D6 Probabilities

I’ve been toying around with substituting multiple d6’s for percentile dice in some situations, so I naturally needed to know the probabilies of throwing any given number or less with d6’s. Here are the numbers, just in case anyone else needs ’em handy:

Roll 1d6 2d6 3d6 4d6 5d6
1 16.667%
2 33.333% 2.778%
3 50.000% 8.333% 0.463%
4 66.667% 16.667% 1.852% 0.077%
5 83.333% 27.778% 4.630% 0.386% 0.013%
6 100% 41.667% 9.259% 1.157% 0.077%
7 58.333% 16.204% 2.701% 0.270%
8 72.222% 25.926% 5.401% 0.720%
9 83.333% 37.500% 9.722% 1.620%
10 91.667% 50.000% 15.895% 3.241%
11 97.222% 62.500% 23.920% 5.877%
12 100% 74.074% 33.565% 9.799%
13 83.796% 44.367% 15.201%
14 90.741% 55.633% 22.145%
15 95.370% 66.435% 30.517%
16 98.148% 76.080% 39.969%
17 99.537% 84.105% 50.000%
18 100% 90.278% 60.031%
19 94.599% 69.483%
20 97.299% 77.855%
21 98.843% 84.799%
22 99.614% 90.201%
23 99.923% 94.123%
24 100% 96.759%
25 98.380%
26 99.280%
27 99.730%
28 99.923%
29 99.987%
30 100%

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Wargamer and RPG'er since the 1970's, author of Adventures Dark and Deep, Castle of the Mad Archmage, and other things, and proprietor of the Greyhawk Grognard blog.

7 thoughts on “D6 Probabilities

  1. I'm not a mathematician, nor do I know much about probability, but are those numbers right?

    I'm thinking that the first list for 1d6 should all have 16,667 % probability (as each side has equal probability to show up). The way I'm reading the table now indicates that it's 100 % certain that I get a result of 6 when throwing 1d6…?

    Similar with the other lists, with the difference that they should produce a bell curve with higher probability towards the mean value.

    But, as I said, I may just as well be reading your tables wrong!

  2. If you want to stay away from percentage dice (d100) but would prefer easier numbers to deal with, may I recommend a d20; it's a simple 5% a side. As I don't know the specific situation, I don't know if that's helpful or not but, to me, it seems preferable to rolling a bunch of d6s.

  3. They'll work similar to percentile dice. When you roll the two dice, you should get a total less than or equal to 75, approximately 75% of the time, for example. You could add a third die numbered 0, 0, 1, 1, 2, 2 for a little more accuracy.

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