# D&D 2014 — miss, hit, or critical

**R02 · Advanced · Scoped component**

## Question and scope

A D&D 2014 attack with +5 targets AC 15. A natural 1 automatically misses; a natural 20 is a critical hit. How do these exceptions differ from L21’s ability check? Predict what happens against impossibly high AC.

Source sections are linked under Rules below; primary-source review is recorded in the release dossier. Independent human and browser/usability review are separate gates.

## Inputs and model limits

Integer attack bonus and AC; defaults +5 and 15. Natural 1 misses, natural 20 critically hits. No expanded critical range or damage.

## Complete runnable model

`if` tests a condition; `==` compares equality, while `>=` means at least. Indentation controls each branch. `return` exits the function immediately, so test exceptions before ordinary success. Pass the function **name**, without calling it, to `classify`; it will receive each possible natural face.

```dice
bonus = 5
ac = 15
bands = scale().step("Miss").step("Hit").step("Critical")
def attack(face):
    if face == 1:
        return "Miss"
    if face == 20:
        return "Critical"
    if face + bonus >= ac:
        return "Hit"
    return "Miss"
result = classify(d(20), bands, attack)
output("Attack categories", result)
output("Hit including critical", result.p_at_least("Hit"))
```

## Reading the report and independent checks

At defaults: miss 9/20, ordinary hit 10/20, critical 1/20. Total chance to hit is 11/20. No extra “fumble” effect is assumed. The die passed to `classify` is unmodified because its natural face matters.

## Safe changes

Set AC to 100: only critical remains a hit, 1/20. Set AC to 1: natural 1 still misses, so hit including critical is 19/20.

## Composition and boundary checks

Use advantage by replacing `d(20)` with `keep_highest(2, 20, 1)`. Answer: hit including critical 319/400 and critical 39/400 at defaults. Checkpoint: classify a new rule with explicit equality and exception boundaries before trusting the graph.

Do not combine separate marginal reports and assume they preserve the same
rolled faces. When an event depends on several properties of one roll, keep
those properties together inside a single classifier or pool callback.

## Rules

[D&D Basic Rules 2014, Combat: Attack Rolls and Rolling 1 or 20](https://www.dndbeyond.com/sources/dnd/basic-rules-2014/combat). Ordinary attack categories only; no expanded critical range, damage, or house-rule fumbles.

## Related learning

[Lesson L22](../tutorial/22-natural-face-exceptions.html) explains the modelling idea step by step.
[Cookbook index](index.html) offers both game and mechanic views of these same recipes.