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.