Number of possible starting setups

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.

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

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

Fantastic. I'm almost there!

Beat you there!!!

(Waits for arenson9 to get some time to see this thread... )

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

No.

Then it isn't accurate. :p

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.

Ooh! Ooh! Promos!

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

/math

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

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

And thanks for the backup. 

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.

I loved combinatorics, got a minor in it!

[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.

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.

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).

(See? )

Imagine you only have the core game and you only ever play with four heroes:

4 villains * 4 environments * 10 choose 4 heroes = 16 * 10!/6!*4! = 16*10*9*8*7/4*3*2 = 16*10*3*7 = 3,360

Can you imagine ONLY having 3,360 ways to play the game? 

Now imagine that all you care about is getting to play each hero against each villain plus each hero in each environment:

10*4 + 10*4 = 80

Geez, only 80 different ways to play the game. That's barely 79 ways more than Settlers of Catan.

It should actually be less, as this appears to include Vengeance games with e.g. 5 villains but 3 heroes.

I would think it would be (still including the caveat of no promos):

Unique 3 player games = 17*(39-1-5)*2600 = 1,458,600

Unique 4 player games = 17*(39-1-10)*14,950 = 7,116,200

Unique 5 player games = 17*(39-5-10)*65,780 = 26,838,240

Total unique games = 35,413,040

I only know one way to play Settlers.

1. Pick sensible starting spots with the most probable numbers.

2. Watch as your numbers never come up. Do nothing.

3. Do nothing while the other players get resources and build stuff and buy cards. Do nothing. 

4. Curse everyone else for refusing to trade with you because all you have is one lousy sheep. Continue to do nothing. 

5. Get a few lucky rolls and obtain enough resources to finally build something! Wait impatiently for your turn, knowing that you have no way of catching up now everyone else has huge global empires but at last you'll get to do something other than rolling 4 and sighing as the other players also roll 4s.

6. Roll a 7 and get half your stuff stolen. Build a single sodding road.

7. Repeat until someone else wins. Never play again.

Basic Settlers has 244,432,188,000 possible board configurations. (discussion)

... and still only 1 way to play.

SotM has only 1 way to play too =) unless you guys got more rulebooks than me.

I count at least 2, standard and Vengeance style!

Point taken, though I was thinking that the set up of the tiles is akin to the order of the decks, while Settlers has nothing like SotMs differing powers, effects, etc. between decks.

Nice catch.

True - but the board configuration of Settlers makes a big difference in what you do. And of course it has a deck that has an ordering. Two decks, if you're playing with the dice-cards instead of dice =)

BTW Silverleaf - if you hate the dice in Settlers, try using the cards (a deck of all possible 2 die rolls that you use instead of dice).

This is why I ask people to check my math. Thanks for pointing out the error.

Promo villains would be easy to add to the calculations.  There are 4, right?  Bomber Blade, Cosmic Omintron, Spite Agent of Gloom, and Gloomweaver Skinwalker.  That's easy enough to just add to the villain section of the calculations.

3 Player = 1,635,400

4 Player = 8,132,800

5 Player = 31,311,280

Total = 41,079,480

Still doesn't factor promo heroes into it, but getting closer.

oh the humanity! Won't someone think of the children!?!?!?

My back-of-the-napkin math, assuming 5 unique gamers each game, minus promos, minus WotC, was something like 703,000,000 possible starting combos. Some of the same hero teams. But with different people playing them each time.

Also, my base set is missing the dice and note pad to track HP totals… /joke done/

I've now officially spent far too much time on this, but this is what I got:

With Hero Promos and Villian Promos:

With WotC (9 heroes with no promos, 11 with 1 and 6 with 2; 23 villains+4 promo + 5 V5; 13 environments):

Permutations: 15,358,044,000

Combinations: 27,080,560

Without WotC:

Permutations: 5,873,840,280

Combinations: 8,925,840