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Combinations and Permutations

Discussion in 'News' started by Roadrunner7431, Jan 17, 2018.

  1. Roadrunner7431

    Roadrunner7431 Well-Known Member
    Aristeia! Warcor

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    I believe that one key aspect of this game is that any given team of four characters may be selected from any of the eight (and soon to be twelve) characters as long as there are no duplicates. I do not trust my math skills but it seems to me there may be as many as 70 possibilities with even the eight characters currently available. As opposed to any other miniatures game that I know, there are no "factions." I welcome any comments and corrections.
     
    ijw likes this.
  2. eronth

    eronth Active Member

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    Yes. And with 12 characters there's 495 combinations. Have fun trying them all!
     
  3. ijw

    ijw Ian Wood aka the Wargaming Trader. Rules & Wiki
    Infinity Rules Staff Warcor

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    Waaaaaaaaaaaaaaay more combinations than that!

    There are already 1680 possible combinations of characters when choosing from the eight in the Aristeia box! 8 choices for your first slot * 7 choices for the second slot * 6 choices for the third slot * 5 choices for the last slot.

    The first expansion will take it up to roughly 20 million possible combinations of characters in a team. :flushed:

    The second expansion (for a total of 16 characters) takes it up to about a trillion.

    The third is roughly 1e17, or a 1 followed by 17 zeroes.

    The fourth is roughly 2.6e22, or 26 followed by 21 zeroes.
     
  4. psychoticstorm

    psychoticstorm Aleph's rogue child
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    Do you take into account each character brings in 2 of their 4 cards in the deck?
     
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  5. eronth

    eronth Active Member

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    Not exactly, using that formula you'll be recounting the same options quite a few times. For example, let's say you just picked any 2. By doing 8 * 7, you'd be including both the situation where you started by picking Gata out of the 8 followed by picking Hexx3r from the remaining 7 AND the situation where you started by picking Hexx3r from the 8 followed by picking Gata, despite both giving the same result.

    The formula you used is a simple form of 'Permutations', which is used when picking an order matters. In other words, your math can be used to show how many different initiative orders can be put together from the whole roster.

    However, for a list where selection order doesn't matter (like a team roster), you want to be using Combination mathematics, which comes up with a far lower number.
     
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  6. the huanglong

    the huanglong Well-Known Member

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    I'm awful at this and want to get better, can you please expand the working out to get to 495 from 12 choices?
     
  7. eronth

    eronth Active Member

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    The full formula can be seen here. You'll want to use 12 for the value of n and 4 for the value of r. The formula is the exact same for Combinations as it is for Permutations, except combinations have an additional 1/(r!) multiplied in. This is essentially just a way to reduce the final value by the number of different ways you can set up the choices. So in our case, 4! comes to 24, that is, for any 4 characters you pick, there are 24 different ways you could sort them. Since sorting doesn't actually matter for picking a team, we wan't to trim down our final result by that factor.
     
  8. the huanglong

    the huanglong Well-Known Member

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    Thanks!
     
  9. ijw

    ijw Ian Wood aka the Wargaming Trader. Rules & Wiki
    Infinity Rules Staff Warcor

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    Doh! Thank you for the correction, it's too many decades since I did much set theory, so I forgot to take into account the sequence being irrelevant... :flushed:
     
  10. Roadrunner7431

    Roadrunner7431 Well-Known Member
    Aristeia! Warcor

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    Using the link posted by eronth above, with the introduction of Smoke and Mirrors and 16 characters to build teams of 4 we have increased from 70 to 495 to now 1820 different possibilities of 4 character teams.
     
  11. Fathi Amirmoez

    Fathi Amirmoez Active Member

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    Once we have all 24 characters by Q1 2019, there'll be no less than 10,626 different combinations.
    So no excuses for copying my original the team donut steal.
     
  12. Roadrunner7431

    Roadrunner7431 Well-Known Member
    Aristeia! Warcor

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    I am waiting for the post from the forum member who claims that have tried every combination and recommends specific best teams. I will share that I was playing a TTS game where my opponent chose Mushashi, 8Ball, Hannibal and Parvati. He beat me 9-0 on Assault. He was a better player but I think that this team is remarkably well balanced.
     
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  13. Flipswitch

    Flipswitch Sepsitorised by Intent
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    bugger me
     
    Fathi Amirmoez likes this.
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