2D6 Score Probabilities
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 white 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
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 %)
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 1
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 2
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%.
