D&D 5e d20 checks with bucket

At the table

A D&D attack or save is not just “did the total beat the DC?” Natural 1 and natural 20 are special on the d20 you keep. Advantage and disadvantage change which natural faces are likely before you add your modifier.

Lesson 11 buckets a raw d20 face into four fixed ranges. That teaches ordered labels, but it is not the same as a DC check with a modifier. Here we stay on the natural die (1d20, 2d20kh1, …) and put the modifier into the target number instead of into the roll.

Adjusted target (stay on 1..20)

Table rule: success when natural + MOD >= DC. For integer faces that is the same as:

T = DC - MOD

advantage_check · Outcomes

p_hit_or_better · Prob

• check_scale builds the four-band scale from T = DC - MOD; call it wherever you need a check (1d20.bucket(check_scale(12, 4)), loops over DCs, and so on).
• at_most / at_least accept expressions; use them when T comes from DC and MOD (range sugar ..(T - 1) only works with numeric literals in source).
• 2d20kh1 is advantage. Use 1d20 for a normal roll or 2d20kl1 for disadvantage.
• Without early=True on crit bands, overlapping open ranges would mis-label nat 1 or nat 20—see lesson 11.

Reading the result

You get a four-row probability breakdown (one row per outcome label) plus p_at_least("SUCCESS"), which includes both ordinary successes and critical successes.

Try this

• Change DC and MOD (or add a for loop) and call check_scale(DC, MOD) for each combination.
• Swap 2d20kh1 for 1d20 and compare probabilities.
• Compare with lesson 11’s fixed bands on 1d20—notice how crit + DC logic differs.

Builtin details: standard library reference (scale, Scale.step, bucket, at_most, at_least, keep_highest, keep_lowest). Use classify when house rules do not fit four face bands.

What’s next

Powered by the Apocalypse (2d6 + stat)—miss / partial / full on the total with bucket, the usual PbtA pattern.

See the user guide index.