# DS Deck: Sith

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### #21 houjix1138

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Posted 04 December 2012 - 02:50 PM

DrNate said:

So, has anyone tried to calculate the number of 10 set combinations possible from the 18 possible card sets?

10 items out of 18, but each of the 18 numbers could be used twice EXCEPT for two of them (only once), and two others are mutually exclusive. Is there an easy formula for that?

It's in the range of 120 milliion. Each x2 objective can be treated as a seperate entity and add 1 of the mutally exclusive objectives. So that is 33C10. For the second mutally exclusive objective you calculate all the combinations it will be a part of, so reduce the set to 9 and the entities to 32. 32C9. Add them together and it comes up to a little over 120 million.

### #22 dbmeboy

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Posted 04 December 2012 - 03:54 PM

houjix1138 said:

DrNate said:

So, has anyone tried to calculate the number of 10 set combinations possible from the 18 possible card sets?

10 items out of 18, but each of the 18 numbers could be used twice EXCEPT for two of them (only once), and two others are mutually exclusive. Is there an easy formula for that?

It's in the range of 120 milliion. Each x2 objective can be treated as a seperate entity and add 1 of the mutally exclusive objectives. So that is 33C10. For the second mutally exclusive objective you calculate all the combinations it will be a part of, so reduce the set to 9 and the entities to 32. 32C9. Add them together and it comes up to a little over 120 million.

Not quite. You can't treat each objective as two distinct sets because then your analysis doesn't count having only one or the other copy as the same thing.

### #23 houjix1138

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Posted 05 December 2012 - 01:40 AM

dbmeboy said:

Not quite. You can't treat each objective as two distinct sets because then your analysis doesn't count having only one or the other copy as the same thing.

Oh, that's right. You have to use the formula that allows repetitions, but you have to eliminate all results that have 1-16 more than twice and 17 more than once. Lets just call it a lot and move on.

### #24 dbmeboy

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Posted 06 December 2012 - 05:15 AM

houjix1138 said:

dbmeboy said:

Not quite. You can't treat each objective as two distinct sets because then your analysis doesn't count having only one or the other copy as the same thing.

Oh, that's right. You have to use the formula that allows repetitions, but you have to eliminate all results that have 1-16 more than twice and 17 more than once. Lets just call it a lot and move on.

Agreed, though like most games that total number of possible decks isn't really a good way to represent the total diversity available as some number of those decks will be so laughably silly that nobody would ever build it.  So yes, the total number of decks possible is rather large (though not as high as something like SWCCG or MtG at their release), but the total number of viable decks will probably be limited to 2-3 per side.  Granted, this happens all of the time in MtG (the same handful of basic deck designs played by multiple players).  The difference is that no longer will those decks differ by a couple of cards between players because you can only change at least 10% of the deck at a time.  That is a legitimate downside to the objective set deck building: the loss of ability to have decks that are almost, but not quite, the same.

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