(Thank you all so much for your help on my last post! I appreciate the explanations, graphs and suggestions given. As I continue to experiment with my homebrew variant, I do a lot of probability graphs on paper and spreadsheets, but sometimes I need your professional opinions to get past a formulaic brick wall. This next elaborate scenario may be too much to ask of you kind folks... but I dare to dream...)
Would you please help me graph/formulate this dice mechanic? I want to compare the probabilities with those of the original rules.
I have altered the dice rules to use pools of d12s, then renumbered them F (risk of fumble), 1-10 (possible normal fails and successes), and R (reroll for "exploding" or "stacking" results; i.e. scores of 11-20 and beyond).
Roll a handful of about 5 dice (varies by character ability) and try to score multiple successes against a target number (average of 7, but varies). Scoring at least one success is an accomplishment, character is successful, his turn is over. Rolling one die exceptionally high represents finesse in accomplishment (and related perks) but the turn is still over. Rolling multiple successful dice represents speed of execution, meaning a normal success and the character gets to go again. Etc.
Rolls of R are guaranteed to score 10 and above, pending a second roll (F is still a guaranteed 10, 1 becomes 11, 2 becomes 12, etc, R guarantees a score of 20 and above pending a third roll). Pools that include an R never fumble.
All pools with dice showing F (but no R) risk a fumble, but may be cancelled in the next step.
The remaining Rolls (of 1-10) meeting or exceeding the target number are counted as success, rolls less than the target number are a normal failure. You may remove an F from the pool by removing a normal success (they cancel each other out). If there are no dice remaining that score a success, but at least one F, then it is a fumble (with dire/hilarious results).
I've been using this as a way to further randomize the fumble results without increasing the risk of fumble with skilled characters (they have large dice pools), but some players say that I'm on the wrong track... am I?