RPG Dice Roll Analyzer

4d6 Drop Lowest is the most common method for generating character ability scores in Dungeons & Dragons 5th Edition. You roll four six-sided dice (4d6), discard the lowest roll, and sum the remaining three. This produces a value between 3 and 18, with a mean of ~12.24 — higher than the standard 3d6 average of 10.5. The method gives players better odds of achieving above-average stats while still allowing for occasional low rolls, creating balanced but interesting characters.

The difference is significant: 4d6 drop lowest shifts the entire distribution upward. With standard 3d6, the mean is 10.5 and you have only a 9.26% chance of rolling 16 or higher. With 4d6 drop lowest, the mean rises to 12.24, and your chance of 16+ jumps to 13.04%. The probability of rolling an 18 increases from 0.46% (3d6) to 1.62% (4d6 drop lowest) — over 3.5× more likely. This makes 4d6 drop lowest the preferred method for heroic fantasy campaigns where characters should feel exceptional.

The mode (most frequent single result) is 13, occurring in 172 out of 1,296 possible combinations — about 13.27% of all rolls. The distribution is roughly bell-shaped but slightly skewed, peaking at 13 and tapering off toward both ends. Scores of 12, 13, and 14 together account for over 38% of all outcomes, making them the "sweet spot" you'll see most often.

The probability of rolling an 18 with 4d6 drop lowest is exactly 21 out of 1,296, or approximately 1.62% (about 1 in 62 rolls). This requires rolling at least three 6s among the four dice. The only combinations that yield 18 are: (6,6,6,6), (6,6,6,5), (6,6,6,4), (6,6,6,3), (6,6,6,2), and (6,6,6,1) — along with all permutations. When generating a full set of 6 attributes, your chance of getting at least one 18 is roughly 9.4%.

It depends on your playstyle. Point buy guarantees balanced, predictable stats (typically totaling 72 across 6 attributes). 4d6 drop lowest averages about 73.5 total across 6 stats, but with significant variance — you could end up with totals ranging from the low 40s to the high 80s. Rolling introduces excitement and can produce exceptionally powerful or memorably flawed characters. Many DMs allow players to fall back on point buy if their rolls are particularly poor (a common house rule: if your total is below 70, you may reroll or use point buy).

This analyzer focuses on 4d6 drop lowest, the gold standard for D&D attribute generation. However, the simulation engine can help you understand the behavior of similar "drop" mechanics. The core principle — rolling multiple dice and discarding the lowest — is widely used in tabletop RPGs including Pathfinder, Shadowrun, and various OSR systems. The cumulative probability table and Monte Carlo simulator give you tools to reason about any similar dice-pool mechanic. For advanced use, you can observe how the simulated distribution converges toward theoretical values as you increase the number of trials.

The simulation uses JavaScript's Math.random() with 4d6 drop lowest logic implemented faithfully. With 1,000 trials, you'll see rough agreement with theoretical values (±2-3% per bin). At 10,000 trials, the fit becomes quite good (±1%). At 100,000 trials, the simulated distribution nearly perfectly matches theory — a beautiful demonstration of the Law of Large Numbers. The simulation bars (amber) are displayed alongside theoretical bars (purple) so you can visually assess convergence in real time.