# One die: a map of possible damage

**Part A · L01 · 5 minutes · No prerequisites**

## The situation and question

A weapon in our example rolls one six-sided damage die. We are modelling **only
that die**, not whether an attack hits, armour, or critical hits. What damage
values are possible, and how often does each occur?

This is a generic damage component, not a complete game rule.

## Predict

Is a 6 less likely than a 1? Can the average damage be a number the die never shows?

## Build

`d(6)` describes all six possible faces of a fair die; it does not roll a random
sample. Parentheses pass information to a function: here, the number of sides.
`output` presents a result. Its first argument is a title inside quotation marks;
the comma separates that title from the value to report. A line beginning with
`#` inside code is a comment for people, not an instruction.

```dice
# Only the damage die, before other rules.
output("One six-sided damage die", d(6))
```

## Run and read

Open this **whole document** in the playground and select **Run** (Shift+Enter).
The report shows a distribution: a map from results to their probabilities.
The row for 6 has probability 1/6, about 16.67%. So does every other row.
This is a deterministic calculation of the finite possibilities, not a simulation.

The mean is 3.5: add 1 through 6 and divide by 6. It describes a long-run average,
not a seventh face. The minimum is 1 and the maximum is 6.

## Change one thing

Change `d(6)` to `d(8)` and update the title. Predict the range first.
**Check:** the range becomes 1–8, each face has probability 1/8, and the mean is 4.5.

## Try it yourself

Make a report for a four-sided damage die without copying the line above.
**Answer check:** use `d(4)` as the second argument to `output`; the mean is 2.5
and each face has probability 25%.

## What you now know

A roll value represents *all* possible results. A report title explains what
those results mean at the table. Always check the range before trusting a mean.

## Where next

Continue to [two dice](02-two-dice.html). Later, the
[damage rounding recipe](../cookbook/fireball-half-damage.html) transforms a
whole damage distribution. That recipe is conditional on the save result.