There are a lot of strong opinions in the D&D community about how you should roll for stats. Using the standard method of generating attributes in DnD by rolling 4d6 and dropping the lowest die, the probability of rolling six attribute scores of 18(+4) is low. ‘Low’ is in fact being supremely generously, it is astronomically unlikely. If someone claims to have done this, they need to be buying everybody lottery tickets as they are clearly a chosen one of Tymora.
What are the odds of rolling six 18 (+4) attribute scores?
The odds of rolling the perfect character are 1 in 55,332,164,805, that’s one in fifty-five billion, three hundred thirty-two million, one hundred sixty-four thousand, eight hundred five. I told you it was low.
What are the odds of rolling a specific single attribute score?
By rolling 4d6 and discarding your lowest roll, you have the following distribution:
| Total of highest 3 dice of 4d6 | Probability |
| 3 (-4 modifier) | 0.08% |
| 4 (-3 modifier) | 0.31% |
| 5 (-3 modifier) | 0.77% |
| 6 (-2 modifier) | 1.62% |
| 7 (-2 modifier) | 2.93% |
| 8 (-1 modifier) | 4.78% |
| 9 (-1 modifier) | 7.02% |
| 10 (+0 modifier) | 9.41% |
| 11 (+0 modifier) | 11.42% |
| 12 (+1 modifier) | 12.89% |
| 13 (+1 modifier) | 13.27% |
| 14 (+2 modifier) | 12.35% |
| 15 (+2 modifier) | 10.11% |
| 16 (+3 modifier) | 7.25% |
| 17 (+3 modifier) | 4.17% |
| 18 (+4 modifier) | 1.62% |
Is 10 a good attribute score?
Despite 10 being “over halfway” to an attribute score of 18, it is actually a statistically below average roll at a 9.41% chance of rolling it, which is a 1 in 10.6 chance of rolling a 10.
What is the most likely attribute score to roll?
With the most combinations of it being rolled, 13 is the most likely attribute score you’ll roll with a 13.27% chance, which is a 1 in 7.5 chance.
What are the chances to roll 18 on an attribute?
You have a 1.62% chance of rolling 18 on an attribute score, only a 1 in 63.73 chance!
What are the odds I will roll an ability score above X?
With this information we can calculate the probability of your ability score being at least a specific roll:
| Ability Score | Probability of being at least as great as |
| 3 (-4 modifier) | 100% |
| 4 (-3 modifier) | 99.92% |
| 5 (-3 modifier) | 99.61% |
| 6 (-2 modifier) | 98.84% |
| 7 (-2 modifier) | 97.22% |
| 8 (-1 modifier) | 94.29% |
| 9 (-1 modifier) | 89.51% |
| 10 (+0 modifier) | 82.48% |
| 11 (+0 modifier) | 73.07% |
| 12 (+1 modifier) | 61.65% |
| 13 (+1 modifier) | 48.76% |
| 14 (+2 modifier) | 35.49% |
| 15 (+2 modifier) | 23.15% |
| 16 (+3 modifier) | 13.04% |
| 17 (+3 modifier) | 5.79% |
| 18 (+4 modifier) | 1.62% |
Well, we did the math – and as you can see – if someone turns up to your game claiming to have rolled 6 sets of 18… They’re gonna need to re-roll.
