The Dark Fortress

# 4D6 Score Probabilities

9 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 chart shown below illustrates the probability of combined dice scores from 4 dice. The red figure under each red bar represent the 4d6 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 14 has the most throwing combinations (146), and you have a 11.27% 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 slightly. 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.

### Table of Probabilities for Rolling 4D6 (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
4 0.08 0.08 100
5 0.31 0.39 99.92
6 0.77 1.16 99.61
7 1.54 2.70 98.84
8 2.70 5.40 97.30
9 4.32 9.72 94.60
10 6.17 15.90 90.28
11 8.02 23.92 84.10
12 9.65 33.56 76.08
13 10.80 44.37 66.44
14 11.27 55.63 55.63
15 10.80 66.44 44.37
16 9.65 76.08 33.56
17 8.02 84.10 23.92
18 6.17 90.28 15.90
19 4.32 94.60 9.72
20 2.70 97.30 5.40
21 1.54 98.84 2.70
22 0.77 99.61 1.16
23 0.31 99.92 0.39
24 0.08 100 0.08

To be fair rolling 4D6 in 40K is a pretty rare occurence. There are some units that have a 4D6 shots stat (the Wyvern Quad Heavy Weapon for example), but that doesn't really demonstrate the chance of getting / or not getting a certain result. In the example below I'm not even sure if the Terminator Sergeant's Auspex is even a thing in 8th Edition. But it's staying as proof of process.

Example
If you need to calculate the probability of throwing a particular score or above, simply add up all the percentages from the score required upwards to the highest score. We can see that if a Deathwing sergeant wants to make his Auspex earn its points he will need to throw 18+ on 4D6. The probability of him achieving this is:

6.17 + 4.32 + 2.70 + 1.54 + 0.77 + 0.31 + 0.08 = 15.89% (or roughly 1 in 6.3).

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