D&D Ability Score Roller
Roll six 4d6-keep-highest-3 ability scores with running modifiers.
Overview
The D&D Ability Score Roller generates six ability scores using the most common method in fifth-edition Dungeons & Dragons: roll four six-sided dice, drop the lowest, and sum the remaining three. This produces a distribution centred around 12-13 with a thin tail toward 18 and a floor of 3.
Each rolled score appears alongside its modifier — the value used for most checks, saves, and attack rolls. The total of the six scores and the average modifier let you compare your set against the standard array, point-buy alternatives, or your table's house rule for a re-roll threshold.
How it works
For each of six ability scores, four d6 are rolled uniformly. The lowest of the four is discarded and the remaining three are summed. Discarding the lowest die shifts the expected score from 10.5 (the 3d6 average) to approximately 12.24, and the chance of rolling an 18 jumps from about 0.5 percent on 3d6 to about 1.6 percent on 4d6kh3.
The exact probability mass function is computable by enumerating the 1296 ordered 4d6 outcomes, sorting each, and tallying the sum of the top three. Doing that for all six ability scores produces a joint distribution from which expected totals, variance, and the probability of generating a "godly" character (e.g. all scores above 14) can be derived analytically.
Examples
- Rolling 6, 4, 4, 1: drop the 1, sum 14 -> ability score 14, modifier +2.
- Rolling 6, 6, 5, 3: drop the 3, sum 17 -> ability score 17, modifier +3.
- Rolling 5, 5, 4, 2: drop the 2, sum 14 -> ability score 14, modifier +2.
- A typical full set might be 16, 14, 13, 12, 10, 9 — total 74 and average modifier +1.
FAQ
Why 4d6 drop the lowest instead of 3d6?
It produces stronger heroes — the median score is 13 instead of 11 — which suits 5e's assumed adventurer power level.
What's the expected total across six scores?
About 73, compared with 63 for straight 3d6 and 72 for the standard array (15, 14, 13, 12, 10, 8).
Should I re-roll bad sets?
Many tables allow a re-roll if the total is below 70 or no score is above 13. Check your DM's preference.
How do modifiers work?
Modifier = (score - 10) / 2 rounded down. Score 10-11 -> +0, 12-13 -> +1, 14-15 -> +2, and so on.
Is rolling fairer than point buy?
Rolling has higher variance — fairer in expectation, less fair across a party. Point buy guarantees equal starting power.