Threshold checks on twenty equal faces
A d20 has 20 equally likely values, so a target of 15 or higher succeeds on 15, 16, 17, 18, 19, or 20: six faces out of 20, or 30%. The expected face is 10.5. This makes the die useful for pass-or-fail checks because a target number can be translated directly into a visible count of successful faces.
A check with a bonus
For a target of 15 and a +3 modifier, a raw 12 becomes 15 and succeeds. The raw faces 12 through 20 work, giving 9 successful values and a 45% chance when no special rules apply. Write the inequality before rolling: raw roll + modifier at least target. That prevents a bonus from being confused with a reroll or with an automatic success rule.
Advantage changes the curve
Rolling two d20s and keeping the higher is not a +1 bonus. Against target 15, one roll succeeds 30% of the time; advantage succeeds unless both rolls are 14 or less, so the chance is 1 - 0.70² = 51%. A kept-lowest rule has the opposite effect. These mechanics need their own tool because they change the distribution rather than simply shifting the threshold.
Rules beyond the raw check
This page reports one face. It cannot know whether a particular game treats a natural 1 or 20 specially, whether ties pass, or whether a modifier is capped. Use the game text for those exceptions and use a custom roll when several dice, exploding results, or resistance rules are part of the same event.
Separate chance from difficulty
Raising a target from 15 to 16 removes one successful face, reducing an unmodified chance from 30% to 25%. That five-point percentage change comes from one face out of twenty. A difficulty label such as hard or routine has no mathematical content until it is connected to an actual target and any stated bonus.
Questions about this dice rule
What chance is a target of 15?
Six of twenty raw faces meet it, so it is 30% before modifiers.
Does this page apply critical rules?
No. Natural-roll exceptions are defined by the game using the result.