Margin, Degree of Success, and Progress

Margin is the single number the game runs on. One roll produces it; everything downstream reads it.

This completes one-roll resolution. Magnitude is not a second die and not a second roll — it is the same number, read for different purposes.

Design derivation and the influence trail are in notes/01-degree-of-success.md.

RESOLVED — roll-over. This section is kept as the record of how the question arose. The d6-only exploding pivot settled it: exploding dice push totals upward, so under roll-under a lucky 6 would drive a character toward failure. Margin = Roll − Target Number. See 04-dice.md and OQ-23.

The threshold bands further down are calibrated to the superseded 2d10 engine and are wrong. Under 3d6 exploding the expected Margin per attempt is about 2.93 at 57% success, and — because the exploding tail is long — the Margin given a success stays near 4 to 5 across almost the whole difficulty range. That is a real design property and an unexamined one: a desperate 9% shot that lands hits about as hard as a routine one. Every band below needs regenerating, and the flat conditional-Margin behaviour needs a decision. Tracked in OQ-24.

⚠ Superseded: which direction does the roll go?

The worked example that prompted this document describes roll-over, not roll-under:

Target Number 11, rolled 15, earned 4 points.

15 − 11 = 4, so Margin = Roll − Target Number, and a roll above the target succeeds. The founding brief specifies the opposite — roll-under, with Margin = Target Number − Roll, where a 15 against a Target Number of 11 is a failure.

Both are coherent. They cannot both be the system. Tracked as OQ-23.

This is cheap to change and the analysis is unaffected. Roll-under and roll-over are mathematically symmetric: every distribution, Edge rate, and Margin shape measured so far mirrors exactly and transfers unchanged. What differs is presentation and how skill enters the equation:

The roll-over form is more familiar to most players and makes Difficulty a single clean number, which suits the PA and the no-opposed-rolls lock. The roll-under form is what every existing number in the brief assumes.

Everything below is written direction-agnostically. Substitute whichever definition of Margin wins; nothing else changes.

Progress thresholds

An extended task has a threshold: total Margin required to complete it. Each roll represents one time window — a round, an hour, a shift, a week — set by the fiction. Margin earned on a success is added to the accumulated total. A failure adds nothing.

The worked example: a task with a threshold of 20, a character whose roll produces a Margin of 4, banks 4 points and needs 16 more.

This generalizes across the whole game, which is the point:

One procedure covers combat repair, downtime crafting, and an arm-wrestling match. That directly serves the brief's unified-resolution goal, and it means the PA needs exactly one task model.

Expected Margin is the tuning constant

Because Margin drives progress, expected Margin per attempt converts a threshold into table time. From analysis/resolution-comparison.md, for 2d10 (provisional — OQ-20 is not closed):

Provisional threshold bands

Calibrated to a competent character at roughly 75% success, earning ~2.84 Margin per attempt. Every value here is provisional and untested.

The skill-scaling warning

Expected Margin ranges from 0.56 to 5.20 across the competence band — a 9x spread. A 20-point threshold is 4 attempts for an expert and 36 for a novice.

That is a much steeper skill effect than the raw success rates suggest, and it is the same convexity flagged in OQ-07: Margin-driven systems amplify skill differences far beyond their effect on hit-or-miss. Here it is arguably correct — an expert genuinely should finish the work several times faster — but it must be deliberate, because the identical amplification applied to damage is the OQ-07 problem.

Consequence: a threshold tuned for an expert is unplayable for a novice, and vice versa. Task thresholds cannot be set without knowing the intended competence of whoever attempts them.

Open design questions