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:

For each entry in a table simulated with a c# program, I ran 100 million simulated rolls.

Calculated with anydice.com

• Ability check against a difficulty
• Advantage on skill checks
• Rolling to hit
• Rolling initiative
• Making Skill checks
• Skill focus expected values
• Rolling a target value on a damage or healing roll
• Rolling ability scores

Calculated with c#

• Ability check against an opponent
• Rolling Aiki
• Rolling Psychometry
• Rolling Retrocognition
• Rolling Clairvoyance