Exploration of D&D Potion Brewing Rules and Strategy

Welcome to The Nonlinear Library, where we use Text-to-Speech software to convert the best writing from the Rationalist and EA communities into audio. This is: D&D.Sci Alchemy: Archmage Anachronos and the Supply Chain Issues Evaluation & Ruleset, published by aphyer on June 18, 2024 on LessWrong.
This is a follow-up to last week's D&D.Sci scenario: if you intend to play that, and haven't done so yet, you should do so now before spoiling yourself.
There is a web interactive here you can use to test your answer, and generation code available here if you're interested, or you can read on for the ruleset and scores.
RULESET
There are two steps to brewing a potion:
STEP 1: MAGICAL POTENCY
Any ingredient that doesn't exist in the mundane world is Magical, while any ingredient that exists in the mundane world is not:
Magical
Not Magical
Angel Feather
Badger Skull
Beholder Eye
Beech Bark
Demon Claw
Crushed Diamond
Dragon Scale
Crushed Onyx
Dragon Spleen
Crushed Ruby
Dragon Tongue
Crushed Sapphire
Dragon's Blood
Eye of Newt
Ectoplasm
Ground Bone
Faerie Tears
Oaken Twigs
Giant's Toe
Powdered Silver
Troll Blood
Quicksilver
Vampire Fang
Redwood Sap
The first step of potion-brewing is to dissolve the magical potency out of the Magical Ingredients to empower your potion. This requires the right amount of Magical Ingredients: too few, and nothing magical will happen and you will produce Inert Glop, while too many and there will be an uncontrolled Magical Explosion.
If you include:
0-1 Magical Ingredients: 100% chance of Inert Glop.
2 Magical Ingredients: 50% chance of Inert Glop, 50% chance OK.
3 Magical Ingredients: 100% chance OK.
4 Magical Ingredients: 50% chance OK, 50% chance Magical Explosion.
5+ Magical Ingredients: 100% chance Magical Explosion.
If your potion got past this step OK, move on to:
STEP 2: DIRECTION
Some ingredients are used to direct the magical power into the desired resulting potion. Each potion has two required Key Ingredients, both of which must be included to make it:
Potion
Key Ingredient 1
Key Ingredient 2
Barkskin Potion*
Crushed Onyx
Ground Bone
Farsight Potion
Beholder Eye
Eye of Newt
Fire Breathing Potion
Dragon Spleen
Dragon's Blood
Fire Resist Potion
Crushed Ruby
Dragon Scale
Glibness Potion
Dragon Tongue
Powdered Silver
Growth Potion
Giant's Toe
Redwood Sap
Invisibility Potion
Crushed Diamond
Ectoplasm
Necromantic Power Potion*
Beech Bark
Oaken Twigs
Rage Potion
Badger Skull
Demon Claw
Regeneration Potion
Troll Blood
Vampire Fang
*Well. Sort of. See the Bonus Objective section below.
Some ingredients (Angel Feather, Crushed Sapphire, Faerie Tears and Quicksilver) aren't Key Ingredients for any potion in the dataset. Angel Feather and Faerie Tears are nevertheless useful - as magical ingredients that don't risk creating any clashing potion, they're good ways to add magical potential to a recipe. Crushed Sapphire and Quicksilver have no effect, including them is entirely wasteful.
If you've gotten through Step 1, the outcome depends on how many potions you've included both the Key Ingredients of:
0 potions: with nothing to direct it, the magical potential dissolves into an Acidic Slurry.
1 potion: you successfully produce that potion.
2 or more potions:
Sometimes (1/n of the time, where n is # of potions you included) a random one of the potions will dominate, and you will produce that one.
The rest of the time, the clashing directions will produce Mutagenic Ooze.
So, for example, if you brew a potion with:
Dragon Spleen, Dragon Scale, Dragon Tongue and Dragon's Blood:
You have included 4 magical ingredients, and the Key Ingredients of one potion (Fire Breathing).
50% of the time you will get a Magical Explosion, 50% of the time you will get a Fire Breathing Potion.
Badger Skull, Demon Claw, Giant's Toe, Redwood Sap.
You have included 2 magical ingredients, and the Key Ingredients of two potions (Rage and Growth).
50% of the time you will get Inert Glop, 25% of the time Mutagenic Ooze, 12.5% of the time G...