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% |
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!
Sorry I wasn't clear– those are the probabilities of rolling that number or less. So it's a cumulative percentage. I'll put in "or less" to make it clearer in the original.
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.
Thanks for the chart! I'm using a 1d6 system, so this is handy for me. A couple of my friends are using a 2d6 system, so it will be handy for them too, I think.
Get two blank six sided dice, number one of them 0, 17, 33, 50, 67, and 83, and the other one 0, 3, 6, 8, 11, and 14.
And do what with them, Eric? That baffles me…
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.