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Success: include the target itself

Part A · L04 · 5–10 minutes · Prerequisite: L03

The situation and question

Our generic task succeeds when two d6 plus a modifier total 8 or more. With no modifier, what is the chance of success? This completes our small invented task rule; named games may add exceptions and different difficulties.

Predict

Is success more or less likely than half? Does rolling exactly 8 count?

Build

A dot asks a value to perform an operation. total.p_ge(target) asks for the probability of a result greater than or equal to the target. The target is included. total.pmf(target) asks for exactly that result instead.

A probability is a number from 0 to 1: 0 means impossible, 1 means certain, and 0.5 means 50%. The report can format it as a percentage; do not multiply by 100 before passing it to a probability report.

modifier = 0
target = 8
total = d(6) + d(6) + modifier
output("Success: eight or more", total.p_ge(target))
output("Exactly eight", total.pmf(target))

Success: eight or more · Prob

Exactly eight · Prob

Run and read

Totals 8, 9, 10, 11, and 12 have 5, 4, 3, 2, and 1 pairs respectively. Success therefore has probability 15/36, about 41.67%. Exactly 8 has probability 5/36, about 13.89%. These outputs are different questions, not categories that should add to 100%: exactly eight is already included in success.

Change one thing

Set modifier = 2. Check: success becomes 26/36, about 72.22%, because the unmodified dice now need only 6 or more. Update titles if you change the target.

Part A checkpoint: try it yourself

Without copying this script, report the success chance for one d8 plus 2, meeting or beating a target of 7. Name both parameters and explain the answer.

Solution reasoning: the die itself needs 5, 6, 7, or 8. Four of eight faces succeed, so the answer is 1/2. Use d(8) + modifier and ask .p_ge(target). Exactly 7 after the bonus is only 1/8. As boundary checks, target 3 is certain and target 11 is impossible.

What you now know

Specify the event before selecting a query. An inclusive threshold is not an exact result, and a plausible average alone does not answer a success question.

Where next

Previous: modifiers · Next: roll-under checks. Continue into Part B to compare choices and build compact reports. The pool-count recipe later asks how often individual faces match, rather than querying their sum.

Content ID: L04 · Review status: pilot