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Define what a tie means before comparing rolls

Part F · L24 · Prerequisite: L23 · One modelling idea

Situation, question, and prediction

A Fate Core overcome action faces active opposition from another character with equal skill. Compare their independent 4dF rolls. Predict whether strict wins and strict losses are equally likely, and whether a tie is failure.

Build

joint_classify(left, right, scale, function) calls the function with one value from each distribution. Subtracting the actual callback values gives their shared margin. For an overcome action, a tie attains the goal at a minor cost; a positive margin succeeds, and margin 3+ succeeds with style.

f = die_faces([-1, 0, 1])
roll = f + f + f + f
bands = scale().step("Below opposition").step("Tie: minor cost").step("Succeed").step("With style")
def compare(left, right):
    margin = left - right
    if margin < 0:
        return "Below opposition"
    if margin == 0:
        return "Tie: minor cost"
    if margin >= 3:
        return "With style"
    return "Succeed"
result = joint_classify(roll, roll, bands, compare)
output("Equal-skill overcome action", result)
output("Tie", result.pmf("Tie: minor cost"))
output("Strictly beat opposition", result.p_at_least("Succeed"))

Equal-skill overcome action · Outcomes

Tie · Prob

Strictly beat opposition · Prob

Run, read, and check

Tie probability is 1107/6561. Strictly beating opposition is 2727/6561, equal to falling below it by symmetry. The denominator is 81×81 sign sequences. A below-opposition result can still lead to success at a serious cost by the game’s rules; this report does not choose that option.

Change one thing

Add +1 to the first roll only. Strict wins increase; symmetry between win and loss is broken. Ties must still be reported under the same convention.

Try it yourself

For two opposed d6, build lose/tie/win categories. Answer: 15/36,6/36,15/36. Checkpoint: name the tie rule and explain why both dice are independent, even if both arguments reference one distribution variable.

Rules and model notes

Fate Core SRD, dice and the ladder. Four independent Fate dice; their faces are equally weighted −1, 0, +1. Other Fate/Fudge variants are not implied. Four Actions: Overcome. Outcome classification only; no invocations, active-defender resources, or choice of serious cost.

What you now know / where next

Define what a tie means before comparing rolls 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-opposition.

Content ID: L24 · Review status: pilot

Prerequisites: L23