How many combinations are actually possible?

[nardavin]

It seems that there are far fewer combinations possible, given the multiple rules that define how the obstacles can be chosen. Here is my math:

4(Position of groups A,B,C,D) * 1(Red position 1: low bar) * 2(Red position 2) * 2(Red position 3 - chosen by audience) * 2(Red position 4) * 2(Red position 5) * 1(Blue position 1 - low bar) * 2(Blue position 2) * 1(Blue position 3 - same as Red 3) * 2(Blue position 4) * 2(Blue position 5)

4*1*2*2*2*2*1*2*1*2*2 = 512

That seems awfully small, and way off of the game manual's 14000 (IIRC) advertised positions. Am I doing something wrong, or was the 14000 calculated without some of the rules in mind?

[jee7s]

It's not just a multiply by 4.

For each of the potential combinations, you need to do two chooses. First choose which group it is, then choose the option for the group for each potential defense location.

So, for one alliance, it's this:
(4*2)*(3*2)*(2*2)*(1*2) = (4!)*(2^4) = 384

When accounting for the second alliance, they have the same audience selected option, so that removes that option:
(3*2)*(2*2)*(1*2) = (3!)*(2^3) = 48

Multiply those together to get the total possibilities = 18342 (correction: 18432)

My math may be off, but I think I'm pretty close based on my recall of probability.

[MechEng83]

Originally Posted by jee7s

Multiply those together to get the total possibilities = 18432

My math may be off, but I think I'm pretty close based on my recall of probability.

I got the same number yesterday. I pretty sure your method is correct.

[caboosev11]

I calculate it to be 18432 (not that it makes much of a difference), Eitherway it a large amount of combinations.

[jee7s]

Yeah, typo on my part. 18432. Flubbed those middle two numbers.

[nardavin]

Ah, got it! I read manual wrong and was under the assumption that they always went in an A,B,C,D order in spots 2, 3, 4, and 5 (So either ABCD, BCDA, CDAB, or DABC). But you can actually put those defenses in any of the remaining 3 spots. That's where the large amounts of permutations come from. Thanks!

[MisterG]

Ignoring line of sight issues there is no real difference from a strategic standpoint from having the same defenses rearranged into different places. i.e. if the rock wall and the ramparts are both on the field in two successive matches but their locations are interchanged is that really a different field?

Therefore I think the OP number of 512 is a more practical way to look at the possibilities.

[rich2202]

Originally Posted by MisterG

Ignoring line of sight issues there is no real difference from a strategic standpoint from having the same defenses rearranged into different places.

In Autonomous, placement does make a difference.

Since order does matter, this is more a Permutation question than a Combination question.