The core mechanic

In STA 2e you roll a pool of d20s — usually 2, sometimes up to 5 with bought dice. Each die that rolls at or below your Target Number (Attribute + Discipline) scores 1 success. A natural 1 always scores 2 successes (a critical). If your task has a Focus, dice that roll at or below your Discipline also score 2 successes.

The number of successes you need is the task's Difficulty (0–5). Any successes over the Difficulty become Momentum, which the group banks for later rerolls, bonus dice, and narrative effects.

Single-die success odds

The chance one d20 scores at least one success at each Target Number:

Note: a natural 1 always crits, so the "expected successes" column is slightly higher than raw P(success) would suggest.

Passing the task: 2d20 vs Difficulty

The standard pool is 2d20. Here's the probability of meeting each Difficulty without Focus, at common Target Numbers:

Most tasks are Difficulty 1 or 2. At a TN of 12 (e.g. Attribute 9 + Discipline 3), a standard 2d20 pool passes a D2 task about 40.0% of the time.

Momentum generation

Momentum is the surplus — successes beyond the Difficulty. The easier the task and the higher your TN, the more Momentum you reliably bank. Expected total successes on 2d20:

Per the rules, you can only bank up to 6 Momentum at any one time, so consistent surplus on routine tasks is more valuable than spiking on one heroic roll.

Buying extra dice

You can buy up to 3 extra d20s by spending Momentum or adding to the Threat pool (1, 2, then 3 Momentum/Threat for the 3rd, 4th, and 5th die). Each extra die adds the same expected successes shown above — so at TN 12, each bought die adds about 0.65 successes on average. That's a fair trade for tough rolls (D3+) and almost always wasted on D1 tasks you'd pass anyway.

Complications

Any die rolling within your Complication Range (by default just 20, widened by trait or environment) triggers a Complication on top of whatever successes you scored. With the base range of 20, every d20 has a flat 5% chance to complicate — so 2d20 has roughly a 9.8% chance of at least one Complication, and 5d20 jumps to about 22.6%. Larger pools succeed more, but they also complicate more.

Try it

Plug your own Attribute, Discipline, Difficulty and Focus into the 2d20.space dice roller and watch the math play out across many rolls.