repeatedly until a certain condition is satisfied.  If that condition is never satisfied, then you simply don't finish resolving Infinite Throne Room and the game does not halt.  Otherwise, that certain condition is met.  If it is met after 2 plays, then you gained +2 VP and + $4.  If it took 20 plays of Monument, then you gained + 20 VP and + $40.  But there is never a circumstance under which your number of victory tokens is anything but a finite, nonnegative whole number.

[SirPeebles]

At no point does anyone ever have a VP total that is not a finite whole number.

IANAM (I am not a mathematician), but I'm pretty sure Sir Peebles is correct. You can't have infinitely many of something, but you can be bounded by infinity, right?

You can't obtain an infinite number of something by starting with a finite amount and adding a finite number to it a finite number of times.  There may be other things that could lead to infinite quantities, but VP or coin tokens from Infinite Throne Room paired with published Dominion card are not in that list.

[Witherweaver]

I don't see a problem.  You play "Infinite Throne Room" on something that gives +VP, and  you are awarded INF VP, where INF is an object that satisfies INF > x for all real x.  What's wrong with that?

Look at what Infinite Throne Room does.  You choose a card in your hand, let's say Monument, and then you play it repeatedly until a certain condition is satisfied.  If that condition is never satisfied, then you simply don't finish resolving Infinite Throne Room and the game does not halt.  Otherwise, that certain condition is met.  If it is met after 2 plays, then you gained +2 VP and + $4.  If it took 20 plays of Monument, then you gained + 20 VP and + $40.  But there is never a circumstance under which your number of victory tokens is anything but a finite, nonnegative whole number.

I didn't think that was what Infinite Throne Room was doing.  I thought we were defining Infinite Throne Room's action to be that if you play it on something that would never resolve (e.g., something that gives +$ or +VP), you simply define it to be resolved by introducing infinity and take everything to be in the extended reals.

[SirPeebles]

I don't see a problem.  You play "Infinite Throne Room" on something that gives +VP, and  you are awarded INF VP, where INF is an object that satisfies INF > x for all real x.  What's wrong with that?

Look at what Infinite Throne Room does.  You choose a card in your hand, let's say Monument, and then you play it repeatedly until a certain condition is satisfied.  If that condition is never satisfied, then you simply don't finish resolving Infinite Throne Room and the game does not halt.  Otherwise, that certain condition is met.  If it is met after 2 plays, then you gained +2 VP and + $4.  If it took 20 plays of Monument, then you gained + 20 VP and + $40.  But there is never a circumstance under which your number of victory tokens is anything but a finite, nonnegative whole number.

I didn't think that was what Infinite Throne Room was doing.  I thought we were defining Infinite Throne Room's action to be that if you play it on something that would never resolve (e.g., something that gives +$ or +VP), you simply define it to be resolved by introducing infinity and take everything to be in the extended reals.

I interpreted the bulleted list to be (incorrect) clarifications of the card's effect.  If we instead take them as additional rules, then I still object to the use of "infinite VP".  Just say that if you play a card granting VP, then you will win at the end of the game and that VP no longer determines winners.  That's a lot simpler than introducing the arithmetic of extended real numbers.

[Witherweaver]

I don't see a problem.  You play "Infinite Throne Room" on something that gives +VP, and  you are awarded INF VP, where INF is an object that satisfies INF > x for all real x.  What's wrong with that?

Look at what Infinite Throne Room does.  You choose a card in your hand, let's say Monument, and then you play it repeatedly until a certain condition is satisfied.  If that condition is never satisfied, then you simply don't finish resolving Infinite Throne Room and the game does not halt.  Otherwise, that certain condition is met.  If it is met after 2 plays, then you gained +2 VP and + $4.  If it took 20 plays of Monument, then you gained + 20 VP and + $40.  But there is never a circumstance under which your number of victory tokens is anything but a finite, nonnegative whole number.

I didn't think that was what Infinite Throne Room was doing.  I thought we were defining Infinite Throne Room's action to be that if you play it on something that would never resolve (e.g., something that gives +$ or +VP), you simply define it to be resolved by introducing infinity and take everything to be in the extended reals.

I interpreted the bulleted list to be (incorrect) clarifications of the card's effect.  If we instead take them as additional rules, then I still object to the use of "infinite VP".  Just say that if you play a card granting VP, then you will win at the end of the game and that VP no longer determines winners.  That's a lot simpler than introducing the arithmetic of extended real numbers.

It seems to me like the question was, "What rules do we have to assign so that this card can resolve?" 

I don't really see a difference between using the extended reals and defining "you win at the end of the game," "you are unrestrained by $ when you make buys," "you can buy any number of cards," "you can play any number of actions".  I mean, the whole point of the card is making sense of "infinite plays," so using an "infinity" object doesn't seem far fetched.

[SirPeebles]

There's no difference in theory, but come on.  Dominion is a rather approachable card/board game.  Do you really want to rules to reference the extended real numbers?

[Witherweaver]

There's no difference in theory, but come on.  Dominion is a rather approachable card/board game.  Do you really want to rules to reference the extended real numbers?

Well the whole point was a puzzle.. I don't think anyone was going to think of publishing this card.

[soulnet]

I interpreted the card as leaving the game state in the limit of the game states after n=1,2,3,... plays. As long as that does not require an infinite number of decisions, that is a perfectly well determined thing (or not, depending on whether the limit exist). The limit of playing Monument infinitely can be defined rather well as having infinite $ and infinite VP, as specified by the FAQ.

However, the limit of things with decisions require more careful analysis. Infinitely playing Chapel or Courtyard requires you to do infinitely many decisions, and that is a little harder to define. However, if we consider two sets of decisions that yield the same limit as an equivalent class, there are finitely many decisions, because there are finitely many game states. Thus, the game with ITR can stil be regarded as a finite game, where some quantities that previously could only be integer numbers (like the amount of VP or money), can now also be infinite.

The only problem with those rules is having infinite coin tokens, because you can play those, which means you can end up subtracting infinites. But, as long as we do not play with coin tokens, everything sounds sound.

Of course, adding infinitary limits complicates the game a lot, and I would not use this for anything other than a brain teaser. But I don't think using infinite as an object is as problematic as some of you seem to think.

[markusin]

In this case, you can't say you have "infinite VP" because any player who plays ITR-Monument after you did should be able to surpass your lead in VP by playing Monument x + 1 times, where x is the number of times you played Monument with ITR up to that point. However, you can't say (∞ + 1)  > ∞.

[Witherweaver]

In this case, you can't say you have "infinite VP" because any player who plays ITR-Monument after you did should be able to surpass your lead in VP by playing Monument x + 1 times, where x is the number of times you played Monument with ITR up to that point. However, you can't say (∞ + 1)  > ∞.

Huh?  When you play ITR on Monument, the result is INF VP points.  INF is a number such that INF > x for all real numbers x.  If someone else plays ITR on Monument, the result is they get INF VP points.  It is not true that INF > INF (note that INF is not a real number), so you do not beat them, and they do not beat you.  In this case, you can define the result to be a tie.

If you play ITR on Monument, you certainly don't play Monument x times.  That would never resolve.. that's the whole point of defining special rules.  You played it once with ITR, giving INF VP points.

[Witherweaver]

The only problem with those rules is having infinite coin tokens, because you can play those, which means you can end up subtracting infinites. But, as long as we do not play with coin tokens, everything sounds sound.

I don't think this is a problem.  If you play ITR on Baker, you get INF coin tokens.  This just means that you're able to generate $N (by spending N coin tokens) for any real number N every turn thereafter. Since N is finite, you're still left with INF coin tokens.

[markusin]

In this case, you can't say you have "infinite VP" because any player who plays ITR-Monument after you did should be able to surpass your lead in VP by playing Monument x + 1 times, where x is the number of times you played Monument with ITR up to that point. However, you can't say (∞ + 1)  > ∞.

Huh?  When you play ITR on Monument, the result is INF VP points.  INF is a number such that INF > x for all real numbers x.  If someone else plays ITR on Monument, the result is they get INF VP points.  It is not true that INF > INF (note that INF is not a real number), so you do not beat them, and they do not beat you.  In this case, you can define the result to be a tie.

If you play ITR on Monument, you certainly don't play Monument x times.  That would never resolve.. that's the whole point of defining special rules.  You played it once with ITR, giving INF VP points.

Special rules?

...
On right, special rules. They're in the OP.

In the OP, ITR-Monument is said to guarantee that you don't lose while still allowing the card to resolve.

Carry on then.

[SirPeebles]

You play an ITR on a Monument.  The Copper and Curse piles are empty, not a Ruins game.

I play ITR on a Candlestick Maker.  I have a Goons in play and a Trader in hand.  I want to buy Estate repeatedly while revealing Trader.  What happens?  Am I able to share victory?  How do you model this with the extended real numbers?

[Witherweaver]

You play an ITR on a Monument.  The Copper and Curse piles are empty, not a Ruins game.

I play ITR on a Candlestick Maker.  I have a Goons in play and a Trader in hand.  I want to buy Estate repeatedly while revealing Trader.  What happens?  Am I able to share victory?  How do you model this with the extended real numbers?

You could have just played ITR on the Goons; I think the Candlestick Maker is not needed.  But anyway.

I think you get INF VP tokens here, as long as you claim you are revealing Trader each time you buy an Estate.  The first N times, you gain N Silvers, where N is the number of Silvers remaining.  Then (in hypothetical space) you continue to buy Estates, which is fine because the Estate pile is not empty, get the VP token for the buy, fail to gain a Silver (since the pile is empty).  This process has the defined resolution: Silver pile empty, all Silvers gained by you, INF VP to you.

So the game ends in a tie (INF to INF), or a loss if you're first player.

The thing that would be hard to resolve, however, is: Do you have more buys left?  That isn't really defined.  But I don't think it actually has to be.  It only matters if you have more buys left if you want to buy something else.  In which case, you could make any number of (finite) buys (say, to empty piles if there wasn't going to be a three-pile ending), and then resolve the unlimited buy, unlimited Trader reveal scenario. 

[florrat]

The word "infinite" means something, and you hurt it when you say things like "you have infinite VP".

The only problem which I have when someone says "you have infinite VP", I'd want to know "What infinity?" Other than that I have no problem with the statement "If you play monument infinitely often, you have infinity coins and infinite VP chips": if "infinity" is replaced by ω (omega, the "smallest infinity" (yes, there are multiple sizes infinity)), this statement makes perfect sense to me.

[soulnet]

The word "infinite" means something, and you hurt it when you say things like "you have infinite VP".

The only problem which I have when someone says "you have infinite VP", I'd want to know "What infinity?" Other than that I have no problem with the statement "If you play monument infinitely often, you have infinity coins and infinite VP chips": if "infinity" is replaced by ω (omega, the "smallest infinity" (yes, there are multiple sizes infinity)), this statement makes perfect sense to me.

I think I have addressed this above, with the same thought. BTW, omega should actually be aleph 0. Omega is not the cardinal but the ordinal.

I really do not understand people being fine with things like transfinite induction and not finite with something so relatively simple as a non-finitary game. This is not even the first attempt to define a non-finitary game.

[SirPeebles]

The word "infinite" means something, and you hurt it when you say things like "you have infinite VP".

The only problem which I have when someone says "you have infinite VP", I'd want to know "What infinity?" Other than that I have no problem with the statement "If you play monument infinitely often, you have infinity coins and infinite VP chips": if "infinity" is replaced by ω (omega, the "smallest infinity" (yes, there are multiple sizes infinity)), this statement makes perfect sense to me.

Sure, *if* you played a card infinitely often.  But you don't.  Not even with this proposed Infinite Throne Room card.  That is what bothered me.  Also, ω + 1 > ω, whereas 1 + ω = ω, and ω + (-1) is nonsensical as far as I know.  This is not a good start for modeling VP.

[Witherweaver]

The word "infinite" means something, and you hurt it when you say things like "you have infinite VP".

The only problem which I have when someone says "you have infinite VP", I'd want to know "What infinity?" Other than that I have no problem with the statement "If you play monument infinitely often, you have infinity coins and infinite VP chips": if "infinity" is replaced by ω (omega, the "smallest infinity" (yes, there are multiple sizes infinity)), this statement makes perfect sense to me.

I think the extended real line model works better. Arithemtic doesn't work correctly with ordinals (as Peebles said).  Though I think it does work with cardinals, and I think using aleph null would be the same as using the extended reals.  But I don't really know much about this.

Edit: And I think thinking about playing something infinitely often is misleading. Plus what does "infinitely often" mean?  If you "play it once" for every element of the natural numbers, that's different than "playing it once" for every element of the real numbers.

More like when you play infinite throne room and announce its target, the process must resolve.  We therefore must define its action on each card so that the process resolves.  The question is, how to define these things?  The sort of "natural" way would be to think of taking limits and working in a compact set.  "Taking limits" in the sense of.. play it once, what happens?  Play it a second time, what happens?  Play it a third time, etc.  Does this process resolve?  Well, if playing it once means +1 counter, then playing it n times means +n counters, so we might as well take the limit to be +INF counters in the extended reals. 

In general, you would want to define the action of ITR on a target to be the value (game state result) of the limiting process of playing that card sequentially {1,2,3,....}.

[soulnet]

Sure, *if* you played a card infinitely often.  But you don't.  Not even with this proposed Infinite Throne Room card.  That is what bothered me.  Also, ω + 1 > ω, whereas 1 + ω = ω, and ω + (-1) is nonsensical as far as I know.  This is not a good start for modeling VP.

You should not be using \omega, but \aleph_0 instead. Since \aleph_0 = \aleph_0 + 1 = \aleph_0 - 1, and there is nothing with the hability to produce -infinity VP, I see no issue. You really only need \omega is you want to do transfinite induction, but you do not, because there is only one kind of infinite throughout the entire game, so regular limit arithmetic is fine.

The ad-hoc rule that is needed is that decisions are choosing one of the possible equivalence classes of decisions that yield a limiting behavior including the infinites as possible values for VPs, coins, buys and actions. I.e., making decisions that yield oscillating behavior is forbidden.

[Witherweaver]

Technically, Dominion already has an "infinite" action that is defined (or agreed) to resolve, right?  You can continually reveal Trader to continually would-gain the top Silver.  But nothing changes after your first reveal, so we all decide the player should just stop revealing.  The same (or similar) holds of all reaction cards.

[KingZog3]

Technically, Dominion already has an "infinite" action that is defined (or agreed) to resolve, right?  You can continually reveal Trader to continually would-gain the top Silver.  But nothing changes after your first reveal, so we all decide the player should just stop revealing.  The same (or similar) holds of all reaction cards.

All reaction cards that don't discard themselves. So Moat, Trader and Watchtower only.

EDIT: And even then, Watchtower can't be revealed more than once if you trash the gained card.

[Witherweaver]

Technically, Dominion already has an "infinite" action that is defined (or agreed) to resolve, right?  You can continually reveal Trader to continually would-gain the top Silver.  But nothing changes after your first reveal, so we all decide the player should just stop revealing.  The same (or similar) holds of all reaction cards.

All reaction cards that don't discard themselves. So Moat, Trader and Watchtower only.

Well, yes.  And Secret Chamber (if you choose not to put it on top of your deck.. or if you have more than one and cycle through them).

[NoMoreFun]

"Infinite VP" = You win (you might share the victory with another person with Infinite VP. It's countable infinity unless someone can prove there's another way)

[sudgy]

"Infinite VP" = You win (you might share the victory with another person with Infinite VP. It's countable infinity unless someone can prove there's another way)

(Also, player 2 might win on turn if they both have Infinite VP)

[soulnet]

(Also, player 2 might win on turn if they both have Infinite VP)

Is not shared victory: the game does not end. The optimal strategy for player 2 once they both have infinite VP is to not end the game (which you can always do by not buying/gaining anything on your turn). Thus, player 1 can either lose buy ending the game or also refrain to do it, which is of course the optimal choice.

[silverspawn]

well, mathematical theory states that there is an infinite number of finite numbers. thus, you have infinite different possibilities of how often you want to play your throne room, but you're never playing it for an infinite amount of times.

as for the vp thing, i imagine that to be pretty unexciting, because it's the same as "once this is played, when the game ends, the person who played this most recently wins." If i play infinite monument and make myself a million VP Tokens, my opponent can just make 2 millions next. If i make 10^(10^100) my opponent can just make 2*10^(10^100). it doesn't matter how high the number is, really, because the next guy can always just double it. whoever played it most recently wins.

if noone has gotten infinite tokens yet, it's actually better to play a market, then you win the game instantly

[soulnet]

that's not infinite throne room, that's a different card (unbounded throne room? arbitrarily large throne room?)

[WalrusMcFishSr]

If you were somehow able to play ITR on another ITR, and then play infinite Monuments, would that count as a higher "cardinality" or whatever of victory? Or is that still "countable"?

Also, if you play ITR-Pirate Ship and your opponent has infinite or renewable treasure cards, you could go for the -$1/12...

[soulnet]

If you were somehow able to play ITR on another ITR, and then play infinite Monuments, would that count as a higher "cardinality" or whatever of victory? Or is that still "countable"?

No, it is still countable. As long as you have countably many Monuments, you won't be able to leave the countable world, independently on how many ITRs you have.

Also, if you play ITR-Pirate Ship and your opponent has infinite or renewable treasure cards, you could go for the -$1/12...

Oh, that fallacy again... it is hunting me...