The multiple size d6 pool roll under mechanic seems a little complicated, with varying dice pool sizes, roll under, compare highest, plus special rules for 1’s & 6’s (in most cases irrelevant), but an interesting way to preserve 50/50 chance between two arbitrarily high similar scores, while preserving differences at lower scores.

Most systems have trouble comparing both 8 vs 9 and 80 vs 90; using a different dice range would be one approach.

Ignoring details (like all 1’s, ties, what if you both fail, etc), the probabilities can be calculated by breaking the rolls at the shared (lower) range where the probabilities are 50/50.

e.g. For Str 25 vs Str 30 with 6d6.

  • A < 25, B < 25 is a 50/50 chance of who wins.
  • A < 25, 25 <= B < 30, B wins because they are higher than A can possibly get.
  • A < 25, B >= 30, A wins.
  • A >= 25, B < 30, B wins.
  • A >= 25, B >= 30, both fail

You can get the probabilties from AnyDice `output 6d6`

This is easiest layed out in a table:

A \ B < 25 (79%) < 30 (19%) >= 30 (2%)
&lt 25 (79%) 2x 31% each 15% B 1.5% A
>= 25 (21%) 17% B 4% B 0.5% neither

A (Str 30) has a 67% chance to win, B (Str 25) has a 32.5% chance, so about 2/3 vs 1/3 chance.

In contrast with a Str 8 hobbit, the chance of rolling less than 8 on 6d6 is 0.02%, so their chance of winning is almost zero.

The upper end is always small (as the dice changes to be just higher than the maximum), so the key is the lower scored participant gets 50% of the shared chance (which is the lower chance vs the entire dice range).

Example 1: Str 15 vs Str 20, with 4d6, the shared (< 15) is 66% chance, of 0.56 * 0.56 * 0.5 ~ 16% chance for Str 15 to win.

Example 2: Compared to Str 55 vs Str 60, with 11d6, where the chance is 0.998 * 0.998 * 0.5 ~ 50%; the chance of both rolling under 45 on 9d6 is almost certain, so it is a straight 50/50 contest.

So, if the lower score is about half the maximum dice range, the shared chance will be about 50%, giving the lower score a 25% chance to win. Lower scores will be less than 25%, and higher scores up to 50% (both non-linear changes).

A lot depends on what the system is trying to achieve, e.g. in D&D, a game of heroic fantasy where individual heroes can defeat mighty monsters, they use bounded accuracy with a linear systems: the halfling hero could very well have Strength 20, and the cloud giant only Strength 27, so comparable, especially if the halfling has proficiency in athletics. This is the kind of movie / heroic action scene, and as everything is kept within a small range, comparing two giants is also easy.

The other end is having a scale system, e.g. Savage Worlds heavy armor and heavy damage, where normal weapons simply can’t hurt tanks (at all) and two tanks just compare normal weapon ratings. Cortex Prime has something similar with Scale Die, but also allows heroics (as characters can spend plot points to include extra dice).