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Dominion: Seaside» Forums » General

Subject: Possible Number of Kingdom Combinations rss

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Ben Jaberg
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According to my math, there will be a grand total of 1,258,315,963,905 unique combinations of kingdom cards come Seaside. 161,322,559,475 of them will contain any specific card. And I suck at math. Thanks to those who know their stuff.
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kSwingrÜber
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Dang... now I've got analysis-paralysis trying to figure out which set of 10 to play!

Thanks a lot! LOL
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Carsten ◄► Wesel
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sniprpenguin wrote:
According to my math, there will be a grand total of 1,125,861,651,915 unique combinations of kingdom cards come Seaside.
I don't have your math, but do you have a list for me?
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Ian Kelly
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(78 choose 10) = 1,258,315,963,905
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Ben Jaberg
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Peristarkawan wrote:
(78 choose 10) = 1,258,315,963,905


That's right. I made an error. My bad.
 
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Jeff Wolfe
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And the smaller number is (77 choose 9) = 161,322,559,475
 
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Grzegorz Kobiela
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Only 1.2 trillion possible sets of 10 kingdom cards? Feasible...
 
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Chris Rudram
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That's only 360,000 years for 200 geeks playing heads up one game every 15 minutes.

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Kenny VenOsdel
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does this include the different deck that you can build each time for the black market card? Or are you assuming the black market card has one of every other kingdom card rather than 15 cards.
 
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Rick Teverbaugh
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Black Market doesn't alter the possible mixes of 10 kingdom cards.
 
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Damen Parker
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Given how much hype is surrounding the new cards and all the 'powerful' 2 card combos that could ruin the game or make the game really fantastic depending on your view point. Does anybody know what the stats are for any 2 named kingdom cards being drawn in the same game?

For example. What are the odds of Island & The Great Hall being drawn from all available kingdom cards when creating the initial set up?

Cheers
D.
 
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Werner Bär
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DeviousDamen wrote:
What are the odds of Island & The Great Hall being drawn from all available kingdom cards when creating the initial set up?

Number of different cards: 78
card 1 in the game (occupies one out of 10 slots): 10/78
in addition, card 2 in the game (one out of 9 remainig slots): 9/77
total odds: 1.5%
 
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Ian Kelly
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DeviousDamen wrote:
Given how much hype is surrounding the new cards and all the 'powerful' 2 card combos that could ruin the game or make the game really fantastic depending on your view point.


What 2-card combos? There are lots of interesting combos being discussed right now, but I don't see any of them as potential game-breakers.
 
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Grzegorz Kobiela
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Werbaer wrote:
DeviousDamen wrote:
What are the odds of Island & The Great Hall being drawn from all available kingdom cards when creating the initial set up?

Number of different cards: 78
card 1 in the game (occupies one out of 10 slots): 10/78
in addition, card 2 in the game (one out of 9 remainig slots): 9/77
total odds: 1.5%


Another possibe way to compute this number:

(76 choose 8)/(78 choose 10)
 
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Børge N
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Another way to look at it: Given that one of the cards in your favorite two card combo is in the game, what are the chances that the other card is there also?

9/77 = 11.7%
 
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Børge N
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Ponton wrote:

Another possibe way to compute this number:

(76 choose 8)/(78 choose 10)


But that way of doing it is really unwieldy unless you're using WolframAlpha: http://www.wolframalpha.com/input/?i=%2876+choose+8%29%2F%28.....
 
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Grzegorz Kobiela
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borgemik wrote:
Another way to look at it: Given that one of the cards in your favorite two card combo is in the game, what are the chances that the other card is there also?

9/77 = 11.7%


Sure? It's 1/77. It's one specific card among 77 other cards. The first one (of the combo) is already there.
 
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Grzegorz Kobiela
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borgemik wrote:
Ponton wrote:

Another possibe way to compute this number:

(76 choose 8)/(78 choose 10)


But that way of doing it is really unwieldy unless you're using WolframAlpha: http://www.wolframalpha.com/input/?i=%2876+choose+8%29%2F%28.....


I love WolphramAlpha, but Google does the same and is easier to access:

http://www.google.de/search?hl=de&source=hp&q=%2876+choose+8...
 
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Chris Edwards
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Ponton wrote:
borgemik wrote:
Another way to look at it: Given that one of the cards in your favorite two card combo is in the game, what are the chances that the other card is there also?

9/77 = 11.7%


Sure? It's 1/77. It's one specific card among 77 other cards. The first one (of the combo) is already there.


With 9 chances to get it (because there will be 9 more Kingdom cards in the game). So, 9/77.
 
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Ian Kelly
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Ponton wrote:
borgemik wrote:
Another way to look at it: Given that one of the cards in your favorite two card combo is in the game, what are the chances that the other card is there also?

9/77 = 11.7%


Sure? It's 1/77. It's one specific card among 77 other cards. The first one (of the combo) is already there.


Yes, but there are 9 slots left to fill. So it's actually 1/77 + 76/77 * 1/76 + 76/77 * 75/76 * 1/75 + ... + 76/77 * 75/76 * 74/75 * 73/74 * 72/73 * 71/72 * 70/71 * 69/70 * 1/69 = 9 * 1/77 = 9/77.
 
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Grzegorz Kobiela
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Peristarkawan wrote:
Ponton wrote:
borgemik wrote:
Another way to look at it: Given that one of the cards in your favorite two card combo is in the game, what are the chances that the other card is there also?

9/77 = 11.7%


Sure? It's 1/77. It's one specific card among 77 other cards. The first one (of the combo) is already there.


Yes, but there are 9 slots left to fill. So it's actually 1/77 + 76/77 * 1/76 + 76/77 * 75/76 * 1/75 + ... + 76/77 * 75/76 * 74/75 * 73/74 * 72/73 * 71/72 * 70/71 * 69/70 * 1/69 = 9 * 1/77 = 9/77.


You're right. It's late here, I'm sorry.

(76 choose 8)/(77 choose 9)
 
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Damen Parker
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Thanks for the responses. I was just curious.

Cheers
D.
 
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