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  • ...more then 500 thousand !

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  • ...more then 500 million !

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  • ...more then 500 billion !

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Thread: How many different hero combinations in 5v5 game are there?

  1. #1
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    Lightbulb How many different hero combinations in 5v5 game are there?

    Hi Dota players. At the moment there are 112 heroes in the map. Anyone ever wondered how many different hero setups exists? Disregard for a moment that some heroes are vastly more popular then others, lets say mode is AR. I just calculated it and its damn huge number. Will not tell you yet, lets see first some guesses (or an answer) from dota vets or forum regulars.

  2. #2
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    Too lazy to do the math atm xd

    Its not really hard, its just long but easy

  3. #3
    Administrator Cen's Avatar
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    If it matters which player owns the hero (aka, if hero is in different slot it's a different variation):
    n!/(n-k)! = 112!/(112-10)! = 205368317946676684800

    If it does not matter and we only care which heroes were picked:
    n!/k!*(n-k)! = 112!/10!*(112-10)! = 56594002961496

    If you ask cen:
    1 because Spec ftw!

    Undefeated Mad Balls Arena champion

  4. #4
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    hmmm.

    No it doesn't matter which exact slot got which hero. Team with "A" "B" "C" "D" "E" heroes is == as team playing "C" "D" "E" "B" "A" heroes.

    Your second calculation is strange. It doesn't even compute to what you wrote (5.6 x 10^13) but to some vastly bigger number with 337 digits.

    Maybe it doesn't say much but my calculation is somewhere in between of those 2 numbers

  5. #5
    Administrator Cen's Avatar
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    [url]http://www.wolframalpha.com/input/?i=112!%2F%2810!*%28112-10%29!%29[/url]

    Undefeated Mad Balls Arena champion

  6. #6
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    Yep, that looks right. Basically we are picking 10 from the set of 112. Without factorials, can be simply written as: (112*111*110*109*108*107*106*105*104*103) / (1*2*3*4*5*6*7*8*9*10) which results to:

    >>> 56 594 002 961 496 <<< as Cen actually wrote in first post.

    In English that reads as 56 trillion 594 billion 2 million 961 thousand 496 differnet hero combinations.

    For comparison, there is "only" something like 15 million of different combinations in standard lottery (7/39) so that makes around million times more chance that you will guess/win lottery then which 10 heroes will be randomed in dota AR match.

    And every AR game in the history of dota is guaranteed to have/been its own unique hero setup (implying that game/map can actually generate random numbers every time and there are no pre-seeding; I'm personally not sure how randomization in dota map exactly is done, tech wise).

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