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A count is itself a distribution

Part D · L15 · Prerequisite: L14 · One modelling idea

Situation, question, and prediction

In a generic hits-counting component, each d6 showing 5 or 6 is one hit. Roll three dice. Is the average number of hits the same thing as the chance of at least one hit? Predict before running.

Build

.count([5, 6]) preserves the chance of each possible number of matching dice. The brackets describe acceptable faces, not two separate throws. .p_at_least(2, [5, 6]) queries whether enough dice match.

pool = dice_pool(3, 6)
hits = pool.count([5, 6])
output("Number of hits", hits)
output("Any hit", pool.p_any([5, 6]))
output("At least two hits", pool.p_at_least(2, [5, 6]))

Number of hits · DieRoll · mean 1.000

Any hit · Prob

At least two hits · Prob

Run, read, and check

Counts 0,1,2,3 have probabilities 8/27,12/27,6/27,1/27. Mean hits is 1; any hit is 19/27, and at least two is 7/27. A mean count of 1 is not a 100% success chance. For zero hits, all three dice must miss: (2/3)^3.

Change one thing

Count sixes only. Mean hits falls to 1/2; at least two sixes is 16/216 = 2/27.

Try it yourself

Build a two-die count report for 5–6. Answer: probabilities 4/9,4/9,1/9 for counts 0,1,2. Checkpoint: choose .sum, .p_any, or .count based on whether the rule asks for total, any match, or number of matches.

Rules and model notes

Generic building block. It resembles a raw-hits component used by some games, but makes no claim to implement Shadowrun 5e limits, Edge, or glitches; edition-source verification is still required for that named recipe.

What you now know / where next

A count is itself a distribution is the reusable idea. Follow the generated previous/next links below, or return to the course index. For a complete self-contained application, see count-high-faces.

Content ID: L15 · Review status: pilot

Prerequisites: L14