5ePointBuy

Rolling ability scores with 4d6, drop the lowest

Four six-sided dice, the lowest one discarded, repeated six times. It is the oldest of the three methods and the only one that can hand one player an 18 and the player beside them a 9, which is exactly why some tables love it and others ban it.

Roll six scores

Nothing is rolled until you ask for it. The page arrives with no result on it at all, because a number generated before you pressed anything is not your roll — it is decoration that happens to look like one.

Nothing has been rolled yet. Press the button to roll 4d6 six times.

Ability Dice Dropped Score Modifier
STR
DEX
CON
INT
WIS
CHA
Total

What this array would cost in point buy

A rolled array can be priced against the 27-point budget only when every score falls between 8 and 15. Roll first and this line will say whether yours does.

Rolled scores can be compared against the 27-point budget only when every one of them is something the budget could have bought. Point buy sells nothing below 8 or above 15, so an array containing a 17 has no purchase price at all, and this page says so rather than inventing one.

The exact odds behind one score

The odds below are not a simulation and not an estimate. Four dice have 1,296 possible outcomes, and every one of them is counted here, so the columns are exact counts rather than the results of a sample.

All 1296 outcomes of four six-sided dice, counted by the score that remains once the lowest die is dropped.
Score Modifier Ways to roll it Chance This or better
3 -4 1 0.08% 100.0%
4 -3 4 0.31% 99.9%
5 -3 10 0.77% 99.6%
6 -2 21 1.62% 98.8%
7 -2 38 2.93% 97.2%
8 -1 62 4.78% 94.3%
9 -1 91 7.02% 89.5%
10 +0 122 9.41% 82.5%
11 +0 148 11.42% 73.1%
12 +1 167 12.89% 61.7%
13 +1 172 13.27% 48.8%
14 +2 160 12.35% 35.5%
15 +2 131 10.11% 23.1%
16 +3 94 7.25% 13.0%
17 +3 54 4.17% 5.8%
18 +4 21 1.62% 1.6%

The average, and why it is the wrong thing to look at

Six rolls average 73.5 between them. The standard array totals exactly 72, and a fully spent 27-point budget lands somewhere in a narrow band around it depending on the shape bought — never on one fixed number. Rolling sits a little above that band on average and far, far outside it in either direction, which is the part worth arguing about.

One score, on average
12.24, which rounds to a +1 modifier.
Six scores, on average
73.5 in total.
The standard array, for comparison
Exactly 72, every time, because it is the same six numbers.
A fully spent 27-point budget
Between 69 and 75, depending on the shape bought — 12,282 arrays spend the budget exactly and 72 is the total more of them reach than any other.
Chance a single roll reaches 18
1.6% of the time.
Chance a single roll reaches 16
13.0% of the time.
Chance a single roll reaches 15
23.1% of the time.
Chance a single roll reaches 14
35.5% of the time.

Questions about rolling

How do you roll stats in D&D 5e?

Roll four six-sided dice, discard the lowest die, and add the other three. That gives one ability score between 3 and 18. Repeat until you have six numbers, then assign them to abilities in whatever order you like.

What is the average of 4d6 drop lowest?

The exact average of one score is 12.2446, which comes to 73.5 across all six abilities. That figure is the mean of all 1,296 outcomes of four dice, not an approximation from rolling a few hundred sample characters.

What are the odds of rolling an 18?

Twenty-one of the 1,296 outcomes produce an 18, which is 1.62% for a single ability. Across six abilities the chance of seeing at least one 18 is a little under one character in ten, so most rolled characters never see one.

Is rolling for stats better than point buy?

Six rolls average 73.5 between them, which is a shade above what a spent budget reaches, so on average the two are close. The difference is variance: a rolled character can total 90 or 55, and no way of spending 27 points produces either.

Should you reroll a bad array?

That is a table rule rather than a printed one. Common house rules are rerolling when the total falls below 70 or when no score reaches 14, both of which quietly convert rolling into a floor-limited method closer to point buy.

  • The standard array — The method with no variance at all, and the one most tables offer as the alternative to rolling.
  • Price a rolled array — If your six numbers all landed between 8 and 15, the calculator will tell you what they would have cost.