How do I calculate probabilities for an RPG game?

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I want to create a probability calculator for an RPG. I am not a professional programmer and definitely not a mathematician ;) I just want to challenge myself.

How do I go about the logic? The roll I want to make the calculator for uses a number of D6 dice and D12 dice, and the sum of dice in a roll must exceed the "target number". For example, I might roll 3D6 + D12, and the total must be at least 15.

Do I need to write a function that:

  1. makes all the possible rolls for a combination of D12s and D6s
  2. counts how many of these achieved the required result
  3. divides the number of successful rolls by the number of all rolls, and the result converted to percentage is the probability?

If I want to treat a 12 on the D12 as an automatic success regardless of the other dice, where does that fit into this logic?

I know of anydice.com, but want to see if I can handle such a hobby project.