4d6 drop lowest is an old argument at the character-creation table: do you take a set of numbers everyone agrees on, or do you throw dice and live with what comes up? This page rolls it for you (four dice per score, six scores, with the discarded die shown so you can see what you gave up) and then tells you what those numbers are worth compared with the standard array and point buy. All the probabilities below are our own, calculated over the complete set of 1,296 outcomes of four six-sided dice.
On this page
How the method works
One ability score is four six-sided dice, added up minus the worst one:
- Roll four d6.
- Drop the lowest die. If two dice tie for lowest, it makes no difference which you drop.
- Add the three that are left. That total, between 3 and 18, is one ability score.
- Do it six times and assign the six results to Strength, Dexterity, Constitution, Intelligence, Wisdom and Charisma however you like.
The rulebook words it from the other end (roll four d6s and record the total of the highest three), which is the same arithmetic. "Drop the lowest" is how players say it, and it is the phrase the roller above uses: each set of four shows the three dice it kept and the one it threw away.
The roller starts with twelve dice because twelve is exactly three sets of four, and twelve is also the most this site can put on the table at once. So a stat line takes two throws, not one. Press Roll, watch three sets land, press Roll again, and the six-row table fills in. Prefer instant numbers to the tumble? The Fast roll button under the dice removes the suspense and settles them almost immediately.
Want a different table? The pencil button next to Roll opens the dice manager, where you can change how many dice are on the table and what type each one is. Ability scores need four d6 per set, so leave it at twelve d6 while you are rolling stats. Afterwards, set up whatever your session needs, like a single d20.
What a rolled set usually looks like
A single 4d6 drop lowest score averages 12.24, and its most likely single value is 13. But nobody plays one score. You roll six and then sort them, and sorting changes the picture. Averaged over every possible set, the six scores in descending order come out at:
| Position | 4d6 drop lowest | Standard array | Difference |
|---|---|---|---|
| Highest | 15.66 | 15 | +0.66 |
| 2nd | 14.17 | 14 | +0.17 |
| 3rd | 12.96 | 13 | −0.04 |
| 4th | 11.76 | 12 | −0.24 |
| 5th | 10.41 | 10 | +0.41 |
| Lowest | 8.50 | 8 | +0.50 |
| Total | 73.47 | 72 | +1.47 |
Rounded off, that is a 16, 14, 13, 12, 10, 9 line against the array's 15, 14, 13, 12, 10, 8, though the rounding flatters both ends, since 15.66 and 8.50 are both borderline. So rolling gains you about two thirds of a point on your best score and about half a point on your dump stat, and loses a fraction of a point in the middle. Over the whole set it is worth about one and a half points, or +0.24 of a single ability modifier. That is not a lot.
Which is the real point of this page: on average, 4d6 drop lowest and the standard array produce nearly the same character. The difference is not the average. It is the spread.
The odds for a single score
Four dice have 6 × 6 × 6 × 6 = 1,296 equally likely outcomes. Counting how many of them produce each score gives the exact distribution, with no simulation or approximation:
| Score | Ways (of 1,296) | Chance | This score or higher |
|---|---|---|---|
| 3 | 1 | 0.08% | 100% |
| 4 | 4 | 0.31% | 99.92% |
| 5 | 10 | 0.77% | 99.61% |
| 6 | 21 | 1.62% | 98.84% |
| 7 | 38 | 2.93% | 97.22% |
| 8 | 62 | 4.78% | 94.29% |
| 9 | 91 | 7.02% | 89.51% |
| 10 | 122 | 9.41% | 82.48% |
| 11 | 148 | 11.42% | 73.07% |
| 12 | 167 | 12.88% | 61.65% |
| 13 | 172 | 13.27% | 48.77% |
| 14 | 160 | 12.35% | 35.49% |
| 15 | 131 | 10.11% | 23.15% |
| 16 | 94 | 7.25% | 13.04% |
| 17 | 54 | 4.17% | 5.79% |
| 18 | 21 | 1.62% | 1.62% |
The peak sits at 13, the median is 12, and the mean is 12.24, noticeably above the 10.5 you would get from plain 3d6, because dropping the worst of four dice removes most of the very low results. A score of 3 needs all four dice to show a 1: one chance in 1,296. If you want the same counting done for ordinary rolls, the page on dice probability works through the two-dice case step by step.
The odds across all six scores
Six independent scores make the interesting questions possible. All of these follow from the table above:
| In a full set of six scores… | Chance | Roughly |
|---|---|---|
| at least one 18 | 9.3% | 1 set in 11 |
| at least one 17 or better | 30.1% | 1 set in 3 |
| two or more scores of 15+ | 42.2% | 2 sets in 5 |
| nothing above a 14 | 20.6% | 1 set in 5 |
| nothing above a 15 | 43.2% | 2 sets in 5 |
| nothing above a 12 | 1.8% | 1 set in 55 |
| at least one score of 8 or lower | 48.6% | 1 set in 2 |
| total of the six modifiers is +0 or worse | 9.3% | 1 set in 11 |
| total of the six modifiers is +10 or better | 11.3% | 1 set in 9 |
Compare two of the rows. A set with an 18 in it, the thing everyone rolls for, arrives about 9% of the time. A set with nothing above a 14 arrives twice as often. The two tails are almost balanced in modifier terms: 9.3% of sets end up at +0 or worse in total modifiers, 11.3% at +10 or better, against an average of +5.2. You roll once and live with the result for a whole campaign.
On average you get 1.39 scores of 15 or higher per set, and 0.63 scores of 8 or lower. Most rolled characters have one good stat and one bad one. That is what "rolled stats feel more like a character" means in numbers.
Standard array vs. rolling vs. point buy
Three ways to get six numbers, and they are trying to do different jobs.
| Method | What you get | Best for |
|---|---|---|
| Standard array | 15, 14, 13, 12, 10, 8: fixed, assigned as you like. Total 72, modifiers +5. | Fast starts, one-shots, and anyone who wants every character at the table to begin from the same footing. |
| Rolling (4d6 drop lowest) | Six random scores from 3 to 18, averaging 73.5 in total and +5.2 in modifiers, but anything from a disaster to an 18. | Tables that enjoy the drama, long campaigns where an odd stat line becomes part of the character. |
| Point cost (point buy) | 27 points spent on scores from 8 to 15. Costs run 8 = 0, 9 = 1, 10 = 2, 11 = 3, 12 = 4, 13 = 5, 14 = 7, 15 = 9. | Players who want to shape the character exactly, and DMs who want strict parity. |
Buy the standard array with point cost (9 + 7 + 5 + 4 + 2 + 0) and it comes to exactly 27, the whole budget. The array is one legal point-buy result, already spent for you. Rolling is the only one of the three whose generated numbers can go past 15: it can hand you a 16, 17 or 18 straight off the dice, while point buy and the array both stop at 15.
All three then get the same treatment: under the 2024 rules you increase your scores using your background (one by 2 and a different one by 1, or all three of its listed abilities by 1), and no increase can take a score above 20. That happens during character creation, so a point-buy or standard-array 15 is already a 17 by the time you sit down to play.
What the rules actually say
This is where a lot of pages get it wrong, so it is worth being precise. The 2024 Player's Handbook gives three ways to determine ability scores, and it presents them in this order:
- Standard Array: use 15, 14, 13, 12, 10, 8.
- Random Generation: "roll four d6s and record the total of the highest three dice", five more times.
- Point Cost: 27 points, spent on the table above.
Standard Array comes first, and the book adds that your DM might prefer you to use a particular one. So 4d6 drop lowest is fully official (it is Random Generation, word for word), but it is not the default, and the choice isn't yours alone. Several sites describe rolling as the standard or default method. That is not what the book says.
Two smaller points that follow from the same passage: you generate all six numbers first and then assign them to abilities, so a low roll does not have to land on your class's main ability; and the published Random Generation method contains no reroll clause at all. Anything you have heard about rerolling is a house rule.
House rules, and where tables disagree
Because the book stops at "roll four, keep three", every group fills in the rest themselves, and they do not agree. The common variations, all of them house rules rather than published options:
- Reroll 1s. Any die that shows a 1 is rolled again, sometimes only once, sometimes until it is not a 1. This raises every score noticeably and is the single most common way rolled characters end up stronger than the array.
- A floor with a reroll. Throw out the whole set and start over if no score reaches 15, or if the six modifiers total +0 or worse. By our numbers those two conditions catch about 21% and 9% of sets respectively, so a floor changes more than it sounds.
- Roll seven, drop one. Generate seven scores and discard the weakest. It is a small boost, and it removes the hopeless sets without inflating the top end.
- One set for the whole party. Everybody plays the same rolled line, assigned individually. You keep the randomness and lose the unfairness, which is often what a group actually wanted.
- Roll, then fall back. Roll a set, and take the standard array instead if you prefer it. This is strictly better than the array, so it makes rolling risk-free. Keep that in mind before offering it.
Whatever you use, decide it before the dice come out. The one thing every version of this argument has in common is that it goes badly when the rule is invented after someone has already rolled a 5.
Rolling stats with the group around a TV? The same dice run on Chromecast and Google TV through the free Android app, so everyone watches the same twelve dice land instead of leaning over one laptop.
If you want to know why a d20 sits alongside those d6s in the first place, the page on types of dice explains what each shape in a polyhedral set is for. If you would rather roll something with rules attached, there are plenty of dice games to choose from.
Frequently asked questions about 4d6 drop lowest
What does 4d6 drop lowest mean?
You roll four six-sided dice, ignore the lowest of the four, and add the remaining three together. That total is one ability score, somewhere between 3 and 18. Repeat the whole process six times and you have a full set of six scores to assign to Strength, Dexterity, Constitution, Intelligence, Wisdom and Charisma. The 2024 Player's Handbook words the same method from the other side: roll four d6s and record the total of the highest three.
Is 4d6 drop lowest the official way to roll D&D stats?
It is one of three official methods, but it is not the default. The 2024 Player's Handbook presents Standard Array first, then Random Generation (which is the 4d6 method), then Point Cost, and it adds that your DM might prefer you to use a particular one. Plenty of dice sites call rolling the standard approach; the rulebook does not.
What is the average ability score from 4d6 drop lowest?
A single score averages 12.24, and 13 is the single most likely result at 13.3 percent. Because you sort six independent scores, the set as a whole averages about 15.7, 14.2, 13.0, 11.8, 10.4 and 8.5 from highest to lowest, near enough a 16, 14, 13, 12, 10, 9 line. These figures are our own calculation over all 1,296 outcomes of four dice.
What are the odds of rolling an 18?
A single 4d6 drop lowest score comes out as 18 in 21 of the 1,296 possible outcomes, or 1.62 percent. Across a full set of six scores the chance of seeing at least one 18 is 9.3 percent, about one character in eleven. A 17 or better turns up in about 30 percent of sets.
Is rolling better than the standard array?
On average, barely. Six rolled scores total 73.5 on average against the standard array's 72, and the average total of the six ability modifiers is +5.2 against the array's +5. What rolling gives you is variance: about one set in five has nothing above a 14, and about one in eleven contains an 18. If you want a predictable character, take the array. If you like surprises, roll.
Can I reroll a bad set of stats?
Not by the rules. The published Random Generation method says nothing about rerolling. Rerolls are a house rule, and tables handle them differently: some reroll any 1s that come up on the dice, some let you throw out the whole set when no score reaches 15 or the total of your modifiers is +0 or worse, and some roll a single set that the entire party shares. Agree on the rule before anyone rolls.