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.
