2D6 Score Probabilities

4 March 2020 | 8th Edition

Knowing the probability of throwing a certain dice score can often be the difference between success or failure in gaming terms — or dictate whether you include a certain weapon or wargear item in your list.

The 2D6 throw occurs frequently in Warhammer 40K — the Leadership/Morale and Psychic tests are two examples. The chart shown below illustrates the probability of combined dice scores from 2 dice. The red figure under each red bar represent the 2D6 combined dice score; the figures above each bar show the possible combinations for each dice score; the figures along the bottom of the chart are the mathematical probabilities of achieving each score.

So we can see that the score of 7 has the most throwing combinations (6), and you have a 16.66% chance of throwing this score.

Remember — this chart is based on the results of many thousand dice throws — in the real world these probabilities vary due to the likelihood of any particular score being scored at any particular time. So keep these figure in mind as a rough guide only.

By knowing the likelihood of a particular dice result you can start to plan ahead.

Example 1
Let's say I have a Ravenwing Biker sergeant and I am considering giving him a melta bomb. What armour can he hope to damage to make it worthwhile?

Providing he hits, he gets 2D6+8 for armour penetration — meaning an average of 7+8=15 giving me a possible penetrating hit on AV14! So yes the melta bomb is well worth taking.

Table of Probabilities for Rolling 2D6 (as a %)

If you need to calculate the probability of throwing a particular score or a greater or lesser one, simply consult the chart below and cross reference the score required by the outcome required.

Dice Score	Result exactly	Result or less	Result or more
2	2.77	2.77	100
3	5.55	8.33	97.22
4	8.33	16.66	91.66
5	11.11	27.77	83.33
6	13.88	41.66	72.22
7	16.66	58.33	58.33
8	13.88	72.22	41.66
9	11.11	83.33	27.77
10	8.33	91.66	16.66
11	5.55	97.22	8.33
12	2.77	100	2.77

Example 2
A Devastator unit wants to target an enemy unit other than the nearest one. In order to do this they will need to pass a Leadership Test by scoring an 8 or less on 2D6 — so what are their chances?

The probability of them passing the test (by scoring an 8 or less) is: 72.22%. The probability of them failing the test (by scoring a 9 or more) is: 27.77%.

Example 3
Consider a Dark Angel Librarian who wants to use his Hellfire psychic power, he will need to pass a Psychic Test by scoring a 9 or less 2D6.

The probability of him passing (by scoring a 9 or less) is: 83.33%.
Now, if it was Ezekiel at Ld10, the probability of him passing leaps to: 91.66%.

And that's it. I hope it proves some help to you in your 40K gaming.