Supplement Four
SOC-14 5K
Just to throw more wood on the fire, I calculated the probabilities of Spectacular Successes (any 3 dice rolling 1), Spectacular Failures (any 3 dice rolling 6's), and Spectacularly Interesting rolls (3 1's and 3 6's). I have segregated the odds of Spectacularly Interesting from both Spectacular Success and Spectacular Failure so it is never counted with them. The branch of math used to figure out these probabilities is "combinatorics."
ON 3 DICE: SS, SF each: 1/216 (0.463%)
ON 4 DICE: SS, SF each: 21/1,296 (1.620%)
ON 5 DICE: SS, SF each: 276/7,776 (3.549%)
ON 6 DICE: SS, SF each: 2,886/46,656 (6.186%) SI: 20/46,656 (0.0429%)
ON 7 DICE: SS, SF each: 26,181/279,936 (9.352%) SI: 630/279,936 (0.225%)
ON 8 DICE: SS, SF each: 215,109/1,679,616 (12.807%) SI: 11,382/1,679,616 (0.678%)
ON 9 DICE: SS, SF each: 1,641,634/10,077,696 (16.290%) SI: 154,812/10,077,696 (1.536%)
ON 10 DICE: SS, SF each: 11,829,624/60,466,176 (19.564%) SI: 1,761,552/60,466,176 (2.913%)
You're welcome.
Yes, T5 should consider something akin to what I did with the UGM.
To quote from a page from those rules (see the link in my sig):
Characters with higher natural ability (higher stats) and higher expertise (higher skill level) will be more likely to roll Critical Success and less likely to roll Critical Failure. The opposite is true for those characters with lower attributes and lower (or no) skill level--those characters will throw Critical Success less often and Critical Failure more often.
The UGM skews Critical Success or Failure results in accordance with a character's ability and expertise. Your "klutz" characters will be more likely to throw Critical Failures, and your characters who are highly skilled experts are more likely to throw Critical Successes.
Also note that the same is true for the difficulty of the task. On tasks of easier difficulty, it will be easier to avoid Critical Failures and easier to obtain Critical Successes. On more difficult tasks, it is harder to avoid Critical Failures and harder to achieve Critical Successes.
With the UGM, Critical Success and Critical Failure is not a blanket random chance equal among all character no matter their experience, natural ability, or the difficulty of the task being attempted. The UGM takes all these factors into account before a Critical Success or Critical Failure is indicated.