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[SirPeebles]

As someone who teaches math for a living, it is really fascinating to see how often this confusion comes up.

For anyone who has been confused by this, are you similarly confused in Settlers of Catan?  A road costs less than a settlement, but not less than a development card.  But of course, neither does the development card cost less than the road.

I wonder if the issue is that Dominion's coins and potions don't feel like they are on an equal footing the way that Catan's wood and sheep are.  It is though coins are the real money, and somehow potions need to be shoehorned into that price scale, rather than just being its own independent resource.

Well, in that case, I think a more likely mistake would be to compare them by quantity and claim that a road costs less than a development card because roads only need 2 resources while dev cards need 3.

Of course, Settlers of Catan is largely about relative scarcity.  While the costs of roads and dev cards can't be compared in the abstract, within the context of the game it is a bit different.  There is essentially an economy which develops, which allows one to compare value within the context of the moment.  Similar to how in real life, a laptop is more valuable than a potato (usually), despite there being no intrinsic value in either.

But then, coins and potions aren't consumed in the way that Catan's resources or real world resources are consumed or exchanged.

[Showdown35]

Ok. One last time. I do get it. The math all makes sense, and mathematically you compare the two costs on two different scales, then you can answer the question.  I'm not just talking mathematically. In general, the question can't be answered by definitively because the two costs are incomparable. Mathematically, yes, you can say they are on different scales, so yes, there is an answer. But math is not the only way to compare things. There are different ways to look at it, sometimes you can buy Golem and not Mine, sometimes you can buy Mine and not Golem, so using logic, not advanced math, sometimes Golem is less expensive, sometimes its more, you can't answer definitely so you have to answer no. I understand that the answer to the question is no. What I'm saying is there is an explanation as to why it is no. The costs are not comparable, so that's why its no.

[SirPeebles]

 

[eHalcyon]

Ok. One last time. I do get it. The math all makes sense, and mathematically you compare the two costs on two different scales, then you can answer the question.  I'm not just talking mathematically. In general, the question can't be answered by definitively because the two costs are incomparable. Mathematically, yes, you can say they are on different scales, so yes, there is an answer. But math is not the only way to compare things. There are different ways to look at it, sometimes you can buy Golem and not Mine, sometimes you can buy Mine and not Golem, so using logic, not advanced math, sometimes Golem is less expensive, sometimes its more, you can't answer definitely so you have to answer no. I understand that the answer to the question is no. What I'm saying is there is an explanation as to why it is no. The costs are not comparable, so that's why its no.

Are you saying that you're using a different definition of "more expensive"?  You say "using logic, not advanced math" -- well, this isn't advanced math, and you should note that logic is actually a branch of math.  What we're talking about isn't some illogical grad level math stuff... it's math, and it's logical.

You say that "sometimes Golem is less expensive [than Mine]" -- that's false.  It is never less expensive than Mine.
You say that "sometimes it's more [expensive than Mine]" -- also false.  It is never more expensive than Mine.
You can answer definitively that no, it is neither more expensive nor less expensive than Mine.

The costs are comparable by comparing coins to coins and potions to potions.  You cannot compare potions directly to coins, but you can compare costs as a whole.  Note that this does not mean it is possible to order a set of cards by cost (without additional rules) because of situations like Golem vs. Mine.

And perhaps related to your confusion, there is a different between "less expensive" and "not more expensive".

"Golem is less expensive than Mine."  That's false.
"Golem is not more expensive than Mine."  That's true.



Maybe we should stop?  It's just hard for us to say "agree to disagree" because this is actually not a matter of opinion.

[Showdown35]

Is Familiar more expensive that Silver?  $3 == $3 and 1P > 0P so yes.
Is Familiar more expensive than Estate?  $3 > $2 and 1P > 0P so yes.
Is Golem more expensive than Familiar?  $4 > $3 and 1P == 1P so yes.
Is Golem more expensive than Mine?  $4 < $5 and 1P > 0P, so no!
Is Golem less expensive than Mine?  $4 < $5 and 1P > 0P so no again!

Is Familiar more expensive that Silver?  $3 == $3 and 1P > 0P so yes.--> AGREED!
Is Familiar more expensive than Estate?  $3 > $2 and 1P > 0P so yes.-->AGREED!
Is Golem more expensive than Familiar?  $4 > $3 and 1P == 1P so yes.-->AGREED!
Is Golem more expensive than Mine?  $4 < $5 and 1P > 0P, so no!
Is Golem less expensive than Mine?  $4 < $5 and 1P > 0P so no again!

Looking at those last two statements, the two cards look to be equal. Golem is more expensive in one aspect, and less expensive in another, so if there is no relational value between the two aspects, then you can state Golem=Mine and be true (I'm not saying I believe that to be true).  By saying beyond a shadow of a doubt that Golem is NOT less expensive than Mine, you are stating that there is a way to combine the two values together and come up with a definitive answer. Now, the question should be, "Is Golem less expensive than Mine in each measurable aspect?" That is clearly no, which is how I think you are all answering the question, but without "each measurable aspect" in the question, you are trying to determine the complete value of one card compared to the complete value of another, which is what is impossible to do. That is all I'm trying to say, you CAN'T definitively say the complete value of Golem is less than the complete value of Mine because it can't be known.  You CAN definitively say that not all measurable values of Golem are less than those of Mine, which is how you get your answer of NO!

So yes, I do get it.

And I find this debate very stimulating.


EDIT: I'm not saying I disagree with the answer being "No, Golem is not less expensive than Mine," I'm simply saying how I understand that we arrive at that answer.

[SirPeebles]

I can't wait for Alchemy week in the Treasure Chest contest.  My entry is going to troll y'all so hard!

[LastFootnote]

Is Familiar more expensive that Silver?  $3 == $3 and 1P > 0P so yes.
Is Familiar more expensive than Estate?  $3 > $2 and 1P > 0P so yes.
Is Golem more expensive than Familiar?  $4 > $3 and 1P == 1P so yes.
Is Golem more expensive than Mine?  $4 < $5 and 1P > 0P, so no!
Is Golem less expensive than Mine?  $4 < $5 and 1P > 0P so no again!

Is Familiar more expensive that Silver?  $3 == $3 and 1P > 0P so yes.--> AGREED!
Is Familiar more expensive than Estate?  $3 > $2 and 1P > 0P so yes.-->AGREED!
Is Golem more expensive than Familiar?  $4 > $3 and 1P == 1P so yes.-->AGREED!
Is Golem more expensive than Mine?  $4 < $5 and 1P > 0P, so no!
Is Golem less expensive than Mine?  $4 < $5 and 1P > 0P so no again!

Looking at those last two statements, the two cards look to be equal. Golem is more expensive in one aspect, and less expensive in another, so if there is no relational value between the two aspects, then you can state Golem=Mine and be true (I'm not saying I believe that to be true).  By saying beyond a shadow of a doubt that Golem is NOT less expensive than Mine, you are stating that there is a way to combine the two values together and come up with a definitive answer. Now, the question should be, "Is Golem less expensive than Mine in each measurable aspect?" That is clearly no, which is how I think you are all answering the question, but without "each measurable aspect" in the question, you are trying to determine the complete value of one card compared to the complete value of another, which is what is impossible to do. That is all I'm trying to say, you CAN'T definitively say the complete value of Golem is less than the complete value of Mine because it can't be known.  You CAN definitively say that not all measurable values of Golem are less than those of Mine, which is how you get your answer of NO!

So yes, I do get it.

And I find this debate very stimulating.

See, you're still making the implicit assumption that all cards can be valued on a single scale. Each card has a well-defined, measurable cost. It's not that we don't know if Mine costs more or less than Golem. We know that Mine costs neither more or less than Golem. Nor are the two costs equal. The problem is that the question, "Which costs the most: Mine or Golem?" isn't a valid question. You might as well be asking, "How many motorsports can siphon an alternative tax credit?" It's a grammatically valid question, but it's not meaningful.

Examples: The question, "Which member of this set is the greatest? {4, 23, 17}" has an answer because that set is a totally ordered set. If the set isn't totally ordered, that question loses meaning. "Which member of this set is the greatest? {4, lime, Canada, disappointment}" is an unordered set. {4, 7, Godzilla} is a partially ordered set. Is 7 > 4? Yes. Is 7 > Godzilla? No, but neither is Godzilla > 7. Because the set isn't fully ordered, we can't meaningfully ask which member is the greatest.

SirPeebles, let me know if I'm off base with this stuff. I haven't touched math or logic in a while.

[SirPeebles]

Hmm, I think I'm starting to understand what Showdown is trying to say.  I think he is trying to say that there are two ways to compare costs: compare the coin costs, or compare the potion costs.  Thus, if someone asks whether Mine costs less than Golem, Showdown is arguing that it is impossible to know the answer since we have incomplete information.  That is, we haven't been told whether we are to compare coins or compare potions.

If so, then the misunderstanding is that the rest of us are comparing cost, as a single, holistic quantity.

[eHalcyon]

Your last post suggests that you are indeed using a different definition.

SirPeebles will be better equipped to present the proper formal definition, but when I say that quantity A is less than quantity B (or that quantity B is more than quantity A), it basically means that quantity B has all of quantity A and more.  This is why people brought up the shopkeeper example.

So is Golem more expensive than Mine?  Because the cost of Golem does not encompass all of the cost of Mine, Golem is NOT more expensive.  But because the cost of Golem is not encompassed by the cost of Mine, neither is Mine less expensive.

There is no need to combine the two scales to determine a complete value; you can compare each scale separately.

Your confusion seems to be rooted in something I tried to address already.  You say this:

you CAN'T definitively say the complete value of Golem is less than the complete value of Mine because it can't be known

And you are absolutely correct.  Nowhere have we stated that Golem costs less than Mine.  In fact, we stated that Golem does NOT cost less.  We have also said that Golem does NOT cost MORE.



So the part that seems to confuse you -- saying "A does not cost more than B" is not equivalent to saying "A costs less than B".  It is possible that A costs neither more nor less than B without being equal to it, and this is the case between Golem and Mine.  Golem does not cost more, it does not cost less, and it does not cost the same.

[Showdown35]

Hmm, I think I'm starting to understand what Showdown is trying to say.  I think he is trying to say that there are two ways to compare costs: compare the coin costs, or compare the potion costs.  Thus, if someone asks whether Mine costs less than Golem, Showdown is arguing that it is impossible to know the answer since we have incomplete information.  That is, we haven't been told whether we are to compare coins or compare potions.

If so, then the misunderstanding is that the rest of us are comparing cost, as a single, holistic quantity.

Thank you! That's exactly what I'm trying to say!! And like last footnote said, 4 is not less than godzilla. But why? Because they have no comparable value, therefore I can't say yes. But really, I can't say no either, like you say, its a meaningless comparison.  So is Golem less expensive than Mine? Well, the game needs to have answer to tell you if you can or can't do somehing. Since its a meaningless comparison, it has to say you can't do it.


Because the question doesn't specify "in coins", "in potions", "in coins OR potions", or "in coins AND potions", you have to compare the card as a whole, which means comparing all measurables. Well, there is no known value of a potion in coins, so there is no way of knowing if the potion covers the cost of the one coin, so we say it doesn't. So that is how we arrive at the answer of no. It is an arrived at conclusion, not a statement of fact. I know that not exactly how its done mathematically, it not that we just say it doesn't. We say that because not all measurables are less, then it is not less. That's what makes it difinitive. Not all measurables are less, so its not less... epiphany!! You arrive at the answer of no because not all measurables of Golem are less than those of Mine.  It is a logical conclusion even though it is impossible to compare potions to coins.

[Showdown35]

Your last post suggests that you are indeed using a different definition.

SirPeebles will be better equipped to present the proper formal definition, but when I say that quantity A is less than quantity B (or that quantity B is more than quantity A), it basically means that quantity B has all of quantity A and more.  This is why people brought up the shopkeeper example.

So is Golem more expensive than Mine?  Because the cost of Golem does not encompass all of the cost of Mine, Golem is NOT more expensive.  But because the cost of Golem is not encompassed by the cost of Mine, neither is Mine less expensive.

There is no need to combine the two scales to determine a complete value; you can compare each scale separately.


Your confusion seems to be rooted in something I tried to address already.  You say this:

you CAN'T definitively say the complete value of Golem is less than the complete value of Mine because it can't be known

And you are absolutely correct.  Nowhere have we stated that Golem costs less than Mine.  In fact, we stated that Golem does NOT cost less.  We have also said that Golem does NOT cost MORE.



So the part that seems to confuse you -- saying "A does not cost more than B" is not equivalent to saying "A costs less than B".  It is possible that A costs neither more nor less than B without being equal to it, and this is the case between Golem and Mine.  Golem does not cost more, it does not cost less, and it does not cost the same.

The quote of mine you gave was actually a typo on my part. I was trying to so you CAN'T definitively say Golem is NOT less than Mine. That was not the confusion. See my post above, that explains what I'm trying to get across the best.

[AJD]

The quote of mine you gave was actually a typo on my part. I was trying to so you CAN'T definitively say Golem is NOT less than Mine. That was not the confusion. See my post above, that explains what I'm trying to get across the best.

Ah, well. In that case, you're wrong, you CAN definitively say that.

[Showdown35]

Haha... blunt, but I like it!!

Please tell me you were in fact referencing The Princess Bride earlier. It's my all time favorite movie.

[Showdown35]

Oh, and here's my next card idea.

 It's pretty straightforward and self-explanatory, so it probably won't cause much discussion or rules issues on this forum.


Master Debater
(P)(P) - Action
-$2
Each player gains a copy of the highest
costing card in his hand if it does not cost
more than the lowest costing card you
have in play.  You may trash a card in the
supply that costs more than the average
cost of all cards in your discard pile.

Thoughts?

[AJD]

Please tell me you were in fact referencing The Princess Bride earlier. It's my all time favorite movie.

Naturally.

[AJD]

It's pretty straightforward and self-explanatory, so it probably won't cause much discussion or rules issues on this forum.

Well played.

[sudgy]

Next topic of discussion: How does Golem's cost compare with Mint's?

[Awaclus]

Next topic of discussion: How does Golem's cost compare with Mint's?

And what about Yours?

[AJD]

Next topic of discussion: How does Golem's cost compare with Mint's?

And what about Yours?

that one doesn't even

[Jack Rudd]

You say that "sometimes it's more [expensive than Mine]" -- also false.  It is never more expensive than Mine.

My five-Highway turn disagrees with you.

[Showdown35]

I would like to take one more shot at explaining myself, and then I will apologize to everyone for putting you through this.

After having a night to think about it, I think I can explain it so it makes more sense for everyone.

Imagine the following:
 I want to buy a car, I find a strange dealer who has a Toyota Prius, and a Jaguar.  He tells me the price of the Prius is $5, and the price of the Jag is $4 (I get excited), but then he says the Jag also costs a bar of gold, of which he specifies the weight and purity. (crap.)
 I go home and tell my wife I want the Jag, she says, "You can buy it if it costs less than the Prius. Does it cost less?"
 To this question I can give her an answer.  Since gold has an equivalent value in dollars, I can add that to it's price in dollars and come up with a total in dollars that is not less than $5 (the bar of gold in question is valued at more than $1), so I can tell her, as an absolute truth, the Jag does not cost less. (no Jag for me)

Now Imagine the same scenario, except instead of a bar of gold, the dealer says the Jag also costs a vial of baby tears.
My wife again says, "Does it cost less?"

I can tell her, yes, in dollars it costs less! But that was not the question.  I can tell her, no, in baby tears it does not cost less. But that was not the question either. I can't convert baby tears into dollars at this time (since there is no dollar value that exists for baby tears that I know of), so I can't add the costs together and see if it's less than $5.  I can tell her that no, it does not cost less in each and every measurable value, but that was not the question either! She asked me if it costs less, that's all.  So to find out if I can buy the Jag or not, I have to come to a logical conclusion. So I compare what I can measure, and run it through a series of tests, if it passes all tests, then the answer is yes, if it doesn't pass all tests, then the answer is no.  Does it cost less in dollars? YES! Does it cost less in baby tears? NO! So it didn't pass all tests, therefore, the logical conclusion is that it does NOT cost less.

So I guess what I'm saying is that, yes, I suppose it is a definitive answer, and I apologize for arguing that it is not. It is definitive in that you can define the answer by doing logical tests.  What I should have been saying is that it is not an absolute truth, it is a logical conclusion that will always yield an answer of no, and as such, a definitive answer.

I know it's pretty nit-picky, and I am sorry that I kept going with it.  I should have just said I understand and agree that the answer is no instead of going on and on.  I also realize that this post is not completely consistent with all my previous posts, and I apologize for that.  I was having trouble finding the right words and there were times that I was not making total sense.  Again, I'm sorry.  I hope everyone was finding more enjoyment in the discussion rather than frustration or annoyance.

I also want to thank everyone for their input and comments about the cards, and I will have more cards to post soon.  I will absolutely avoid anything that needs to know the highest or lowest costing card, unless it specifies in coins.

Thanks everyone!

[SirPeebles]

Are you talking about US dollars?  If so, the US has been off of the gold standard for a long time; the bar of gold does not have an equivalent in US dollars.  Gold is sold in commodities markets where buyers and sellers negotiate prices.  But then there is also added value from the purifying process, which is separate from the market price for an equivalent mass of gold still embedded in ore.

[eHalcyon]

@JR, oops.

@Showdown -- all is well.  As far as debates go, that was really quite mild, and I was more worried about you being offended.  You have nothing to apologize for.  It can't be fun to have a bunch of people telling you that you're wrong, but your upbeat attitude never wavered.

If A costs less than B in general, then it must cost less in all aspects -- coins, potions, dollars, baby tears.  Glad you understand it now.



Also... you can't convert baby tears into dollars?  Well, I guess plan 37 is out the window now.  That's gonna set me back a couple months. 

[WalrusMcFishSr]

You can buy Baby's Tears for about $5 online!

http://www.liveaquaria.com/product/prod_display.cfm?c=747+892+2679&pcatid=2679&cmpid=13csegpl&ref=6113&subref=AA&CAWELAID=560925192&catargetid=1600565562&cadevice=c&cagpspn=pla

[SirPeebles]

Also... you can't convert baby tears into dollars?  Well, I guess plan 37 is out the window now.  That's gonna set me back a couple months. 

This made me think of baby tears and rule 34