Why 3d6 is not a d20

01The same number, two different lives

Roll a d20 against a difficulty of 11. You succeed on exactly half the faces. Roll 3d6 against a difficulty of 11. You succeed on roughly half the combinations — the distribution peaks near 10–11, so a target of 11 sits almost exactly in the middle of the range. So far, so equivalent.

Now raise the difficulty to 16. On the d20, you succeed on 25% of rolls: five faces out of twenty, every face equally probable. On 3d6, you succeed on roughly 5% of rolls. Move the target one step further to 17 and the d20 gives you 20%, while 3d6 gives you about 2%. That gap is not a rounding error. It is the difference between a skill that occasionally fails and a skill that almost never succeeds. The two systems are not doing the same thing with difficulty numbers. They are making completely different claims about what "hard" means.

The reason is the shape of the distribution. A single d20 is a flat line: every integer from 1 to 20 appears with identical 5% probability. Three six-sided dice summed produce a bell curve centred near 10–11. Low totals require every die to show low; high totals require every die to show high. Either extreme is a combination of rare events compounded together. A 3 requires three 1s; an 18 requires three 6s. Each occurs on only one of the 216 possible combinations — just under 0.5% of the time. A d20's 1 and 20 each occur 5% of the time, ten times as often as 3d6's extremes.

02What the bell does to a difficulty number

Understanding the shape matters because difficulty numbers are claims about probability. When a designer writes "DC 15" on a task, they are deciding how often a typical character should fail it. On a d20, a flat modifier system turns that into a clean linear relationship: each +1 bonus shifts your success chance by exactly 5 percentage points. Predictable, transparent, and deliberately heroic — with enough levels, a character stops failing routine tasks entirely, and even hard tasks become reachable on a lucky roll.

On a bell curve, no such linearity exists. Near the centre, a +1 bonus can shift your probability by 9 or 10 percentage points, because you are climbing the steep shoulder of the bell where combinations cluster. Near the edges, a +1 might move you by only 2 or 3 points, because combinations thin out sharply. A modifier of +2 near average is dramatically more powerful than the same +2 applied to an extreme task. This means that difficulty thresholds set near the edges of 3d6's range are nearly impassable no matter how good your character is — not because the designer said so, but because the arithmetic enforces it.

This is not a flaw. It is a design philosophy. A game built on 3d6 is saying: competence is real, extremes are rare, and the wild swing that saves a mediocre character against a hard obstacle is not supposed to be a regular feature of play. The bell punishes the lucky guess. The flat die rewards it.

03The experience at the table

These distributions create genuinely different fictional textures. On a d20, any character can crit. Any monster can drop a hero in an unexpected turn. Rare events are, in absolute terms, not that rare: you will roll a natural 20 about once every twenty rolls, which at a busy table might happen twice in a combat. The flat distribution produces genuine drama because high and low results are perpetually possible. A beginner fighter and a veteran fighter both have that 1-in-20 shot at the spectacular, and the 1-in-20 shot at the catastrophe.

On 3d6, the distribution produces competence. A high-attribute character who has built toward a task will succeed at it most of the time, because the bell concentrates results in the middle range that their modifiers already cover. Failure is meaningful precisely because it is unusual. When a skilled character fails on 3d6, it feels like genuine bad luck rather than an expected variance in the series. The system is modelling a world where practiced people do the things they are practiced at. The curve enforces a kind of statistical realism that a flat die cannot provide.

The tradeoff is tension. Flat dice produce sessions where anything can happen at any moment, a narrative engine that generates surprises but can also feel arbitrary. Bell curves produce sessions where you mostly see the thing you expected to see, punctuated by real exceptions. Neither is objectively superior; they are different tools for different imaginative goals.

04Ancestry and application

The contrast is historical as much as mechanical. The d20 became the signature of American fantasy roleplaying partly through its physical novelty — a neat platonic solid, equal faces, easy to read — and partly through Dungeons & Dragons, where the attack roll, saving throw and later the unified skill check all ran on that flat line. The 3d6 approach has older and more direct roots in wargaming, where it entered early roleplaying through games that wanted to model human attributes on something closer to a real statistical spread. If you have ever seen a stat array generated by 3d6 in order and wondered why most characters feel similar and occasionally exceptional, that is the bell at work: it makes average characters likely and outliers rare, in roughly the proportions you would expect from a real population.

Both approaches are coherent. What a designer must not do is set difficulty numbers for one distribution while using the mechanics of the other. A DC written assuming a flat line will be trivial or impossible on a bell, because the scaling is entirely different. The question is not which die is better. The question is what the curve promises to the person rolling it — and whether the difficulty numbers on your table are keeping that promise.

Roll the d20 when you want every session to feel like anything might happen. Pick up the three sixes when you want the world to be a place where training, preparation and genuine skill reliably matter, and where the monster is mostly as dangerous as it looks.