Character creation
4d6 Drop Lowest Stat Roller
Roll six ability scores the standard way: four d6, drop the lowest, keep three. Then see where your array sits against every array this method can produce.
The shape of one score
Your six scores are marked in white. This is the distribution of a single 4d6 drop lowest roll.
- Lowest
- 3
- Highest
- 18
- Average
- 12.24
- Most likely
- 13
- Chance of 13
- 13.3%
- Possible totals
- 16
Peak at 13 (13.3%). Average 12.24. Range 3–18.
Dropping the lowest of four dice raises the average from 10.50 on 3d6 to 12.24, and it does so without changing the range, which stays 3 to 18 because three dice are kept either way. What changes is the shape: the curve leans right, so 13 becomes the most common score and an 18 goes from 0.463% to 1.62%.
The shape of a whole character
Six scores added together. This is what the percentile above is measured against.
- Lowest
- 18
- Highest
- 108
- Average
- 73.47
- Most likely
- 74
- Beats standard array
- 56.2%
- Any 18
- 9.34%
Six-score total. Average 73.5. Standard array totals 72.
The standard array (15, 14, 13, 12, 10, 8) totals 72. A rolled set beats it 56.2% of the time, which is why rolling feels generous. The other side of that coin is the left tail: 6.75% of rolled characters have at least one score of 5 or lower, which the array can never give you. For a proper comparison of every method, see how to roll stats.
Rerolling 1s
A common house rule rerolls any die that shows a 1, as many times as it takes. That is exactly the same as rolling dice numbered 2 to 6, and it is what the Reroll 1s toggle on the roller does: the chart, the table and the ranking against every possible array all switch to it.
The effect is bigger than it sounds. The average score rises from 12.24 to 13.43, an 18 goes from 1.62% to 2.72%, and nothing can come in under 6. A full set of six averages 80.6 instead of 73.5, and beats the standard array 91.6% of the time rather than 56.2%. Some tables reroll a 1 only once and keep the second result even if it is another 1; that averages 13.27, most of the way to the full rule, because a second 1 in a row only happens one time in 36.
Every score, with odds
One 4d6 drop lowest roll, every possible result.
| Total | Chance | Odds | This or higher | This or lower |
|---|---|---|---|---|
| 3 | 0.077% | 1 in 1,296 | 100.0% | 0.077% |
| 4 | 0.309% | 1 in 324 | 99.9% | 0.386% |
| 5 | 0.772% | 1 in 130 | 99.6% | 1.16% |
| 6 | 1.62% | 1 in 62 | 98.8% | 2.78% |
| 7 | 2.93% | 1 in 34 | 97.2% | 5.71% |
| 8 | 4.78% | 1 in 21 | 94.3% | 10.5% |
| 9 | 7.02% | 1 in 14 | 89.5% | 17.5% |
| 10 | 9.41% | 1 in 11 | 82.5% | 26.9% |
| 11 | 11.4% | 1 in 9 | 73.1% | 38.3% |
| 12 | 12.9% | 1 in 8 | 61.7% | 51.2% |
| 13 | 13.3% | 1 in 8 | 48.8% | 64.5% |
| 14 | 12.3% | 1 in 8 | 35.5% | 76.9% |
| 15 | 10.1% | 1 in 10 | 23.1% | 87.0% |
| 16 | 7.25% | 1 in 14 | 13.0% | 94.2% |
| 17 | 4.17% | 1 in 24 | 5.79% | 98.4% |
| 18 | 1.62% | 1 in 62 | 1.62% | 100.0% |
Common questions about 4d6 drop lowest
What is the average of 4d6 drop lowest?
The average of 4d6 drop lowest is 12.24, against 10.50 for plain 3d6. Dropping the lowest of 4 dice raises the average by 1.74 without changing the range, which is still 3 to 18 because you keep 3 dice either way.
What are the odds of rolling an 18 on 4d6 drop lowest?
The odds of an 18 on 4d6 drop lowest are 1.62%, or 1 in 62, compared with 0.463% on 3d6. Across a full set of six scores, the chance that at least one is an 18 is 9.34%.
What is the most likely result of 4d6 drop lowest?
The most likely single score from 4d6 drop lowest is 13, at 13.3%. The most likely six-score total is 74, and the average total is 73.5.
Is 4d6 drop lowest better than the standard array?
On average, yes: six rolled scores total 73.5 against 72 for the standard array, and a rolled set beats 72 56.2% of the time. The trade is variance. 43.8% of rolled characters end up at or below the array, and 6.75% of them carry at least one score of 5 or lower.
What does rerolling 1s do to 4d6 drop lowest?
Rerolling 1s raises the average score from 12.24 to 13.43, and the chance of an 18 from 1.62% to 2.72%. The lowest possible score becomes 6. A full set of six then averages 80.6 and beats the standard array 91.6% of the time. The Reroll 1s toggle on the roller above applies the rule.
Is 4d6 drop lowest the same as rolling 4d6?
No. Plain 4d6 adds all four dice, for a range of 4 to 24 and an average of 14.00. 4d6 drop lowest discards the smallest die first, so the range is 3 to 18 and the average is 12.24. Typing 4d6 into a general dice roller gives you the plain sum, which is not an ability score: anything above 18 is the dropped die you forgot to drop.
How do you roll 4d6 drop lowest?
To roll 4d6 drop lowest, roll four six-sided dice, discard the lowest, and add the other three. Do that six times for six ability scores, then assign them to abilities in whatever order suits the character. The roller above does all six in one tap and marks the dropped die on each row.