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Captain's Draft: CM-restricted heroes do not appear in the hero pool

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  • Captain's Draft: CM-restricted heroes do not appear in the hero pool

    NEVERMIND, ignore this! Apparently Phantom Lancer showed up once, which I missed.

    So far in the four games for the XMG Captain's Draft Invitational 2.0, none of the 6 heroes that are banned in Captain's Mode have shown up in the hero pool even once. There have been 5 hero pools so far (one was remade), and if Captain's Draft were working properly, the chance of this happening is extremely low.

    For one hero pool of 27, the chance that none of these heroes show up is 16.342%*. For five hero pools, the chance is 0.16342^5, or 0.01166%. Because this is so extremely low, it's very likely that Captain's Draft is bugged.

    I'll be unable to test this for a few hours. It would be helpful if someone could try a few more Captain's Draft games to further confirm this.

    *The pool includes 9 heroes from each primary attribute. 2 strength heroes, 3 agility heroes, and 1 intelligence hero are banned. The chance that each category includes none of the restricted heroes is independent from each other category. So we find the chance for each category and multiply them together to find the probability for the entire pool.
    For example, with Strength, you can pick the first hero from 34/36 strength heroes. For the second, 33/35, then 32/34, etc. This simplifies to (34! / (34 - 9)!) / (36! / (36 - 9)!), or nPr(34, 9) / nPr(36, 9). The method was used for the other categories.
    Last edited by agag; 10-31-2014, 03:06 PM. Reason: clarified wording, used more accurate math
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