The probability data posted on this site has two sources. The first is the anydice website, where formulas can be created to calculate odds. The second is a c# program I wrote in order to run simulations on the more difficult probabilities found on this site
I tested the c# random function by simulating a d6 and rolling it 1 billion times:
| Dice Result | Result Count | Frequency |
|---|---|---|
| 1 | 166,665,894 | 16.6665894% |
| 2 | 166,653,084 | 16.6653084% |
| 3 | 166,659,559 | 16.6659559% |
| 4 | 166,663,262 | 16.6663262% |
| 5 | 166,693,578 | 16.6693578% |
| 6 | 166,664,623 | 16.6664623% |
For each entry in a table simulated with a c# program, I ran 100 million simulated rolls.
Calculated using anydice.com
Calculated using c#