As previously mentioned, I had problems unifying my karma mechanic (roll a 50-50 roll if stats are equal, otherwise highest stat wins) with the two other die mechanics.

Those were: 1D12+skill to beat 7+opponent skill
and
roll StatD12. Every roll beating opponent Stat is one success. Reroll 12's give bonus dice.

I had an idea as follows:
Roll StatD12, target number goes from 1 to 11, from very non-random to extremely random. Reroll 12's to give bonus die.

Opposed tests, both roll, most successes wins.
Test against target number: reach success threshold.

At target number 1, if you have stat x you will always achieve at least 6 successes (more if you roll 12s)

At higher target numbers the chances go down somewhat.

Opposed tests give for example (my mother at Strength 3 vs Arnold Schwarzenegger at Strength 7):

Target number is 1 (predictable): My mother wins 0.004% of the time(that's pretty bad odds)
Target number is 5 (unpredictable): My mother wins 3% of the time
Target number is 11(maximum randomness): My mother wins 23% of the time.

Target number should increase representing stress and possible unfavourable conditions (slippery grass, treacherous steps and so on). The "Stat" gives the usual performance level, which can be higher in case of exceptional luck, or lower if conditions require it.

Concessions and complications you ask? Just work on those established successes I guess. Incidentally one could let the "Inspirations" work by increasing the range of the crit (and thus exceptional results) by a significant degree. Or simply use extra dice. The behaviour is different. The former yields more gain the higher your stat is, as the chance of rolling a crit is proportional to the number of dice. The second version gives an equal overal boost to any rating.

I'm not quite clear on what I prefer. Maybe none of the above.