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Author Topic: How special can a card be?  (Read 2168 times)

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ConMan

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How special can a card be?
« on: June 09, 2016, 01:10:05 am »
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Including Empires, what is the most "special" a pile of cards can be? By special I mean it has the most things you need to remember about it, possibly marked with tokens of some kind. For example, the best I can get is:

Duchess
* Built-in on-buy-Duchy trigger
* (Embargo token) On-buy trigger
* (Young Witch) Is the Bane card
* (Defiled Shrine) On-gain trigger
* (Adventures Events) On-play trigger x4
* (Ferry) Price is modified
* (Plan) On-buy trigger
* (Tax) On-buy trigger
* (Obelisk) Worth VP

I know it's a bit vague, especially around whether various Landmarks count if they look at multiple piles of cards, but can anyone beat it?
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Davio

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Re: How special can a card be?
« Reply #1 on: June 09, 2016, 03:37:59 am »
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Don't forget to put all of your tokens on it!
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Burning Skull

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Re: How special can a card be?
« Reply #2 on: June 09, 2016, 04:11:38 am »
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Try as you can, but Scout will still be more special than all of that.

faust

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Re: How special can a card be?
« Reply #3 on: June 09, 2016, 04:14:39 am »
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Don't forget to put all of your tokens on it!

I don't think putting the -1 card and -1$ tokens on a pile are legal moves.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

Burning Skull

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Re: How special can a card be?
« Reply #4 on: June 09, 2016, 04:18:49 am »
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Don't forget to put all of your tokens on it!

I don't think putting the -1 card and -1$ tokens on a pile are legal moves.

Pirate Ship token might be fine though

faust

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Re: How special can a card be?
« Reply #5 on: June 09, 2016, 04:19:05 am »
0

Including Empires, what is the most "special" a pile of cards can be? By special I mean it has the most things you need to remember about it, possibly marked with tokens of some kind. For example, the best I can get is:

Duchess
* Built-in on-buy-Duchy trigger
* (Embargo token) On-buy trigger
* (Young Witch) Is the Bane card
* (Defiled Shrine) On-gain trigger
* (Adventures Events) On-play trigger x4
* (Ferry) Price is modified
* (Plan) On-buy trigger
* (Tax) On-buy trigger
* (Obelisk) Worth VP

I know it's a bit vague, especially around whether various Landmarks count if they look at multiple piles of cards, but can anyone beat it?

Add (Contraband) cards from this pile cannot be bought.

Doctor and Stonemason have the same properties, replacing the Duchy on-buy condition with overpay.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

ephesos

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Re: How special can a card be?
« Reply #6 on: June 09, 2016, 06:56:38 pm »
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Well, for the Split card piles, they can be in some permutation, if you've returned some of them to the Supply. Given that most of your "special things" have only 2 states, and this has 252 possible states, it should count for ~8 things :)(2^8=256).
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Marcory

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Re: How special can a card be?
« Reply #7 on: June 10, 2016, 12:09:44 am »
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What about these properties (which can also be true of Duchess):
-- (X is the card named by Doctor/Journeyman/Wishing Well/Mystic).
-- (X is the card that Inherited Estate/BoM/Overlord are acting as)
-- (X is the card that was played and trashed by Possession (for the purposes of Royal Carriage))
« Last Edit: June 10, 2016, 12:10:59 am by Marcory »
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faust

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Re: How special can a card be?
« Reply #8 on: June 10, 2016, 11:11:31 am »
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What about these properties (which can also be true of Duchess):
-- (X is the card named by Doctor/Journeyman/Wishing Well/Mystic).
-- (X is the card that Inherited Estate/BoM/Overlord are acting as)
-- (X is the card that was played and trashed by Possession (for the purposes of Royal Carriage))

While the title question refers to "a card", the question in the OP actually specifies "a pile of cards". These conditions aren't relevant for piles of cards.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

faust

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Re: How special can a card be?
« Reply #9 on: June 10, 2016, 11:15:24 am »
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Well, for the Split card piles, they can be in some permutation, if you've returned some of them to the Supply. Given that most of your "special things" have only 2 states, and this has 252 possible states, it should count for ~8 things :)(2^8=256).

By this reasoning, the Knights pile has 10! (Awaclus must be so proud of me) states. Since 2^18 < 10! < 2^19, this accounts for at least 18 things.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

faust

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Re: How special can a card be?
« Reply #10 on: June 10, 2016, 11:17:57 am »
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The Castles pile potentially has even more states in a 3-player game, but I'm too lazy to calculate that.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

Deadlock39

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Re: How special can a card be?
« Reply #11 on: June 10, 2016, 11:45:17 am »
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The Castles pile potentially has even more states in a 3-player game, but I'm too lazy to calculate that.

The Castles pile is always in order.

Dingan

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Re: How special can a card be?
« Reply #12 on: June 10, 2016, 12:37:14 pm »
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Band of Misfits?  It can do everything Duchess does, and also you have to remember it's a Duchess.  Although it wouldn't be the Bane or have the on-gain stuff or anything.  So I guess not.

Or Inherited Estates as Duchesses (or as BoM)?
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eHalcyon

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Re: How special can a card be?
« Reply #13 on: June 10, 2016, 02:24:18 pm »
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The Castles pile potentially has even more states in a 3-player game, but I'm too lazy to calculate that.

The Castles pile is always in order.

You can reorder it with Ambassador.
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Burning Skull

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Re: How special can a card be?
« Reply #14 on: June 10, 2016, 03:14:47 pm »
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The Castles pile potentially has even more states in a 3-player game, but I'm too lazy to calculate that.

The Castles pile is always in order.

You can reorder it with Ambassador.

Can you?

faust

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Re: How special can a card be?
« Reply #15 on: June 10, 2016, 05:41:03 pm »
+1

The Castles pile potentially has even more states in a 3-player game, but I'm too lazy to calculate that.

The Castles pile is always in order.

You can reorder it with Ambassador.

Can you?

Um, sure? Just make sure that all your opponents have a Champion in play, then gain all the Castles and go ahead.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

faust

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Re: How special can a card be?
« Reply #16 on: June 10, 2016, 05:41:58 pm »
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Band of Misfits?  It can do everything Duchess does, and also you have to remember it's a Duchess.  Although it wouldn't be the Bane or have the on-gain stuff or anything.  So I guess not.

Or Inherited Estates as Duchesses (or as BoM)?

Both of these are not pile properties though.
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Since the number of points is within a constant factor of the number of city quarters, in the long run we can get (4 - ε) ↑↑ n points in n turns for any ε > 0.

mith

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Re: How special can a card be?
« Reply #17 on: June 13, 2016, 12:22:32 pm »
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The Castles pile potentially has even more states in a 3-player game, but I'm too lazy to calculate that.

Yup; 12!/16 > 10!

(And you were off a digit; lg(9!) = 18.47; lg(10!) = 21.79; lg(12!/16) = 24.83.)
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ephesos

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Re: How special can a card be?
« Reply #18 on: June 13, 2016, 03:32:38 pm »
+2

Hmmm, then for the Ruins pile, 6 player game, that's 50 Ruins for 50!/(10!^5), which Google tells me is around 4e31. Which is greater than 2^105.

However, there's the Wild Hunt pile, which can have any number of VP tokens on it.... I think we have a winner

*very carefully avoids using the word infinity....*
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florrat

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Re: How special can a card be?
« Reply #19 on: June 14, 2016, 08:22:29 am »
+3

There are actually an infinite (yes, infinite) number of configurations of every supply pile, just determined by the number of embargo tokens on top of it. Since there can be arbitrarily many (but not infinite) embargo tokens on top of any pile, there are an infinite number of configurations of any pile.
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liopoil

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Re: How special can a card be?
« Reply #20 on: June 14, 2016, 12:16:08 pm »
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I guess you have to use BoM as embargo and graverobber?
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