# Roll-under checks: low can be good

**Part B · L05 · 5–10 minutes · Prerequisite: L04**

## The situation and question

In **Call of Cthulhu 7th edition**, the Keeper asks for a regular-difficulty
Spot Hidden check. Your investigator has skill 50. Roll percentile dice and
succeed if the result is **equal to or below** the skill. How often do you succeed?

This is one unopposed regular-difficulty check, without bonus/penalty dice,
pushing, or spending Luck. We ask whether you meet the requirement, not whether
you get *exactly* the game's Regular success level: better successes count too.

## Predict

Does skill 50 succeed on 49 faces, 50 faces, or 51 faces? Does rolling 50 count?

## Build

`d(100)` represents the 100 equally likely percentile results **1–100**. It
never produces zero. At the table, two percentile dice encode these results;
the double-zero combination means 100, not zero.

In L04, `.p_ge(target)` counted results at or above a threshold. `.cdf(skill)`
counts results at or **below** it, including the boundary. CDF means *cumulative
distribution function*: accumulate the chances from the lowest result through
the number you supply. You need not memorise the mathematical name to use it.

```dice
skill = 50
percentile = d(100)
output("Meet regular difficulty", percentile.cdf(skill))
output("Roll exactly the skill value", percentile.pmf(skill))
```

## Run and read

Faces 1 through 50 succeed: 50 out of 100, or **50%**. Exactly 50 is just one
face, **1%**. The second question is included in the first; the two outputs are
not mutually exclusive categories.

Increasing the skill helps even though *lower rolls* are good. You are moving
the acceptable boundary upwards, not changing the die or its mean of 50.5.

## Change one thing

Change `skill` to 65. **Check:** success rises to 65%; exactly the skill remains
1%. Do not use `.p_ge(65)`—that asks the opposite-direction question.

## Try it yourself

Write a report for skill 40. Then explain the difference between “below 40” and
“40 or below.” **Answer check:** regular difficulty succeeds 40% of the time;
strictly below 40 is only 39%. Count 1–39 and then include the boundary face.

## What you now know

First decide which direction is favourable and whether equality counts. A
roll-under rule can be modelled with an inclusive lower-tail query.

## Rules and model notes

Source: Chaosium's [7th-edition Quick-Start Rules](https://www.chaosium.com/cthulhu-quickstart/),
**Reading D100 (Percentile Dice)** and **Skill Rolls and Difficulty Levels**
(p. 10 in the linked PDF), checked 2026-09-15. This lesson uses integer skills
1–99 and deliberately does not distinguish Hard, Extreme, critical, or fumble
results. Do not extrapolate it to skills 100+ or bonus/penalty dice.

## Where next

[Previous: success](04-success.html) · [Next: averages and chances](06-averages-and-chances.html).
The [regular-check recipe](../cookbook/coc7-regular-check.html) compares several
skills and states what this component leaves out.