Third ingredient is really just for experimenting, or when you are trying to make a potion with multiple effects.
I can't remember exact effects of reagents, so here's a few entirely made up examples.
Reagent 1: Fortify Health, Restore Health, Regenerate Health, Damage Stamina
Reagent 2: Restore Health, Resist Cold, Invisibility, Resist Disease
Reagent 3: Resist Cold, Resist Fire, Resist Shock, Resist Poison
Example 1:
Mixing Reagent 1 and 2 will give you a potion of Restore Health
Mixing Reagent 2 and 3 will give you a potion of Resist Cold
Mixing Reagent 1 and 3 will fail
Mixing Reagent 1, 2 and 3 will give a potion of Restore Health AND Resist Cold
Example 2:
You don't know the effects of the above ingredients.
Mixing Reagent 1 and 2 will reveal that both have Restore Health
Mixing Reagent 2 and 3 will reveal that both have Resist Cold
Mixing Reagent 1 and 3 will fail
Mixing Reagent 1, 2 and 3 will reveal that 1 and 2 have Restore Health, and 2 and 3 have Resist Cold.
Pro of making a potion with multiple effects:
-Uses 3 ingredients to get 2 effects instead of 4 ingredients.
Con of making a potion with multiple effects:
-Have to get both effects at once, so if you don't want resist cold, and only want to restore health tough cause they're combined.