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Author Topic: Edge-cases  (Read 12402 times)

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manthos88

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Re: Edge-cases
« Reply #25 on: October 21, 2013, 08:19:24 am »
0

According to the Alchemy rulebook, a card that costs [(X) Coins + Potion] costs higher than a card that costs (X) Coins but lower than a card that costs (X+1) Coins.
No, that is not what the Alchemy rulebook says. It says "References to cards costing “up to” some cost only include P if P is in the given cost. If P is in the cost, a player can drop the P and it is still "up to," but a player cannot add P if it is not there."


Then, can you please explain to me what it says?

Cause i'm definitely missing something here... :D
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Awaclus

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Re: Edge-cases
« Reply #26 on: October 21, 2013, 08:22:55 am »
0

According to the Alchemy rulebook, a card that costs [(X) Coins + Potion] costs higher than a card that costs (X) Coins but lower than a card that costs (X+1) Coins.
No, that is not what the Alchemy rulebook says. It says "References to cards costing “up to” some cost only include P if P is in the given cost. If P is in the cost, a player can drop the P and it is still "up to," but a player cannot add P if it is not there."


Then, can you please explain to me what it says?

Cause i'm definitely missing something here... :D
I edited my post and changed it to a more relevant quote from the Alchemy rulebook. I hope that helps.
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Grujah

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Re: Edge-cases
« Reply #27 on: October 21, 2013, 11:04:03 am »
+2

defense against knights.
Knights can't trash Alchemists.


The Knights cards state: "Each other player reveals the top 2 cards of his deck, trashes a card costing from (3) to (6) Coins and discards the rest."

According to the Alchemy rulebook, a card that costs [(X) Coins + Potion] costs higher than a card that costs (X) Coins but lower than a card that costs (X+1) Coins.
So, Alchemist costs more than (3), but less than (4) Coins, which is within trashing cost-range of the Knights.

I don't see why Alchemist can't be trashed by the Knights...

3P is more than 3.
3P is more than 2P, and less than 4P.
3P cannot be compared with 4.

Comparable with Complex numbers, potions being imaginary part.
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flies

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Re: Edge-cases
« Reply #28 on: October 21, 2013, 11:37:05 am »
+1


3P is more than 3.
3P is more than 2P, and less than 4P.
3P cannot be compared with 4.

Comparable with Complex numbers, potions being imaginary part.

Like all analogies, this one has its limits.  3+i can be made to appear greater than 3 if you compare ||3+i|| to ||3||, but then how is it that 3+i can't be compared with 4?

X+P "costs more" than Y if Y <= X.  (The reciprocal is also true: Y "costs less" than X+P if Y <= X.)
X+P "costs less (more)" than Y+P if X<Y (X>Y).
X+P never "costs less" than Y.
X+P is never in the range Y to Z.

Complex numbers give the sense that there are two separate dimensions of cost, and the second two rules are intuitive in this analogy, but the first two rules are not.  If there is a better mathematical analogy I'm not aware of it. 
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Awaclus

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Re: Edge-cases
« Reply #29 on: October 21, 2013, 12:04:07 pm »
+10

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Tables

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Re: Edge-cases
« Reply #30 on: October 22, 2013, 02:53:06 pm »
+6


3P is more than 3.
3P is more than 2P, and less than 4P.
3P cannot be compared with 4.

Comparable with Complex numbers, potions being imaginary part.

Like all analogies, this one has its limits.  3+i can be made to appear greater than 3 if you compare ||3+i|| to ||3||, but then how is it that 3+i can't be compared with 4?

X+P "costs more" than Y if Y <= X.  (The reciprocal is also true: Y "costs less" than X+P if Y <= X.)
X+P "costs less (more)" than Y+P if X<Y (X>Y).
X+P never "costs less" than Y.
X+P is never in the range Y to Z.

Complex numbers give the sense that there are two separate dimensions of cost, and the second two rules are intuitive in this analogy, but the first two rules are not.  If there is a better mathematical analogy I'm not aware of it. 

The costs form a partial order. This diagram shows what costs more than what:



You can see that e.g. 3P costs more than 2P, 3P costs more than 3, but 2P neither costs more, less or the same as 3.
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.

flies

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Re: Edge-cases
« Reply #31 on: October 23, 2013, 10:43:14 am »
+4


The costs form a partial order.

Perfect.  The next time I'm asked about this, I'll just make the analogy to partial ordering and all confusion will instantly evaporate. :)
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Witherweaver

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Re: Edge-cases
« Reply #32 on: October 23, 2013, 11:32:36 am »
0


The costs form a partial order.

Perfect.  The next time I'm asked about this, I'll just make the analogy to partial ordering and all confusion will instantly evaporate. :)

It was said in the other thread, but consider the cost of a card to be an element of N_0x{0,1}, where N_0 is the natural numbers plus {0}.  The first coordinate is the cost in coins and the second coordinate is the cost in potions. (You could expand {0,1} to all of N_0, but it isn't necessary as long as the highest potion cost is one potion.)  So Possession's cost would be (6,1), Village's cost would be (3,0), Vineyard's cost would be (0,1), etc.

The partial ordering in question is the product order:

(x,y) <= (a,b) if x<=a and y <=b.

The ordering has the corresponding strict ordering: (x,y) < (a,b) if (x,y)<=(a,b) and (x,y)!=(a,b)

So in the example from before 3p costs more than 2p is saying (2,1) < (3,1) (since 2<=3, 1<=1 and (2,1)!=(3,1)).  3P costs more than 3 corresponds to (3,0)<(3,1).

2P and 3 aren't related in the ordering since neither (2,1) <=(3,0) nor (3,0) <=(2,1) are true.

There are other partial orderings (lexicographical, for example), so you may not instantly evaporate the confusion by just saying it's a partial ordering :)
« Last Edit: October 23, 2013, 11:40:41 am by Witherweaver »
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eHalcyon

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Re: Edge-cases
« Reply #33 on: October 23, 2013, 03:59:46 pm »
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There are other partial orderings (lexicographical, for example), so you may not instantly evaporate the confusion by just saying it's a partial ordering :)

[that's the joke] :P
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Witherweaver

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Re: Edge-cases
« Reply #34 on: October 23, 2013, 04:27:02 pm »
0

There are other partial orderings (lexicographical, for example), so you may not instantly evaporate the confusion by just saying it's a partial ordering :)

[that's the joke] :P

I think the joke was that the person he was talking to wouldn't understand what a partial ordering is.  I chose to misunderstand the premise of his joke and assume the person he was talking to would understand partial orderings enough to know that the explanation leaves ambiguity as to which partial ordering it is :P
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serakfalcon

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Re: Edge-cases
« Reply #35 on: October 23, 2013, 10:37:54 pm »
+1

What my brain sees:
It was said in the other thread, but consider the cost of a card to be an element of...
....
Math... my old nemesis... WHYYY??!?!
.....
There are other partial orderings (lexicographical, for example), so you may not instantly evaporate the confusion by just saying it's a partial ordering :)

What I understand: lexicography means making dictionaries!

I like the picture though: Pictures are always nice and comforting.


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Markov Chain

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Re: Edge-cases
« Reply #36 on: October 31, 2013, 08:35:15 pm »
+1

You have five cards left in your deck, know that you will have enough buying power with those five, and want to buy a card and not have it and the Alchemist miss the reshuffle.

You don't want to decrease the value of a Philosopher's Stone which you know you will draw next turn.  (Example: you have 25 cards, and the last five are PS, Gold, Copper, Province, Estate.  If you discard the Alchemist, you can draw those five and the PS is worth 4, so you can buy a province.  If you keep the Alchemist and don't get all three treasures with it, you only have 7, and when you play the Alchemist, you now have those five cards plus one more, but the PS is only worth three, so if your extra card is a victory card, you can't buy a province.)

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AJD

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Re: Edge-cases
« Reply #37 on: October 31, 2013, 09:45:02 pm »
+2

The word edge can also mean 'blade', as in "the edge of my sword". For this reason I keep wanting "edge cases" to mean, like, 'scabbards'.
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Re: Edge-cases
« Reply #38 on: November 01, 2013, 01:20:19 am »
0

I like the picture though: Pictures are always nice and comforting.



The picture (I prefer diagram actually) is very useful. I should point out I wasn't the one who made it, though. IIRC it was SirPeebles, but I might be wrong in that as well.
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...spin-offs are still better for all of the previously cited reasons.
But not strictly better, because the spinoff can have a different cost than the expansion.
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