Just something I hadn’t thought about. Dice probability is always interesting, but the way that, say, 2d6 and 1d8+1d4 differ in probability even with the same average and range might actually be useful for nudging probabilities.

2d6 1d8+1d4

Both 2d6 and 1d8+1d4 produce results between 2 and 12, with an average result of 7. But while 2d6 has a standard deviation of 2.415, 1d8+1d4’s deviation is 2.550, slightly higher.

All of the middling values (5-9) of 1d8+1d4 have the same probability, while 2d6 is a straight triangle distribution. All values but 6-8 are more common in 1d8+1d4 than in 2d6. I wonder if this can be used for anything… but it feels like it could be another tool in my arsenal of dice stuff.

3d6 1d8+1d6+1d4
It seems 1d8+1d6+1d4 differs less from 3d6, but is still slightly more random.



2 thoughts on “Interesting Effects of Dice Pairs

  1. Makes me wonder . . .

    We use 4d6 (drop the lowest) for stats. Which combination would get similar results?

    2d8 (drop low) + 1d6 + 1d4
    1d8 + 2d6 (drop low) + 1d4, or
    1d8 + 1d6 + 2d4 (drop low)

    And how far off are the stats? Could one of these be a suitable substitute?

    Not that a substitute is needed, perse, but it is interesting to consider these things.


    1. I don’t think I can do images in comments, but all of those have a lower average than 4d6D1.

      2d8 (drop low) + 1d6 + 1d4: average 11.8, standard deviation 2.8
      1d8 + 2d6 (drop low) + 1d4: avg 11.5, std. dev. 2.9
      1d8 + 1d6 + 2d4 (drop low): avg 11.1, std. dev. 3.0
      4d6D1 has an average of 12.25 and std. dev. of 2.85

      What this dice replacement shenanigans seem to do is mostly increase the standard deviation and thus the range of results that commonly occur. It gets a little more complicated with dropped dice here, I think, but specifying which die gets another roll is probably the reason for their lower results.

      If you do 1d8+1d6+1d4, reroll the lowest, it seems to average out to around 12.21 though, with a standard deviation of 2.65, lower that 4d6D1!


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