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BTW, http://www.anydice.com is a great tool to answer questions such as these.

- Go to anydice.com
- type: output 3d6 – 2*(2d6)
- select “at least”
- read out the result for the value 1 in any of the various output formats (you want the value 1, because if 3d6 > 2*(2d6), that means 3d6 – 2*(2d6) >= 1

A trick:

When comparing dice distributions like this, you can also work with the complementary distribution. The distribution of a single d6 is the same as the distribution of 7-d6 (see also my blogpost http://wargaming-mechanics.blogspot.be/2018/01/whats-probability-xd6-beats-yd6.html).

Thus:

probability (3d6 – 2*(2d6) > 0)

= probability (3d6 – 2 *(14-2d6) > 0)

= probability (3d6+2*(2d6) > 28)

Again you can compute this using http://www.anydice.com, by asking for the distribution of 3d6+2*(2d6)

- This reply was modified 3 years, 8 months ago by Phil Dutré.

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