# 4d6 Drop Lowest: D&D Ability Score Probabilities

See the exact 4d6-drop-lowest distribution, odds of high scores across six rolls, ability modifiers, and comparisons with standard array and point cost.

---

- **Canonical URL:** https://dothecalculation.com/blog/hobby/dnd-ability-score-probabilities
- **Category:** Hobbies & Leisure Utilities
- **Author:** Do The Calculation Team
- **Published:** 2026-06-06
- **Last updated:** 2026-07-01
- **Reading time:** 17 min read
- **Publisher:** Do The Calculation (https://dothecalculation.com)
- **Methodology:** https://dothecalculation.com/methodology

---

Rolling four six-sided dice and discarding the lowest feels simple, but its distribution is not the same as rolling 3d6. The extra die shifts the average upward, makes middle-high scores more common, and still leaves a small chance of extreme arrays. That randomness is the point—and the reason a table should agree on the method before anyone rolls.

This guide enumerates all 1,296 outcomes for one 4d6-drop-lowest score, then extends the result to six independent rolls. It also documents the DTC calculator: six 4d6-drop-lowest results are generated, sorted from highest to lowest, and summarized without assigning them to named abilities.

## Quick Answer: Key 4d6 Drop Lowest Numbers

- One score has 6^4 = 1,296 equally likely ordered dice outcomes.
- The mean score is about 12.245, compared with 10.5 for ordinary 3d6.
- The most likely single score is 13 at about 13.27%.
- A single roll is 15 or higher about 23.15% of the time.
- A single roll is 18 exactly 21/1,296, or about 1.62% of the time.
- Across six independent scores, the chance of at least one 18 is about 9.34%.
- The expected total of six scores is about 73.47; actual arrays can be much higher or lower.

## Three Ability-Score Methods in the 2024 Basic Rules

The official 2024 D&D Basic Rules describe Standard Array, Random Generation, and Point Cost. Standard Array uses 15, 14, 13, 12, 10, and 8. Random Generation rolls four d6, totals the highest three, and repeats until six numbers exist. Point Cost gives 27 points and permits buying scores from 8 through 15 using the published cost table. A Dungeon Master can require a particular method.

_[Figure: Choose the method for the campaign goal — The method changes variance and fairness, not just arithmetic.]_

## How 4d6 Drop Lowest Is Calculated

**One ability score**

```
Score = Sum of the highest three dice from four independent d6 rolls
```
- Minimum: 1 + 1 + 1 = 3 after one of four 1s is discarded.
- Maximum: 6 + 6 + 6 = 18 when at least three dice show 6.
- Repeat independently six times to produce an array.

_[Figure: How the DTC stat roller builds an array — The tool performs the same sequence for each of six scores.]_

## Exact Probability Distribution for One Score

Because there are only 1,296 ordered outcomes, the distribution can be calculated exactly by enumerating every four-die result, dropping the minimum, and counting the remaining sum.

**Exact 4d6-drop-lowest distribution**
| Score | Outcomes out of 1,296 | Probability | Score | Outcomes | Probability |
| --- | --- | --- | --- | --- | --- |
| 3 | 1 | 0.08% | 11 | 148 | 11.42% |
| 4 | 4 | 0.31% | 12 | 167 | 12.89% |
| 5 | 10 | 0.77% | 13 | 172 | 13.27% |
| 6 | 21 | 1.62% | 14 | 160 | 12.35% |
| 7 | 38 | 2.93% | 15 | 131 | 10.11% |
| 8 | 62 | 4.78% | 16 | 94 | 7.25% |
| 9 | 91 | 7.02% | 17 | 54 | 4.17% |
| 10 | 122 | 9.41% | 18 | 21 | 1.62% |

_[Figure: Chance that one score reaches a threshold — Cumulative probabilities from exact enumeration of 1,296 outcomes.]_

## From One Score to a Six-Score Array

**At least one qualifying score in six rolls**

```
P(at least one) = 1 - (1 - P(one roll qualifies))^6
```
- This assumes six independent scores generated by the same method.
- For an 18: 1 - (1 - 21/1,296)^6 = about 9.34%.

**Chance of at least one high score across six rolls**
| Threshold | One score | At least one of six |
| --- | --- | --- |
| 14 or higher | 35.49% | 92.80% |
| 15 or higher | 23.15% | 79.40% |
| 16 or higher | 13.04% | 56.76% |
| 17 or higher | 5.79% | 30.07% |
| 18 exactly | 1.62% | 9.34% |

These figures describe at least one qualifying score, not the complete array shape. Two arrays can have the same total but very different top scores, low scores, and modifier sums.

Tool: [Roll a 4d6-Drop-Lowest Array](https://dothecalculation.com/calculators/dnd-stat-roll-calculator) — Generate six scores, sort them high to low, and review the total, average, net ability modifiers, and an extended point-cost comparison.

## Ability Score Modifiers and Breakpoints

**Ability modifier**

```
Modifier = floor((Ability score - 10) / 2)
```
- Scores 10–11 produce +0, 12–13 produce +1, 14–15 produce +2, 16–17 produce +3, and 18 produces +4.
- The DTC calculator adds all six modifiers to show a net modifier sum.

Odd and even scores in the same pair have the same immediate modifier. A 15 and 14 both produce +2; a 16 produces +3. Later character options can change scores, so the value of an odd score depends on the character-building rules in use.

## How to Interpret the Calculator’s Point-Buy Value

The official 2024 Point Cost table covers scores 8 through 15: costs 0, 1, 2, 3, 4, 5, 7, and 9. The DTC calculator uses that table in range but extends it below 8 and above 15 so any rolled array receives a comparison number. It assigns negative costs to 3–7 and extrapolated costs of 12, 15, and 19 to scores 16, 17, and 18.

> **Extended point value is a heuristic** — A rolled 16, 17, or 18 cannot be purchased under the official 8–15 Point Cost table. Treat the calculator’s total as an informal comparison across rolled arrays, not an official point-buy budget or character-creation rule.

## Agree on Fair Table Rules Before Rolling

- Choose random generation, Standard Array, or Point Cost before seeing results.
- Decide whether players roll individual arrays or share one array.
- State whether values are assigned freely or kept in roll order.
- Define any minimum total, minimum high score, or reroll rule in advance.
- Choose whether rolls must be public or recorded.
- Apply the same rule to every player unless the group explicitly agrees otherwise.
- Remember that probability describes long-run frequency, not what one player is owed.

## Common Probability and Rules Mistakes

- Using the 3d6 distribution for 4d6 drop lowest.
- Assuming the mean score is the most likely score; the mean is 12.245 while the mode is 13.
- Multiplying a one-roll probability by six to estimate “at least one” without correcting for overlap.
- Treating an expected six-score total as a guaranteed or typical exact array.
- Comparing rolled scores above 15 directly with official point-buy purchases.
- Assigning the calculator’s sorted Stat 1–6 labels to fixed abilities.
- Calling a pseudorandom browser result cryptographically verifiable dice.
- Changing reroll or minimum rules only after someone sees an unfavorable array.

## Calculator Limitations and Assumptions

The DTC tool uses JavaScript Math.random to produce each d6 value. It is suitable for casual simulation but does not provide a seed, audit trail, physical-dice verification, or cryptographic proof. Each click produces one six-score sample; it does not display the theoretical distribution or run a large simulation.

The calculator sorts scores high to low, computes total and mean, sums standard ability modifiers, and applies its extended point-cost map. Campaign-specific species, background, class, feats, caps, and house rules are outside the calculation.

## Sources to Verify or Cite

- D&D Beyond 2024 Basic Rules, character creation: https://www.dndbeyond.com/sources/dnd/br-2024/creating-a-character
- D&D Beyond 2024 Basic Rules, ability scores and modifiers: https://www.dndbeyond.com/sources/dnd/br-2024/playing-the-game
- Probability values in this article come from exact enumeration of all 6^4 ordered four-die outcomes.
- Use the campaign’s chosen rulebook and Dungeon Master rulings for table-specific character creation.

## Frequently Asked Questions

**What is the average result of 4d6 drop lowest?**

The exact mean is about 12.245 for one score. Six independent scores therefore have an expected total of about 73.47.

**What is the most likely single score?**

A 13 is most likely, with 172 of 1,296 outcomes, or about 13.27%.

**What is the chance of rolling an 18?**

For one score, 21 of 1,296 outcomes produce 18, about 1.62%. Across six independent scores, the chance of at least one 18 is about 9.34%.

**What is the chance of at least one 16 or higher?**

One score is 16 or higher about 13.04% of the time. Across six independent scores, at least one reaches 16 about 56.76% of the time.

**Why is 4d6 drop lowest better than 3d6 on average?**

The fourth die provides a chance to replace a low value before summing three dice, shifting the distribution upward. Ordinary 3d6 has mean 10.5; 4d6 drop lowest has mean about 12.245.

**Does the calculator assign scores to abilities?**

No. It sorts the six values from highest to lowest as Stat 1 through Stat 6. Assignment to abilities is a separate character-creation decision.

**Is the calculator’s point-buy value official?**

Only the 8–15 costs match the official Point Cost table. Values below 8 or above 15 use an extended comparison map and are not official purchasable scores.

**Is a high total always a strong array?**

Not necessarily. Score placement, modifier breakpoints, the highest score, the lowest score, and class needs can matter more than total alone.

**Are the browser rolls cryptographically random?**

No. The implementation uses Math.random. It is appropriate for casual generation, not for a verifiable random process.

**Should a group allow rerolls for weak arrays?**

That is a table rule. If rerolls or minimums are used, define them before anyone rolls and apply them consistently.

## Final Summary

4d6 drop lowest produces a higher and more variable score distribution than 3d6. One score averages 12.245, an 18 appears 1.62% of the time, and six rolls contain at least one 18 about 9.34% of the time. Use those probabilities to set expectations, then use an agreed campaign method and rules for the actual characters.

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_Source: [Do The Calculation](https://dothecalculation.com/blog/hobby/dnd-ability-score-probabilities). Quote freely with attribution and a link to this page._