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Choose a policy before seeing its future roll

Part H · L30 · Prerequisite: L29 · One modelling idea

Situation, question, and prediction

In Fate Core you have one available fate point and a relevant aspect whose invocation is agreed. Against fixed passive opposition +2, your skill is +2. After seeing 4dF, choose +2 or reroll all dice. The objective is strictly exceed opposition without a cost, not merely obtain a tie. Predict which initial rolls need a reroll rather than a guaranteed +2 rescue.

Build

A policy is a function from information already seen to a decision. Keep an already successful roll without spending. If +2 guarantees strict success, choose it. Otherwise reroll and accept the replacement. The callback may inspect the potential reroll only after the decision to reroll has been made.

skill = 2
opposition = 2
f = die_faces([-1, 0, 1])
roll = f + f + f + f
bands = scale().step("Objective missed").step("Strict success")
def policy(first, replacement):
    if first > opposition:
        return "Strict success"
    if first + 2 > opposition:
        return "Strict success"
    if replacement > opposition:
        return "Strict success"
    return "Objective missed"
result = joint_classify(roll + skill, roll + skill, bands, policy)
output("One-invocation policy", result)
output("Strict success chance", result.pmf("Strict success"))
output("Chance of spending the point", (roll + skill).cdf(opposition))

One-invocation policy · Outcomes

Strict success chance · Prob

Chance of spending the point · Prob

Run, read, and check

Initial totals with dice ≥−1 are already successful or can be rescued by +2: 66/81. The remaining 15/81 need a reroll, which strictly succeeds 31/81 of the time. Thus success is 5811/6561. A point is spent on the original non-successes: 50/81. Ties may achieve an overcome goal at a minor cost, but deliberately do not meet our stricter objective.

Change one thing

Change skill to +3. The policy now rerolls only original dice −3 or −4. State the objective and budget again before comparing probabilities.

Try it yourself

Could “look at the replacement, then decide whether to take +2” do better? Yes, but it is illegal future information in this model. Answer check: at the original skill, always taking +2 after any miss succeeds only 66/81; the fixed policy adds the reroll rescue term, not hindsight.

Rules and model notes

Fate Core: Invoking Aspects and Overcome. One paid invocation, no free invokes, defender responses, later resources, or further invocations. Relevant aspect and point availability are assumptions, not outcomes.

What you now know / where next

Choose a policy before seeing its future roll is the reusable idea. Follow the generated previous/next links below, or return to the course index. For a complete self-contained application, see fate-invocation.

Content ID: L30 · Review status: pilot

Prerequisites: L29