So with 3dF you have a 3.7% chance of getting a 3, an 11.11% of getting a 2, a 22.22 of getting a 1 and a 62.96% chance of getting  0.

How do the odds change with 1 bonus die? 2 bonus die? 3 bonus die etc...

Are these tables available somewhere? I just don't have the mathematical/statistical chops to figure it out. (or i'm just really lazy and my google skills failed me).

It looks like crap, but here is the cut and paste from my own Excel spreadsheet, available on request.

Base Roll +1 Bonus +2 Bonus +3 Bonus -1 Penalty -2 Penalty -3 Penalty

3 4% 11% 21% 32% 1% 0% 0%
2 11% 22% 29% 31% 5% 2% 1%
1 22% 27% 27% 23% 12% 6% 3%
0 26% 21% 15% 10% 21% 15% 10%
-1 22% 12% 6% 3% 27% 27% 23%
-2 11% 5% 2% 1% 22% 29% 31%
-3 4% 1% 0% 0% 11% 21% 32%

Untrained
0 63% 40% 23% 14% 81% 91% 96%
1 22% 27% 27% 23% 12% 6% 3%
2 11% 22% 29% 31% 5% 2% 1%
3 4% 11% 21% 32% 1% 0% 0%
37% 60% 77% 86% 19% 9% 4%
Trained
0 37% 19% 9% 4% 60% 77% 86%
1 26% 21% 15% 10% 21% 15% 10%
2 22% 27% 27% 23% 12% 6% 3%
3 11% 22% 29% 31% 5% 2% 1%
4 4% 11% 21% 32% 1% 0% 0%
63% 81% 91% 96% 40% 23% 14%
Expert
0 15% 6% 2% 1% 33% 50% 63%
1 22% 12% 6% 3% 27% 27% 23%
2 26% 21% 15% 10% 21% 15% 10%
3 22% 27% 27% 23% 12% 6% 3%
4 11% 22% 29% 31% 5% 2% 1%
5 4% 11% 21% 32% 1% 0% 0%
85% 94% 98% 99% 67% 50% 37%
Master
0 4% 1% 0% 0% 11% 21% 32%
1 11% 5% 2% 1% 22% 29% 31%
2 22% 12% 6% 3% 27% 27% 23%
3 26% 21% 15% 10% 21% 15% 10%
4 22% 27% 27% 23% 12% 6% 3%
5 11% 22% 29% 31% 5% 2% 1%
6 4% 11% 21% 32% 1% 0% 0%
96% 99% 100% 100% 89% 79% 68%
Grand Master
1 4% 1% 0% 0% 11% 21% 32%
2 11% 5% 2% 1% 22% 29% 31%
3 22% 12% 6% 3% 27% 27% 23%
4 26% 21% 15% 10% 21% 15% 10%
5 22% 27% 27% 23% 12% 6% 3%
6 11% 22% 29% 31% 5% 2% 1%
7 4% 11% 21% 32% 1% 0% 0%
100% 100% 100% 100% 100% 100% 100%

The last line in each section above is the overall chance of greater than a zero result, btw.