Chances of having a Good or a Bad Omen

• Base chance: 50% Good, 50% Bad
  + Add your High Priest's Loyalty / 2
  - Subtract your Impiety * 10
  
  
• Example (common scenario)
  HP Loyalty: 60, Impiety: 0
  50 + (60/2) - (0*10) = 80% Good, 20% Bad
  Then, there is a 5% chance of having the opposite result instead.

Strength of the Omen (If it is good, how good? If bad, how bad?)

• + Take your Ruler's Piety
  + Add your High Priest's Piety
  + Add a random number from 0 to 30
  * Multiply the result by your Religious Unity
  = The result is the Omen strength on a scale from 0 to 50.
  
  
• Example (common hellenistic scenario)
  Ruler Piety: 8, HP Piety: 12, Random: 15, Unity: 30%
  (8 + 12 + 15) * 0.3 = 10.5/50
  An Omen of somewhat weak strength.

Since the Office of High Priest is key in determining both the outcome and the strength of the Omen, his Vanilla ability (increasing Omen Power) has become useless. Therefore he's been given another ability, one that is already available to other forms of government, as to not deviate too much from Vanilla.

The other important factor is Religious Unity: the higher it is, the higher the stakes.

Free Innovations

Each level of Impiety gives 10% chance of having one Free Innovation during the year.
You can't have more than 1 Free Innovation per year using this method.