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Dominion: Empires» Forums » Rules

Subject: Workshop with royal blacksmith rss

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Can you use workshop to gain royal blacksmith? Doesn't royal blacksmith have a cost of 0 coins and therefore is "up to 4 coins"?
 
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David desJardins
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No, Royal Blacksmith has a cost of 0 coins plus 4 debt, which is not less than or equal to 4 coins. This is explained thoroughly in the rulebook.
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DaviddesJ wrote:
No, Royal Blacksmith has a cost of 0 coins plus 4 debt, which is not less than or equal to 4 coins. This is explained thoroughly in the rulebook.


Thanks for the quick response. So the key to the explanation I believe (correct me if I'm wrong) after reading it for the nth time is that since royal blacksmith cost is 0 coins and 8 debt, it is larger than what workshop allows you to get ( up to 4 coins with 0 debt) because 8 debt is greater than 0 debt?

So a workshop could never get you anything with positive debt?
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Chris Schumann
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MoviinTarget wrote:
So the key to the explanation I believe (correct me if I'm wrong) after reading it for the nth time is that since royal blacksmith cost is 0 coins and 8 debt, it is larger than what workshop allows you to get ( up to 4 coins with 0 debt) because 8 debt is greater than 0 debt?


I think you have it just fine... maybe this will help even more?

Cost in Coins and Cost in Debt are orthogonal. That is, a cost of 3 coins is neither greater than nor less than a cost of 4 debt.

The very first example in the rules:
Quote:
4 Debt is not "up to 4 Coins". 4 debt is not more than 4 coins and 4 coins is not more than 4 debt; both have something the other lacks.


If you want to imagine a numeric plane, where the coin cost is the x axis, and the debt cost is the y axis, workshop lets you gain a card with a cost up to 4 coins. This would mean anywhere on the x axis up to 4, but nothing with any debt cost. Nothing (yet) ever costs less than 0, so we can stay in just the first quadrant.

(You could also extrapolate a z axis being a Potion cost, since it is also orthogonal to the other two.)
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David desJardins
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MoviinTarget wrote:
Thanks for the quick response. So the key to the explanation I believe (correct me if I'm wrong) after reading it for the nth time is that since royal blacksmith cost is 0 coins and 8 debt, it is larger than what workshop allows you to get ( up to 4 coins with 0 debt) because 8 debt is greater than 0 debt?


The cost of the Royal Blacksmith is neither greater than 4 coins nor less than 4 coins. In mathematics, this relationship is called "incomparable". In a partially ordered set, it is not always the case that either X > Y, X = Y, or X < Y. There is a fourth possibility which is that X is incomparable with Y.
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Jonathan Kift
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Whizkid wrote:
MoviinTarget wrote:
So the key to the explanation I believe (correct me if I'm wrong) after reading it for the nth time is that since royal blacksmith cost is 0 coins and 8 debt, it is larger than what workshop allows you to get ( up to 4 coins with 0 debt) because 8 debt is greater than 0 debt?


I think you have it just fine... maybe this will help even more?

Cost in Coins and Cost in Debt are orthogonal. That is, a cost of 3 coins is neither greater than nor less than a cost of 4 debt.

The very first example in the rules:
Quote:
4 Debt is not "up to 4 Coins". 4 debt is not more than 4 coins and 4 coins is not more than 4 debt; both have something the other lacks.


If you want to imagine a numeric plane, where the coin cost is the x axis, and the debt cost is the y axis, workshop lets you gain a card with a cost up to 4 coins. This would mean anywhere on the x axis up to 4, but nothing with any debt cost. Nothing (yet) ever costs less than 0, so we can stay in just the first quadrant.

(You could also extrapolate a z axis being a Potion cost, since it is also orthogonal to the other two.)


Now someone needs to find a way to explain complex (or hypercomplex) algebra using Dominion. We might end up with a whole new batch of abstract mathematicians!
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Clive Jones

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As I've noted elsewhere, it's not valid to compare debt costs to imaginary numbers.

We can't tell the two square roots of -1 apart, so we label one of them +i and the other -i arbitraily. If we switched the labels round, all of mathematics would continue to work exactly as before.

This means you can't say that 2i is greater than i. But you can say that a debt of 2 is a greater cost than a debt of 1.
 
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David desJardins
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clivej wrote:
This means you can't say that 2i is greater than i. But you can say that a debt of 2 is a greater cost than a debt of 1.


Sure you can. There are lots of partial orders you can impose on the Gaussian integers. One of them has a+bi >= c+di iff a >= c and b >= d. Another partial order has a+bi >= c+di iff a >= c and b <= d. There are lots of others, too.
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Clive Jones

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Well yes, but those are orders being imposed on the Gaussian integers. There isn't an inherent natural ordering for them in the way that there is for the integers.
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Maarten Robinson
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As a friend of mine once said when we were discussing such things back in the lates 60's .... "Deep"
 
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