Dominion Strategy Forum
Dominion => Dominion General Discussion => Topic started by: DooWopDJ on January 24, 2019, 12:25:34 pm
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Has anyone calculated the number of setup combinations?
Given the following conditions.
1. Follow the recommended setup rules (example: only 2 events, landmarks, projects, etc)
2. Black Market (draw pile combinations should not count as permutations, although that stat would be interesting too)
3. Include all Promos, and 1st Edition and 2nd Edition cards
4. Include Removed 1st Edition cards (Although a stat not including Removed cards would be interesting too)
Thanks
-DooWopDJ
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This has been discussed several times before. It's basically incalculable, due to things such as Colony/Platinum/Shelters/Young Witch. But you can very easily get a lower bound simply by taking the number of different cards choose 10.
http://forum.dominionstrategy.com/index.php?topic=16850
http://forum.dominionstrategy.com/index.php?topic=13647
http://forum.dominionstrategy.com/index.php?topic=2866
Currently there are 334 different Kingdom cards, so there are 4.1555273x10^18 different Kingdoms... only counting which 10 kingdom cards you use and nothing else.
75 Landmarks+Events+Projects gives 2775 possibilities there if you keep the recommended limit of 2.
With second edition rules, we can easily include Shelters and Colony, since they can be used in any game if you want. Just multiply by 4.
So that's 4.6126353x10^22 kingdoms, again not counting Young Witch, Black Market, or Obelisk.
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sorry not sure what common terms that could be put into for us non-mathy people, is that
46,126,353,000,000,000,000,000 sextillion? or Just over 46 Thousand Trillion?
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sorry not sure what common terms that could be put into for us non-mathy people, is that
46,126,353,000,000,000,000,000 sextillion? or Just over 46 Thousand Trillion?
"x10^22" just means you multiply it by 10,000,000,000,000,000,000,000... so yes, 46,126,353,000,000,000,000,000 is correct, as is 46 sextillion. But that's way more than 46 Thousand Trillion... it's 46 thousand quintillion, or 46 thousand thousand thousand trillion.
To get an idea of size... that's about 46 times as many stars as there are in the observable universe.
To have played them all, you would need to have played about 100,000 games PER SECOND, every second, since the beginning of time.
People are always amazed at how crazy huge our universe is, but in the world of math, our universe only deals with tiny numbers.
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So ... not counting ... Obelisk.
I do not understand how the Rules or Setup Obelisk impacts the permutation calculation.
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So ... not counting ... Obelisk.
I do not understand how the Rules or Setup Obelisk impacts the permutation calculation.
Obelisk (http://wiki.dominionstrategy.com/index.php/Obelisk) says "Setup: Choose a random Action Supply pile". If you consider a Kingdom different if a different pile was chosen (which is basically the same idea as having a different set of cards in the Black Market), then for each Kingdom that involves Obelisk, you have to multiply the number by the number of supply piles that are actions.
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sorry not sure what common terms that could be put into for us non-mathy people, is that
46,126,353,000,000,000,000,000 sextillion? or Just over 46 Thousand Trillion?
"x10^22" just means you multiply it by 10,000,000,000,000,000,000,000... so yes, 46,126,353,000,000,000,000,000 is correct, as is 46 sextillion. But that's way more than 46 Thousand Trillion... it's 46 thousand quintillion, or 46 thousand thousand thousand trillion.
To get an idea of size... that's about 46 times as many stars as there are in the observable universe.
To have played them all, you would need to have played about 100,000 games PER SECOND, every second, since the beginning of time.
People are always amazed at how crazy huge our universe is, but in the world of math, our universe only deals with tiny numbers.
I don't even want to think about how many different MtG decks you could construct.
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I don't even want to think about how many different MtG decks you could construct.
The answer is 2: Aggro or Control.
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I don't even want to think about how many different MtG decks you could construct.
The answer is 2: Aggro or Control.
That's like saying there are only two different Dominion boards (engine and money).
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So ... not counting ... Obelisk.
I do not understand how the Rules or Setup Obelisk impacts the permutation calculation.
Obelisk (http://wiki.dominionstrategy.com/index.php/Obelisk) says "Setup: Choose a random Action Supply pile". If you consider a Kingdom different if a different pile was chosen (which is basically the same idea as having a different set of cards in the Black Market), then for each Kingdom that involves Obelisk, you have to multiply the number by the number of supply piles that are actions.
Interesting. We have not been playing that card correctly. We had just assumed that the 'Choose a random Action Supply pile' meant 'from one of the current Kingdom already selected. It is not clear (imho) that the 'chosen Action supply' would be an additional pile (like the Bane/Black Market piles).
An example of this would be one of the Recommended Kingdoms from Empires/Prosperity called 'Big Time'. It does not list the 'Additional' Action Supply' pile. So if the Recommended sets includes the Recommended Bane for Witch (as it does for a few Recommended Kingdoms in the Cornucopia expansion) why does the Recommended setup do the same for the only example for the 'Big Time' Kingdom?
My apologies for seeming to be disputing the explanation, my intention is to understand the intention of each card. Hopefully someone can put this into the 'Other Rules clarifications' section for Obelisk. Thanks.
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Interesting. We have not been playing that card correctly. We had just assumed that the 'Choose a random Action Supply pile' meant 'from one of the current Kingdom already selected. It is not clear (imho) that the 'chosen Action supply' would be an additional pile (like the Bane/Black Market piles).
You were playing correctly.
However, Village, Smithy, Market, Witch, Chapel, Laboratory, Library, Moat, Remodel, Militia, Obelisk choosing Moat is not the same setup as Village, Smithy, Market, Witch, Chapel, Laboratory, Library, Moat, Remodel, Militia, Obelisk choosing Laboratory.
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People are always amazed at how crazy huge our universe is, but in the world of math, our universe only deals with tiny numbers.
Actually, the vast majority of observable math deals only with numbers that are less than 10.
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Actually, the vast majority of observable math deals only with numbers that are less than 10.
What does that even mean? I'm not sure what "observable" is, let alone how you put, say, Newtonian dynamics and integration by parts on some quantitative scale in order to determine a "majority", still less how you can say what numbers lambda calculus "deals with", or whether 12lb/5.4kg is "less than 10".
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I don't even want to think about how many different MtG decks you could construct.
The basic answer is that MtG decks are not (in principle) limited in size, so there's an infinite number of possible different decks.
And even the not-so-basic answer doesn't seem hard either: If you're limited to 4 of each card, then if there are N different magic cards, and you can put 0 through 4 each in a deck, the answer is essentially 5^N. 5 possibilities for how many you put in of each card, and N different cards to choose that for.
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I don't even want to think about how many different MtG decks you could construct.
The basic answer is that MtG decks are not (in principle) limited in size, so there's an infinite number of possible different decks.
And even the not-so-basic answer doesn't seem hard either: If you're limited to 4 of each card, then if there are N different magic cards, and you can put 0 through 4 each in a deck, the answer is essentially 5^N. 5 possibilities for how many you put in of each card, and N different cards to choose that for.
But the basic answer is more correct because you can have as many Basic Lands as you want.
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sorry not sure what common terms that could be put into for us non-mathy people, is that
46,126,353,000,000,000,000,000 sextillion? or Just over 46 Thousand Trillion?
It boggles my mind that 46,126,353,000,000,000,000,000 sextillion is easier for some people to understand than 4.6126353x10^22
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I was just wondering how much this had changed since the last time. I remember it being in the quadrillions; now it's in the sextillions. A great testament to the variety of this game.
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Not really. I mean, there are 5.4e28 different ways to deal a 52-card deck into four hands in Bridge, but that doesn't ensure the kind of variety Dominion offers.
What matters more is how different those possible kingdoms are from one another, and how low the risk is of ending up with something boring or unplayable.