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 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.
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