I know absolutely ZERO about such coding, and am going to sound pathetically ignorant here ("Not for the last time!"). However, am I right in thinking that your mini program runs the odds many times - a millon? - and reports the % of Successes, and so your numbers might fractionally change if they were run again? Assuming that is broadly what it means, then it is an interesting set of numbers and with the numbers used, your conclusions seem valid. Well done & Thanks.
Implication: So, if each PC gets one relevant Council related skill up to level 4, such events should be easy to do almost every time (80 to 90% or so).
Q. I presume that if you had one or two elves in the mix you can always throw in a couple of magical successes if it looks like things are going to go awry?
Yes, it is a simulation so it is not exact. I don't think it should be off by more than a few tenths of a percent however (if the code is correct).
You are also correct in that it does not take into consideration ways to improve your situation:
1) favored, hope, inspirations -- note hope and inspiration hope can be huge in this case because of the potential for extra successes
2) for councils, successful introductions can easily add 1-2 additional rolls (more for higher die pools)
3) other virtues and such
4) in councils -- whether the audience is reluctant, open, and friendly -- getting an extra die on EACH roll or losing a die on each roll can be huge. This is a chance at a little strategy -- appealing to the right people, if different people in a group have different attitudes
This seems to make the lower percentage for say 3S at TN16 seem not too bad, since the party can swing things in their favor by a good introduction and hope use. I do worry at the higher end 4S+ that they might be way too easy. Not sure about the 2S end -- you have to spend hope on every roll I think to get to decent numbers. Hard to fully make conclusions without a full set of tables which I don't think I'm proficient to do.
Here's some odds for success with 3S TN16 and a good introduction roll:
For 3S and TN16 I get a chance of success of (>= the resistance), with tries = resistance (failure on introduction -- happens 46% of the time)
3 resistance = 52.3%
6 resistance = 47.7%
9 resistance = 44.6%
For 3S and TN16 with +1 to length (so 3 succeses in 4 tries, 6 successes in 7 tries, etc.) - happens 24% of the time
3 resistance = 69.9%
6 resistance = 61.5%
9 resistance = 56.4%
For 3S and TN16 with +2 to length -- happens 23% of the time
3 resistance = 81.8%
6 resistance = 72.9%
9 resistance = 66.9%