2014-06-19

3d6 Variable Parameters

Nothing new here, but I find myself continually re-computing this stuff so I'm documenting it here. Consider rolling a 3d6 probability variable, as for ability scores in OD&D, or starting money if we multiply by 10.
  • Curve is bell-shaped.
  • Average is 10.5 (mean or median).
  • Quartiles are 8, 10.5, and 13 (i.e., about one-quarter are 8 or below, etc.)
  • Standard deviation is almost exactly 3 (more specifically: 2.958)
Table & histogram follow:


Edit: My old website also has the 4d6-drop lowest curve.


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6 comments:

  1. UnknownJune 21, 2014 at 4:54 PM

    very cool. i've always wanted to see the probabilities of 4d6 drop lowest done in a similar fashion...

    ReplyDelete
  2. UnknownJune 21, 2014 at 11:01 PM

    anydice.com will calculate graphs like this for most combinations of dice, and will even give you probabilities of getting at least (or at most) a certain number. I've found it highly useful.

    ReplyDelete
    Replies
    1. UnknownJune 23, 2014 at 3:30 AM

      wow, i just checked it out. great site, thanks for sharing.

      Delete
    2. DeltaJune 28, 2014 at 11:33 PM

      OH MY GOD THAT'S AMAZING.

      Am I jealous that I didn't think of that? Yes, a bit. I need to go donate to Jasper now. Dammit, everyone should use that site.

      Delete
    3. DeltaJune 28, 2014 at 11:33 PM

      Thanks Jay for the heads-up.

      Delete

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