3D6 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 3D6 throw occurs rarely in Warhammer 40k – the Shrouding Shooting test is one example. The chart shown below illustrates the probability of combined dice scores from 3 dice. The red figure under each red bar represent the 3D6 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 scores of 10 and 11 have the most throwing combinations (27 each), and you have a 12.50% chance of throwing say, a 10.
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
An enemy unit is attempting to shoot at my allied Grey Knights, but they must
first test to find out if they can actually see the GK unit. The enemy firing
unit needs to throw 3D6 and multiply the result by 3, this is then the maximum
range the firers can see. So from the chart above we know that the likeliest
score is a 10 or 11. This means that the average maximum range my GK can be
seen at is 30-33". Quite useful to know I think, as it means that the
psycannon (range 36") has a 3-6" safe zone within which to operate.
More significant maybe is that roughly 48% of dice thrown will fall somewhere between a 9-12 which equates to a maximum spotting range of 27-36".
Table of Probabilities for Rolling 3D6 (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 |
| 3 |
0.46 |
0.46 |
100 |
| 4 |
1.38 |
1.85 |
99.53 |
| 5 |
2.77 |
4.62 |
98.14 |
| 6 |
4.62 |
9.25 |
95.37 |
| 7 |
6.94 |
16.20 |
90.74 |
| 8 |
9.72 |
25.92 |
83.79 |
| 9 |
11.57 |
37.50 |
74.07 |
| 10 |
12.50 |
50.00 |
62.50 |
| 11 |
12.50 |
62.50 |
50.50 |
| 12 |
11.57 |
74.07 |
37.50 |
| 13 |
9.72 |
83.79 |
25.92 |
| 14 |
6.94 |
90.74 |
16.20 |
| 15 |
4.62 |
95.37 |
9.25 |
| 16 |
2.77 |
98.14 |
4.62 |
| 17 |
1.38 |
99.53 |
1.85 |
| 18 |
0.46 |
100 |
0.46 |
Example
An enemy jump pack unit needs to make a fall back move. You really want them
to fall short of cover that is 15" behind them – so what are their
chances?
The probability of them making the distance (by throwing a 15 or more) is:
9.25%.
The probability of them not making the distance (by throwing a 14 or less)
is: 90.74%.
