Dominion Strategy Forum
Dominion => Rules Questions => Topic started by: theory on December 06, 2011, 11:47:01 am
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Forge: Trash any number of cards from your hand. Gain a card with cost exactly equal to the total cost in coins of the trashed cards.
Remodel: Trash a card from your hand. Gain a card costing up to $2 more than the trashed card.
Question: Why can I use Forge to trash 0 cards and gain a $0, but I can't use Remodel to trash nothing (if my hand is empty) and gain up to a $2?
Is it the "any number of cards" vs "a card" distinction? I don't think so, because Remodel doesn't have a "If you do" clause like Trading Post.
Is it that if you don't have a trashed card, then you can't gain a card that costs up to $2 more than it? I don't think so, because if you have no trashed card, Forge shouldn't be able to gain a card whose cost is equal to it.
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If you choose to trash no cards with Forge, then (mathematically) you have an empty sum. That's just 0. It's defined, since we know what the total cost of {} is (i.e. the sum of {} is 0)
On the other hand, Remodel asks us to gain a card costing 2 more than the trashed card. But we didn't trash a card. How can we add 2 to x when x isn't defined? We can't assume it's 0, since there's no real reason for it to be, except it being in some way 'nice'.
That's how I would think about it, at least.
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For Forge: if we accept that zero is a number and 'the set of trashed cards from your hand' can be null and that such a null set has an equivalent total cost of zero, then forge's action makes sense. The set of trashed cards is defined, and something is done based on that set.
Remodel's second part, however, is contingent on there existing one card that has been trashed. Remodel's second part does not refer to the cost of the trashed card, but rather the trashed card itself. Assuming that the first part creates 'the set containing the one trashed card' doesn't change the fact that Remodel refers to the card itself and not some calculation of the set.
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With regard to Remodel, this is similar to the Ironworks/Trader issue, but even more clear: If there is no "trashed card", then there is no value for "the trashed card" that you can add $2 to. Put another way, you can't follow the 2nd instruction since a necessary referent ("the trashed card") doesn't exist, so you don't follow the instruction.
The thornier question is why you do gain a $0 card if you trash nothing with Forge. The easy answer is to refer to the FAQ, which echoes Tables/play2draw's reasoning: "This is different from how cards like Expand work if you do not trash anything, because Forge looks at the total, not at any one card's cost."
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I appreciate that Remodel can't gain anything, but I find it difficult to swallow that the "cost" of null is undefined, but the "total cost" of null is 0.
I suppose this is just how it is. Wanted to know if there was a more persuasive justification.
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While I agree that 0 is a part of the "any number" set, both cards do refer to "the trashed card(s)" so I'm not convinced either.
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I appreciate that Remodel can't gain anything, but I find it difficult to swallow that the "cost" of null is undefined, but the "total cost" of null is 0.
It's because, to put it in quasi-mathematical terms, the function "total" looks for a set, whereas the function "cost" looks for a card. If there's no card, the function "cost" can't find what it's looking for (i.e., a card), so it can't output a value. But the function "total" isn't looking for a card; it's looking for a set. So even if there's no card, "total" can still find what it's looking for (i.e., a set) because the empty set is still a set, so it has a well-defined output.
In other words, No Cards isn't a card. But it is still a set of cards.
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Ah. The Wikipedia article (http://en.wikipedia.org/wiki/Empty_set#Operations_on_the_empty_set) supports your argument, namely, that the sum of an empty set is defined as 0 (http://en.wikipedia.org/wiki/Empty_sum).
If a Dominion card ever comes out that is Forge but with multiplicative product instead of additive sum, I fully expect it to also conform to mathematical set theory and force you to gain a $1 card if you trash no cards (http://en.wikipedia.org/wiki/Empty_product).
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If a Dominion card ever comes out that is Forge but with multiplicative product instead of additive sum, I fully expect it to also conform to mathematical set theory and force you to gain a $1 card if you trash no cards (http://en.wikipedia.org/wiki/Empty_product).
I would be confused if it didn't.
Say we have about a million people playing Dominion for the first time. Let's count only those who got a 5/2 split. About how many would there be? Now they all play a second time and we require them to have gotten a 5/2 split twice to count them. How many? After n games, let's only count them if they got a 5/2 split in every game they played. Hm let's go back a step. Before they played a game, let's only count them if they got a 5/2 split in every game they played. How many?
I claim the probability of a size 0 conjunction of independent events equaling 1, P({})=1, should now be intuitive. :D
What other f({}) are there in Dominion? Inn... do you get to shuffle your deck? I say yes.
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Eesh, too much set theory.
I see it in programming terms (JavaScript in this instance):
function DominionCard(){
this.cost = 5;
}
var duchy = new DominionCard();
// duchy.cost = 5;
// Remodel:
var trashedCard = null; // nothing was trashed
var remodelValue = trashedCard.cost + 2;
// gives a fatal type error as trashedCard.cost is undefined, so it fails out
// Forge:
var total = 0;
var trashedCards = []; // empty array
for(var i = 0; i < trashedCards.length; i++){
total += trashedCards[i].cost;
}
// gives the correct value, 0
The key part is that a sum/total implies a starting value, that of 0, which things are added to.
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A lot of complex replies to this one. The quoted passage from the FAQ is the clearest explanation, I think. Or maybe like this:
Remodel tells you to trash one card. Then gain a card based on the cost of the card you trashed. If you didn't trash a card, you have no basis for the second part. (So this is an implicit "if you do.")
Forge tells you to trash any number of cards from zero cards and upwards. Then gain a card based on the total cost of the trashed cards. If you trashed zero cards, the total cost is $0.
If Remodel said "Gain a card costing up to $2 more than total cost of the trashed cards" then you would gain a card costing up to $2 when trashing zero cards. The reason is that Remodel now doesn't refer to the specific card you trashed, but the cost of all the cards you trashed, which could either be one (if your hand wasn't empty) or zero (if your hand was empty).
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Outside of Develop, is Remodel the only card which allows you to trash and downgrade the value of a card?
Forge: Trash any number of cards from your hand. Gain a card with cost exactly equal to the total cost in coins of the trashed cards (trashing a Border Village for a Duchy late-game for example) ?
Remodel: Trash a card from your hand. Gain a card costing up to $2 more than the trashed card.
Question: Why can I use Forge to trash 0 cards and gain a $0, but I can't use Remodel to trash nothing (if my hand is empty) and gain up to a $2?
Is it the "any number of cards" vs "a card" distinction? I don't think so, because Remodel doesn't have a "If you do" clause like Trading Post.
Is it that if you don't have a trashed card, then you can't gain a card that costs up to $2 more than it? I don't think so, because if you have no trashed card, Forge shouldn't be able to gain a card whose cost is equal to it.
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Outside of Develop, is Remodel the only card which allows you to trash and downgrade the value of a card?
Forge: Trash any number of cards from your hand. Gain a card with cost exactly equal to the total cost in coins of the trashed cards (trashing a Border Village for a Duchy late-game for example) ?
Remodel: Trash a card from your hand. Gain a card costing up to $2 more than the trashed card.
Question: Why can I use Forge to trash 0 cards and gain a $0, but I can't use Remodel to trash nothing (if my hand is empty) and gain up to a $2?
Is it the "any number of cards" vs "a card" distinction? I don't think so, because Remodel doesn't have a "If you do" clause like Trading Post.
Is it that if you don't have a trashed card, then you can't gain a card that costs up to $2 more than it? I don't think so, because if you have no trashed card, Forge shouldn't be able to gain a card whose cost is equal to it.
Expand. Saboteur if were being picky.
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You don't need set theory for this. You go to the shop. You can buy sweets in packs of ten and packs of twenty. You don't buy any packs. How many sweets have you bought? Zero.
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Outside of Develop, is Remodel the only card which allows you to trash and downgrade the value of a card?
Expand. Saboteur if were being picky.
Mine.
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Feast.
Edit:
Transmute.
Trading post, in a way. (Trash 2 Plat -> Silver).
Horn of Plenty, in a way. (Trash this to gain an Estate).
Edit2:
@Octo - my thoughts exactly, you must initiate a sum with zero, otherwise you cannot calculate it.
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upgrade(village+bm+quarry+upgrade), too nitpicky?
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upgrade(village+bm+quarry+upgrade), too nitpicky?
Upgrade can't do this. "+1 Card +1 Action Trash a card from your hand. Gain a card costing exactly $1 more than it."
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upgrade(village+bm+quarry+upgrade), too nitpicky?
Upgrade can't do this. "+1 Card +1 Action Trash a card from your hand. Gain a card costing exactly $1 more than it."
Actually you can.
Quarry makes Goons cost 4, so now you can upgrade Goons into Duchy.
But you can to that with Remodel, Expand and anything else actually, not just upgrade :D
Also depending on how do you define "trash and downgrade", JoaT can trash a Province and gain a Silver.