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D&D 2014 — one target’s Fireball risk

R05 · Advanced · Scoped component

Question and scope

Graduation brief: model one target’s risk of taking at least 28 damage from a base D&D 2014 Fireball, with Dexterity save bonus +3 against DC 15. A success halves damage, rounded down. No resistance or Evasion. Before reading the solution, write assumptions, choose representations, predict bounds, and construct the report from a blank file.

Source sections are linked under Rules below; primary-source review is recorded in the release dossier. Independent human and browser/usability review are separate gates.

Inputs and model limits

Positive integer HP (default 28), integer save bonus +3 and DC 15. Base 8d6, half rounded down on save. Damage reaching HP is not a death classification.

Complete runnable model

Sample solution: build the independent damage total and natural save, then classify their pair. Preserve the actual damage total while deciding whether to halve it. >= includes damage exactly equal to the target’s HP. The policy does not multiply unrelated hit and damage marginals; both determine one event inside the callback.

hp = 28
save_bonus = 3
save_dc = 15
full = dice_pool(8, 6).sum()
bands = scale().step("Below HP threshold").step("Damage reaches HP")
def harm(raw_damage, natural_save):
    damage = raw_damage
    if natural_save + save_bonus >= save_dc:
        damage = raw_damage // 2
    if damage >= hp:
        return "Damage reaches HP"
    return "Below HP threshold"
result = joint_classify(full, d(20), bands, harm)
output("One-target Fireball risk", result)
output("At least current HP in damage", result.pmf("Damage reaches HP"))

One-target Fireball risk · Outcomes

At least current HP in damage · Prob

Reading the report and independent checks

The save succeeds on natural 12–20: 9/20. A successful save deals at most 24, so cannot reach 28 HP. An independent oracle is therefore (11/20) × P(8d6 ≥28). Count eight-d6 totals by repeated convolution or a separate small dynamic count. Overall mean damage is (11/20)×28 + (9/20)×13.75 = 21.5875, but the risk is a separate question.

Safe changes

Set HP to 49: risk is zero. Set HP to 4: every possible damage result reaches it, so risk is one. At HP 28 with save bonus 20 the risk is zero because all ordinary saves succeed; at bonus −20 it becomes P(8d6 ≥28). These are model boundary checks, not special death-save rules.

Composition and boundary checks

Graduation: invent a two-d6 rule where armour subtracts after taking the higher die, then ask about a specified HP threshold. Deliver a standalone literate file, one independent face count, at least two boundary checks, and exclusions. Acceptance criteria: use 36 equally likely pairs, keep the higher before armour, floor at zero, and query inclusively. Example d6+d6, armour 2, HP 4: only a maximum 6 reaches HP, probability 11/36. Do not reuse this Fireball script unchanged.

Do not combine separate marginal reports and assume they preserve the same rolled faces. When an event depends on several properties of one roll, keep those properties together inside a single classifier or pool callback.

Rules

D&D Basic Rules 2014: Fireball, ordinary saves, and rounding down. One target; no shared multi-target event, concentration, resistance, vulnerability, Evasion, or instant-death interpretation. “Damage reaches HP” is not a claim of death.

Related learning

Lesson L32 explains the modelling idea step by step. Cookbook index offers both game and mechanic views of these same recipes.

Content ID: R05 · Review status: pilot

Prerequisites: L32