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Doom_Shark

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How many possible kingdoms are there?
« on: March 23, 2020, 02:50:05 am »
+4

I know this has been posited before, but that was a while ago (before Renaissance, and I think before Nocturne). I'm also too lazy to hunt down the thread. Dominion setup rules have gotten pretty complex over the years, so I'm going to do this in parts. As I keep the running totals, I'll be correcting rounding errors by just adding the formulas together in Wolfram Alpha, rather than adding the rounded numbers. With all that out of the way, let's do some math!

First, let's do just the kingdom cards. There's a total of 376 kingdom cards (including the removed cards, since they are still techincally possible dominion games). So, without any landscapes, and excluding different possibilities for Young Witch's bane card or shenanigans with the Black Market deck, that gives us 376!/(10! * 366!), or 13.8 quintillion kingdoms, rounded to the nearest 100 quadrillion.

Now, for each of them that has prosperity, there's actually two kingdoms, one with platinum/colony and one without. So how many have prosperity? If we subtract the 25 prosperity kingdom cards from the 376, that leaves us with 351 cards. Using that, we calculate the number of games that don't have prosperity (351!/(10! * 341!)) and subtract that from our 13.8 quintillion to get 6.9 quintillion kingdoms that include platinum/colony.
Running total: 20.7 quintillion kingdoms

Now we add shelters. We do the same thing we did for prosperity, but with dark ages. 376 total cards - 35 Dark Ages cards = 341 non-Dark-Ages cards. 13.8 quintillion kingdoms - (341!/10! * 331!) kingdoms without Dark Ages gives us 8.7 quintillion kingdoms with shelters.
Running total: 29.4 quintillion kingdoms

Now the math starts to get weird, because we need to add the kingdoms that have both platinum/colony and shelters. If we take the number of games without Prosperity and subtract the number of games without Dark Ages or Prosperity, that leaves us with the number of games with Dark Ages and not Prosperity. Subtract that from the 8.7 quintillion total kingdoms with Dark Ages, and we get 4.2 quintillion kingdoms with both.
Running Total: 33.5 quintillion kingdoms

Now we start with landscapes. Each of those kingdoms could be paired with any one of the 115 landscapes. So we multiply that 33.5 quintillion by 116 (adding one for the "no landscape option).
Running Total: 3.9 sextillion kingdoms (rounded to the nearest 100 quintillion)

Now because ways are weird, there's gonna be two parts to having two landscapes. First, we go back to the 33.5 quintillion and multiply that by all the possible combinations of two non-Way landscapes (95!/2 * 93!), giving us 149.8 sextillion kingdoms. That's quite a jump!
Running Total: 153.7 sextillion kingdoms
Note: At this point, Wolfram Alpha broke when I tried to have it run and add all the formulas. So much for correcting rounding error.

Finally, two landscapes, one is a Way. We take our 33.5 quintillion again, multiply by 20 Ways, and then multiply by 95 other landscapes, giving 63.7 sextillion kingdoms.

Grand Total: 217.4 sextillion possible kingdoms
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Gherald

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Re: How many possible kingdoms are there?
« Reply #1 on: March 23, 2020, 04:58:49 am »
+2

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
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silverspawn

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Re: How many possible kingdoms are there?
« Reply #2 on: March 23, 2020, 05:05:40 am »
+1

In mathematical notation: 2.174 * 10^{23}. I.e., a number with 24 digits.

faust

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Re: How many possible kingdoms are there?
« Reply #3 on: March 23, 2020, 06:00:35 am »
+3

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.
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Dominionaer

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Re: How many possible kingdoms are there?
« Reply #4 on: March 23, 2020, 06:01:18 am »
+1

There's a total of 376 kingdom cards (including the removed cards,
??? I count 366 (truth: table sheet does)

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Doom_Shark

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Re: How many possible kingdoms are there?
« Reply #5 on: March 23, 2020, 08:30:36 am »
0

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.

The issue with that is you'd have to figure out how to control for what 2's and 3's are already in the kingdom, which makes it hard. Like I said at the beginning: I'm lazy.
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Re: How many possible kingdoms are there?
« Reply #6 on: March 23, 2020, 08:43:13 am »
0

There's a total of 376 kingdom cards (including the removed cards,
??? I count 366 (truth: table sheet does)

Ah, you're right, I somehow added 10 cards. That's what I get for doing complex math at 2 am.
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GendoIkari

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Re: How many possible kingdoms are there?
« Reply #7 on: March 23, 2020, 09:52:38 am »
0

As of Prosperity edition rulebook, it is officially legal to use Platinum and Colony in games without any Prosperity cards; the rule is "You can include them whenever you want to; they are always used together." So that makes it simpler; the second step can simply be to multiple the total number by 2.

As far as I know, the same update has not happened for Dark Ages and Shelters, though.

One issue with this question is deciding what counts as a different Kingdom. Does the order of Knights count? Various things like that are unclear.

Also, landscapes are not limited to 2 per game.. that's a suggestion, but not the rule. So you have to multiply the non-landscape number by 2^115, or 41,533,837,500,000,000,000,000,000,000,000,000.

That's not counting Obelisk or Way of the Mouse choices.
« Last Edit: March 23, 2020, 09:56:48 am by GendoIkari »
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Re: How many possible kingdoms are there?
« Reply #8 on: March 23, 2020, 10:16:07 am »
0

I know this has been posited before, but that was a while ago (before Renaissance, and I think before Nocturne). I'm also too lazy to hunt down the thread. Dominion setup rules have gotten pretty complex over the years, so I'm going to do this in parts. As I keep the running totals, I'll be correcting rounding errors by just adding the formulas together in Wolfram Alpha, rather than adding the rounded numbers. With all that out of the way, let's do some math!

First, let's do just the kingdom cards. There's a total of 376 kingdom cards (including the removed cards, since they are still techincally possible dominion games). So, without any landscapes, and excluding different possibilities for Young Witch's bane card or shenanigans with the Black Market deck, that gives us 376!/(10! * 366!), or 13.8 quintillion kingdoms, rounded to the nearest 100 quadrillion.

Now, for each of them that has prosperity, there's actually two kingdoms, one with platinum/colony and one without. So how many have prosperity? If we subtract the 25 prosperity kingdom cards from the 376, that leaves us with 351 cards. Using that, we calculate the number of games that don't have prosperity (351!/(10! * 341!)) and subtract that from our 13.8 quintillion to get 6.9 quintillion kingdoms that include platinum/colony.
Running total: 20.7 quintillion kingdoms

Now we add shelters. We do the same thing we did for prosperity, but with dark ages. 376 total cards - 35 Dark Ages cards = 341 non-Dark-Ages cards. 13.8 quintillion kingdoms - (341!/10! * 331!) kingdoms without Dark Ages gives us 8.7 quintillion kingdoms with shelters.
Running total: 29.4 quintillion kingdoms

Now the math starts to get weird, because we need to add the kingdoms that have both platinum/colony and shelters. If we take the number of games without Prosperity and subtract the number of games without Dark Ages or Prosperity, that leaves us with the number of games with Dark Ages and not Prosperity. Subtract that from the 8.7 quintillion total kingdoms with Dark Ages, and we get 4.2 quintillion kingdoms with both.
Running Total: 33.5 quintillion kingdoms

Now we start with landscapes. Each of those kingdoms could be paired with any one of the 115 landscapes. So we multiply that 33.5 quintillion by 116 (adding one for the "no landscape option).
Running Total: 3.9 sextillion kingdoms (rounded to the nearest 100 quintillion)

Now because ways are weird, there's gonna be two parts to having two landscapes. First, we go back to the 33.5 quintillion and multiply that by all the possible combinations of two non-Way landscapes (95!/2 * 93!), giving us 149.8 sextillion kingdoms. That's quite a jump!
Running Total: 153.7 sextillion kingdoms
Note: At this point, Wolfram Alpha broke when I tried to have it run and add all the formulas. So much for correcting rounding error.

Finally, two landscapes, one is a Way. We take our 33.5 quintillion again, multiply by 20 Ways, and then multiply by 95 other landscapes, giving 63.7 sextillion kingdoms.

Grand Total: 217.4 sextillion possible kingdoms

There are 366 different Kingdom piles (including the removed cards), not 376:
Dominion 26(+6)
Intrigue 26 (+6)
Seaside 26
Alchemy 12
Prosperity 25
Cornucopia 13
Hinterlands 26
Dark Ages 35
Guilds 13
Adventures 30
Empires 24
Nocturne 33
Renaissance 25
Menagerie 30
Promos 10
Totals 354(+12)

Besides, there are no hard and fast rules regarding the number of landscapes, so you can potentially have anything from zero to 115 landscapes in any given game. DXV recommends using two in every game, and at most one Way. Using his recommended way of doing things will reduce the number of options considerably. As you're including the 'retired' cards, you're not following his recommendations, so you might as well include every possible combination of landscapes as described.
« Last Edit: March 23, 2020, 11:31:41 am by Oyvind »
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Oyvind

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Re: How many possible kingdoms are there?
« Reply #9 on: March 23, 2020, 10:19:49 am »
0

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, IMHO (the kingdoms contain the exact same cards). Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six, so be sure to take that into account as well.
« Last Edit: March 23, 2020, 11:33:37 am by Oyvind »
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hhelibebcnofnena

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Re: How many possible kingdoms are there?
« Reply #10 on: March 23, 2020, 10:24:02 am »
+1

What about Druid? Do different Druid Boons count as a different kingdom?
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Oyvind

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Re: How many possible kingdoms are there?
« Reply #11 on: March 23, 2020, 11:13:13 am »
0

What about Druid? Do different Druid Boons count as a different kingdom?

Yeah, probably. There are 1,320 different combinations of those, by the way.
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faust

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Re: How many possible kingdoms are there?
« Reply #12 on: March 23, 2020, 11:20:37 am »
+1

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.
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hhelibebcnofnena

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Re: How many possible kingdoms are there?
« Reply #13 on: March 23, 2020, 11:29:58 am »
0

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.

Is it just the top knight which changes the kingdom, then?
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Oyvind

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Re: How many possible kingdoms are there?
« Reply #14 on: March 23, 2020, 11:39:27 am »
+1

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.

I agree that it plays vastly different from other Knights games, but you're talking about different experiences, not different kingdoms. Every shuffle makes each game unique as well, so those should also count, if that's the case. For every shuffle during the game, by the way. Would you say that identical kingdoms are different for two players and six players? Maybe we should multiply everything by five to take that into consideration as well? I don't know. Maybe OP can give us some more guidelines.
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faust

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Re: How many possible kingdoms are there?
« Reply #15 on: March 23, 2020, 11:54:58 am »
0

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.

I agree that it plays vastly different from other Knights games, but you're talking about different experiences, not different kingdoms. Every shuffle makes each game unique as well, so those should also count, if that's the case. For every shuffle during the game, by the way. Would you say that identical kingdoms are different for two players and six players? Maybe we should multiply everything by five to take that into consideration as well? I don't know. Maybe OP can give us some more guidelines.
I mean, I can argue on a more technical level as well that the kingdoms are different because not all cards are in the same place in both kingdoms.

There's an argument to be made to multiply everything by five, yes, since the Curse pile contains a different number of cards in each case. However I usually only think of Dominion through a 2-player lens, so I'm happy enough to ignore that.
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GendoIkari

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Re: How many possible kingdoms are there?
« Reply #16 on: March 23, 2020, 12:20:18 pm »
0

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.

I agree that it plays vastly different from other Knights games, but you're talking about different experiences, not different kingdoms. Every shuffle makes each game unique as well, so those should also count, if that's the case. For every shuffle during the game, by the way. Would you say that identical kingdoms are different for two players and six players? Maybe we should multiply everything by five to take that into consideration as well? I don't know. Maybe OP can give us some more guidelines.

I think one valid definition is "what set of cards and card-shaped things are available this game"? Available meaning "could possibly be available depending on how the game plays out"; so the bottom Knight is considered "available". Under this definition; order of Knights and Black Market cards don't count. Obelisk pick doesn't count. Way of the Mouse and Druid choices do count. Which Ruins are in the game count, but not which order they are in.
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Doom_Shark

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Re: How many possible kingdoms are there?
« Reply #17 on: March 23, 2020, 01:06:45 pm »
0

And here I was hoping for some precise combinatorials involving Young Witch's bane and Way of the Mouse, as well as an adjustment factor for kingdoms that include both.

I am disappoint.
Don't forget Obelisk, the ordering of the Knights pile, and the ordering and composition of the Ruins pile.

The ordering of the Knights pile or the Ruins pile doesn't make different kingdoms, though. Yet, the composition of the Ruins pile do. This will also vary depending on the number of players from two to six.
I'd argue that a Kingdom where Dame Anna is the top Knight plays vastly differently from one where Dame Josephine is, and thus it makes sense to call these different kingdoms.

For the Ruins pile of course it matters less, though occasionally it is relevant whether the top Ruins is RUined Market.

I agree that it plays vastly different from other Knights games, but you're talking about different experiences, not different kingdoms. Every shuffle makes each game unique as well, so those should also count, if that's the case. For every shuffle during the game, by the way. Would you say that identical kingdoms are different for two players and six players? Maybe we should multiply everything by five to take that into consideration as well? I don't know. Maybe OP can give us some more guidelines.

I think one valid definition is "what set of cards and card-shaped things are available this game"? Available meaning "could possibly be available depending on how the game plays out"; so the bottom Knight is considered "available". Under this definition; order of Knights and Black Market cards don't count. Obelisk pick doesn't count. Way of the Mouse and Druid choices do count. Which Ruins are in the game count, but not which order they are in.

I'm inclined to agree with this definition. I'm currently working out the formulas with pen and paper. The question now is: what to do about the Black Market deck? On the one hand, there's what should technically be done, which is just one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). On the other, there's how most people play it: with a deck of only 25-30 cards. Thoughts?
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Wizard_Amul

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Re: How many possible kingdoms are there?
« Reply #18 on: March 23, 2020, 02:03:16 pm »
+1

I'm inclined to agree with this definition. I'm currently working out the formulas with pen and paper. The question now is: what to do about the Black Market deck? On the one hand, there's what should technically be done, which is just one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). On the other, there's how most people play it: with a deck of only 25-30 cards. Thoughts?

Actually, that's not what should technically be done. Here is text from the official FAQ on the card:

"To use the Black Market Kingdom card, you must create a Black Market deck before starting the game. The Black Market deck is made up of Kingdom cards that are not in the Supply of the current game. The players should agree before the game which cards will be used to create the Black Market deck (for example, you could agree to use one of every Kingdom card you own that is not a part of the Supply). It is recommended that the Black Market deck contain at least 15 Kingdom cards, with no duplicates."

The 15 Kingdom cards is a recommended minimum only. I would say the Black Market deck technically has to have between 3 cards minimum (you need to be able to reveal 3 cards for a choice) and one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). Thus, I would think you need to account for all the possibilities of all Black Market deck sizes and Black Market deck compositions.
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GendoIkari

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Re: How many possible kingdoms are there?
« Reply #19 on: March 23, 2020, 02:13:21 pm »
+1

I'm inclined to agree with this definition. I'm currently working out the formulas with pen and paper. The question now is: what to do about the Black Market deck? On the one hand, there's what should technically be done, which is just one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). On the other, there's how most people play it: with a deck of only 25-30 cards. Thoughts?

Actually, that's not what should technically be done. Here is text from the official FAQ on the card:

"To use the Black Market Kingdom card, you must create a Black Market deck before starting the game. The Black Market deck is made up of Kingdom cards that are not in the Supply of the current game. The players should agree before the game which cards will be used to create the Black Market deck (for example, you could agree to use one of every Kingdom card you own that is not a part of the Supply). It is recommended that the Black Market deck contain at least 15 Kingdom cards, with no duplicates."

The 15 Kingdom cards is a recommended minimum only. I would say the Black Market deck technically has to have between 3 cards minimum (you need to be able to reveal 3 cards for a choice) and one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). Thus, I would think you need to account for all the possibilities of all Black Market deck sizes and Black Market deck compositions.

I think a Black Market deck with only 1 or 2 cards is definitely within the rules. There's no issue with needing to reveal 3 when there are less than 3, that can happen normally after lots of cards have been bought from the Black Market. You do as much as you can. Whether or not Black Market with 0 cards is legal is a different question. I think the answer is yes, but an argument can be made that if it contains 0 cards, it doesn't meet the criteria of being "made up of Kingdom cards that are not in the Supply of the current game".
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Re: How many possible kingdoms are there?
« Reply #20 on: March 23, 2020, 02:30:27 pm »
0

I'm inclined to agree with this definition. I'm currently working out the formulas with pen and paper. The question now is: what to do about the Black Market deck? On the one hand, there's what should technically be done, which is just one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). On the other, there's how most people play it: with a deck of only 25-30 cards. Thoughts?

Actually, that's not what should technically be done. Here is text from the official FAQ on the card:

"To use the Black Market Kingdom card, you must create a Black Market deck before starting the game. The Black Market deck is made up of Kingdom cards that are not in the Supply of the current game. The players should agree before the game which cards will be used to create the Black Market deck (for example, you could agree to use one of every Kingdom card you own that is not a part of the Supply). It is recommended that the Black Market deck contain at least 15 Kingdom cards, with no duplicates."

The 15 Kingdom cards is a recommended minimum only. I would say the Black Market deck technically has to have between 3 cards minimum (you need to be able to reveal 3 cards for a choice) and one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). Thus, I would think you need to account for all the possibilities of all Black Market deck sizes and Black Market deck compositions.

I think a Black Market deck with only 1 or 2 cards is definitely within the rules. There's no issue with needing to reveal 3 when there are less than 3, that can happen normally after lots of cards have been bought from the Black Market. You do as much as you can. Whether or not Black Market with 0 cards is legal is a different question. I think the answer is yes, but an argument can be made that if it contains 0 cards, it doesn't meet the criteria of being "made up of Kingdom cards that are not in the Supply of the current game".

If you really want to push that argument, the plural "cards" would also rule out a 1-card deck
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Wizard_Amul

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Re: How many possible kingdoms are there?
« Reply #21 on: March 23, 2020, 02:35:13 pm »
+1

I'm inclined to agree with this definition. I'm currently working out the formulas with pen and paper. The question now is: what to do about the Black Market deck? On the one hand, there's what should technically be done, which is just one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). On the other, there's how most people play it: with a deck of only 25-30 cards. Thoughts?

Actually, that's not what should technically be done. Here is text from the official FAQ on the card:

"To use the Black Market Kingdom card, you must create a Black Market deck before starting the game. The Black Market deck is made up of Kingdom cards that are not in the Supply of the current game. The players should agree before the game which cards will be used to create the Black Market deck (for example, you could agree to use one of every Kingdom card you own that is not a part of the Supply). It is recommended that the Black Market deck contain at least 15 Kingdom cards, with no duplicates."

The 15 Kingdom cards is a recommended minimum only. I would say the Black Market deck technically has to have between 3 cards minimum (you need to be able to reveal 3 cards for a choice) and one of everything (with the exceptions of only one card from each split pile, one knight, and one castle). Thus, I would think you need to account for all the possibilities of all Black Market deck sizes and Black Market deck compositions.

I think a Black Market deck with only 1 or 2 cards is definitely within the rules. There's no issue with needing to reveal 3 when there are less than 3, that can happen normally after lots of cards have been bought from the Black Market. You do as much as you can. Whether or not Black Market with 0 cards is legal is a different question. I think the answer is yes, but an argument can be made that if it contains 0 cards, it doesn't meet the criteria of being "made up of Kingdom cards that are not in the Supply of the current game".

Sure, that is true, actually. I revise my statement to say that a 1 card black market deck is within the rules. A 0 card deck could be seen as a number theory question; I would say a 0 card black market deck is like an empty set, and since the empty set is technically a subset of every set, you can't do a 0 card black market deck (i.e., the empty set is in the Supply of the current game, because the empty set is in the Supply of every game).
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Re: How many possible kingdoms are there?
« Reply #22 on: March 23, 2020, 04:14:27 pm »
+2

A 0 card deck could be seen as a number theory question; I would say a 0 card black market deck is like an empty set, and since the empty set is technically a subset of every set, you can't do a 0 card black market deck (i.e., the empty set is in the Supply of the current game, because the empty set is in the Supply of every game).

Funny, I thought of it mathematically as well and came up with the opposite answer.  The rules don't say that the Black Market deck is a subset of the non-Supply cards, but that all cards in the Black Market deck are not in the supply.  Because the statement "∀ x ∈ ∅, P x" is true for all propositions P, I think a 0-card black market deck is fine.
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   Quote from: sudgy on June 31, 2011, 11:47:46 pm

Wizard_Amul

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Re: How many possible kingdoms are there?
« Reply #23 on: March 23, 2020, 05:38:17 pm »
0

A 0 card deck could be seen as a number theory question; I would say a 0 card black market deck is like an empty set, and since the empty set is technically a subset of every set, you can't do a 0 card black market deck (i.e., the empty set is in the Supply of the current game, because the empty set is in the Supply of every game).

Funny, I thought of it mathematically as well and came up with the opposite answer.  The rules don't say that the Black Market deck is a subset of the non-Supply cards, but that all cards in the Black Market deck are not in the supply.  Because the statement "∀ x ∈ ∅, P x" is true for all propositions P, I think a 0-card black market deck is fine.

I hadn't heard of this last statement before, so thanks. You're also right that the way the card is worded makes it the opposite answer. After thinking about it conceptually also, it seems like a 0 card deck should be valid; if you have a pile of cards in the supply, and then you have a pile of cards not in the supply that you are picking from, picking nothing from the "cards not in the supply" pile is a valid choice (i.e., the empty set is a subset of the "cards not in the supply" pile because the empty set is a subset of every set).
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Re: How many possible kingdoms are there?
« Reply #24 on: March 23, 2020, 05:46:05 pm »
0

So, I'm going to assume that since we don't care about ruins order, knights order, or which card obelisk picks, we also don't care which card specifically is the bane, only that there are 11 kingdom cards including young witch, and at least one of them costs $2 or $3.
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