Number of possible starting setups

General GTG General Discussion
1

I've been doing the math, and if anyone wants to check me on this, please go ahead. According to my calculations, including Wrath of the Cosmos and all promo cards and decks released up to and including those that will be released with it, the total number of possible setup combinations of Heroes, Villains and Environments (treating all possible combinations of the Vengeful Five as a separate villain) for Sentinels of the Multiverse is:

1,175,392,920

I guess I have a few games left before I can say I've tried everything.

2

I'm assuming this takes into account the different player counts?

3

My numbers:

17 Enironments

40 Villains and unique Vengeful Five cominations

16,215 unique 3-player Hero combinations

178,365 unique 4-player Hero combinations

1,533,939 unique 5-Player Hero combinations  

 

17*40*(16,215+178,365+1,533,939)= 1,175,392,920

 

4

Fantastic. I'm almost there!

5

Beat you there!!!

6

(Waits for arenson9 to get some time to see this thread... ![](upload://l1MMla63MCJlCewIYsaArh2tOMW.gif))

7

Are you counting different hero positions on the table in your counts?

8

No.

9

Then it isn't accurate. :p

10

Counting starting Hero position we have the following modifers

3 - Player - x6

4 Player - x24

5 - Player - x120

Increased number of Vengeful Five setups based on position is multiplied by the same factors, resulting in the following:

3 members - 60 options

4 members - 96 options

5 members - 120 options

added to the 25 other villains, this gives us a villain total of 274

The new formula is now:

17*274*(97,290+4,280,760+184,072,680)=877,803,500,340

So we're chasing a trillion now. If you want to start factoring possible starting hands into it, i'm afraid you'll have to do that math on your own.

 

11

Ooh! Ooh! Promos!

12

Yes it is, check the OP. It says "combinations" not "permutations."

/math

13

Don't forget all combinations of all possible deck orderings. The numbers get big. =)

14

Leave the mutants out of it. Are you trying to anger Dawn?

15

 

And thanks for the backup. 

16

Just for the record, I coasted through combinatorics in college. I recall very little. All this is to say, I'm not checking the math.

17

I loved combinatorics, got a minor in it!

18

[quote=imprimis5]

Just for the record, I coasted through combinatorics in college. I recall very little. All this is to say, I'm not checking the math.

[/quote]

And it's not really important to check it either. The number is pretty friggin big is the real point. 

What I like about knowing that, is knowing that my favorite game has such a depth of replayability even in something as simple as how the beginning of the game is set up. Sentinels is a remarkably diverse game where there is always some new combination of things to explore. We could literally play this game every waking moment of the rest of our lives and never exhaust all of its' possibilities. We could definitely exhaust our patience for exploring them, but not the actual possibilities. 

It's always nice to know that no matter how many times I've played it, there is always some new way to play the game left to discover.

19

 

Here's my assessment:

 

Environments: 4EE, 2RC, 2IR, 2ST, 2VE, 2WC, Gulch, Final, OIV = 17

Vengeance Villains: 5 choose 5 (1) + 5 choose 4 (5) + 5 choose 3 (10) = 16

Villains: 16 + 4EE,4RC,4IR,4ST,4WC, Ambuscade, Kismet, Wager = 39

Heroes: 10EE,2RC,2IR,2ST,5VE,2WC, Unity,Scholar,TO BE NAMED = 26

unique 3-player Hero combinations: 26 choose 3 = 26!/(3!23!) = 262524/32 = 26254=26*100= 2,600

unique 4-player Hero combinations: 26 choose 4 = 26!/(4!22!) = 26252423/432 = 262523=14,950

unique 5-player Hero combinations: 26 choose 5 = 26!/5!21!) = 2625242322/5432=26523*22=65,780

1739(2,600 + 14,950 + 65,780)= 55,247,790

This does not include promos. If we allow multiple versions of the same hero to be played in the same game, the number is as easy to calculate, but if we don't, the calculation is more complex. I worked out the equations for that once, but it was before there were heroes that had multiple promo cards. I'm not up to figuring out the details now that Wraith, Legacy, Bunker, Haka, Tempest, and Fanatic are sporting double promos. The promo villains are easier to include, as they simply increase the number of villains.

 

 

20

I definitely failed to in my count of Villainous Five cominations (for some reason i only counte 4 variations with four players instead of 5). Throwing that number off.

I did fail to consider the implications of multiple iterations of the same character/different character card in my numbers, which pushes my numbers up to the higher values Ihave listed since my computations allowed it. It is definitely possible, but you would need to own multiple copies of the game to reach my numbers.

So I'll stand with arenson9's numbers are better representation of what is possible combinations for the vast majority of players (who also take the time to track down/print out all the promo cards).