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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.

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

Meet regular difficulty · Prob

Roll exactly the skill value · Prob

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, 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 · Next: averages and chances. The regular-check recipe compares several skills and states what this component leaves out.

Content ID: L05 · Review status: pilot

Prerequisites: L04

Rules review: source checked 2026-09-15; human review pending