Mutagenic Ooze is a failure mode that can happen if there are essential ingredients for multiple potions (can also get either potion or Inert Glop or Magical Explosion if eligible).
There are 12 “magical” ingredients. An ingredient is magical iff it is a product of a magical creature (i.e.: Angel Feather, Beholder Eye, Demon Claw, Dragon Scale, Dragon Spleen, Dragon Tongue, Dragon’s Blood, Ectoplasm, Faerie Tears, Giant’s Toe, Troll Blood, Vampire Fang).
Inert Glop is a possible outcome if there are 2 or fewer magical ingredients, and is guaranteed for 1 or fewer.
Magical Explosion is a possible outcome if there are 4 or more magical ingredients, and is guaranteed if there are 5 or more.
(Barksin and necromantic power seem “harder” since their essential ingredients are both nonmagical, requiring more additional ingredients to get the magicness up.)
Therefore: success should be guaranteed if you select the 2 essential ingredients for the desired potion, plus enough other ingredients to have exactly 3 magical ingredients in total, while avoiding selecting both essential ingredients for any other potion. For the ingredients available:
To get “Necromantic Power Potion” (actual Barkskin):
Beech Bark + Oaken Twigs + Demon Claw + Giant’s Toe + either Troll Blood or Vampire Fang
To get “Barkskin Potion” (actual Necromantic Power):
Crushed Onyx + Ground Bone + Demon Claw + Giant’s Toe + either Troll Blood or Vampire Fang
To get Regeneration Potion:
Troll Blood + Vampire Fang + either Demon Claw or Giant’s Toe
I expect I’m late to the party here on the solution… (edit: yes, see abstractapplic’s very succinct, yet sufficient-to prove-knowledge comment, and Lorxus’s much, much more detailed one)
Quantitative hypothesis for how the result is calculated:
“Magical charge”: number of ingredients that are in the specific list in the parent comment. I’m copying the “magically charged” terminology from Lorxus.
“Eligible” for a potion: Having the specific pair of ingredients for the potion listed in the grandparent comment, or at the top of Lorxus’ comment.
Get Inert Glop or Magical Explosion with probability depending on the magical charge.
0-1 → 100% chance of Inert Glop
2 → 50% chance of Inert Glop
3 → neither, skip to next step
4 → 50% chance of Magical Explosion
5+ → 100% chance of Magical Explosion
If didn’t get either of those, get Mutagenic Ooze at 1⁄2 chance if eligible for two potions or 2⁄3 chance if eligible for 3 potions. (presumably would be n/(n+1) chance for higher n).
If didn’t get that either, randomly get one of the potions the ingredients are eligible for, if any.
If not eligible for any potions, get Acidic Slurry.
todo (will fill in below when I get results): figure out what’s up with ingredient selection.
edit after aphyer already posted the solution:
I didn’t write up what I had found before aphyer posted the result, but I did notice the following:
hard 3-8 range in total ingredients
pairs of ingredients within selections being biased towards pairs that make potions
ingredient selections with 3 magical ingredients being much more common than ones with 2 or 4, and in turn more common than ones with 0-1 or 5+
and, this is robust when restricting to particular ingredients regardless of whether they are magical or not, though obviously with some bias as to how common 2 and 4 are
the order of commonness of ingredients holding actual magicalness constant is relatively similar restricted to 2 and 4 magic ingredient selections, though obviously whether is actually magical is a big influence here
I checked the distributions of total times a selection was chosen for different possible selections of ingredients, specifically for: each combination of total number of nonmagical ingredients and 0, 1 or 2 magical ingredients
I didn’t get around to 3 and more magical ingredients, because I noticed that while for 0 and 1 magical ingredients the distributions looked Poisson-like (i.e. as would be expected if it were random, though in fact it wasn’t entirely random), it definitely wasn’t Poisson for the 2 ingredient case, and got sidetracked by trying to decompose into a Poisson distribution + extra distribution (and eventually by other “real life” stuff)
I did notice that this looked possibly like a randomish “explore” distribution which presumably worked the same as for the 0 and 1 ingredient case along with a non-random, or subset-restricted “exploit” distribution, though I didn’t really verify this
Followup and actual ingredients to use:
Mutagenic Ooze is a failure mode that can happen if there are essential ingredients for multiple potions (can also get either potion or Inert Glop or Magical Explosion if eligible).
There are 12 “magical” ingredients. An ingredient is magical iff it is a product of a magical creature (i.e.: Angel Feather, Beholder Eye, Demon Claw, Dragon Scale, Dragon Spleen, Dragon Tongue, Dragon’s Blood, Ectoplasm, Faerie Tears, Giant’s Toe, Troll Blood, Vampire Fang).
Inert Glop is a possible outcome if there are 2 or fewer magical ingredients, and is guaranteed for 1 or fewer.
Magical Explosion is a possible outcome if there are 4 or more magical ingredients, and is guaranteed if there are 5 or more.
(Barksin and necromantic power seem “harder” since their essential ingredients are both nonmagical, requiring more additional ingredients to get the magicness up.)
Therefore: success should be guaranteed if you select the 2 essential ingredients for the desired potion, plus enough other ingredients to have exactly 3 magical ingredients in total, while avoiding selecting both essential ingredients for any other potion. For the ingredients available:
To get “Necromantic Power Potion” (actual Barkskin):
Beech Bark + Oaken Twigs + Demon Claw + Giant’s Toe + either Troll Blood or Vampire Fang
To get “Barkskin Potion” (actual Necromantic Power):
Crushed Onyx + Ground Bone + Demon Claw + Giant’s Toe + either Troll Blood or Vampire Fang
To get Regeneration Potion:
Troll Blood + Vampire Fang + either Demon Claw or Giant’s Toe
I expect I’m late to the party here on the solution… (edit: yes, see abstractapplic’s very succinct, yet sufficient-to prove-knowledge comment, and Lorxus’s much, much more detailed one)
Post-solution extra details:
Quantitative hypothesis for how the result is calculated:
“Magical charge”: number of ingredients that are in the specific list in the parent comment. I’m copying the “magically charged” terminology from Lorxus.
“Eligible” for a potion: Having the specific pair of ingredients for the potion listed in the grandparent comment, or at the top of Lorxus’ comment.
Get Inert Glop or Magical Explosion with probability depending on the magical charge.
0-1 → 100% chance of Inert Glop
2 → 50% chance of Inert Glop
3 → neither, skip to next step
4 → 50% chance of Magical Explosion
5+ → 100% chance of Magical Explosion
If didn’t get either of those, get Mutagenic Ooze at 1⁄2 chance if eligible for two potions or 2⁄3 chance if eligible for 3 potions. (presumably would be n/(n+1) chance for higher n).
If didn’t get that either, randomly get one of the potions the ingredients are eligible for, if any.
If not eligible for any potions, get Acidic Slurry.
todo (will fill in below when I get results): figure out what’s up with ingredient selection.
edit after aphyer already posted the solution:
I didn’t write up what I had found before aphyer posted the result, but I did notice the following:
hard 3-8 range in total ingredients
pairs of ingredients within selections being biased towards pairs that make potions
ingredient selections with 3 magical ingredients being much more common than ones with 2 or 4, and in turn more common than ones with 0-1 or 5+
and, this is robust when restricting to particular ingredients regardless of whether they are magical or not, though obviously with some bias as to how common 2 and 4 are
the order of commonness of ingredients holding actual magicalness constant is relatively similar restricted to 2 and 4 magic ingredient selections, though obviously whether is actually magical is a big influence here
I checked the distributions of total times a selection was chosen for different possible selections of ingredients, specifically for: each combination of total number of nonmagical ingredients and 0, 1 or 2 magical ingredients
I didn’t get around to 3 and more magical ingredients, because I noticed that while for 0 and 1 magical ingredients the distributions looked Poisson-like (i.e. as would be expected if it were random, though in fact it wasn’t entirely random), it definitely wasn’t Poisson for the 2 ingredient case, and got sidetracked by trying to decompose into a Poisson distribution + extra distribution (and eventually by other “real life” stuff)
I did notice that this looked possibly like a randomish “explore” distribution which presumably worked the same as for the 0 and 1 ingredient case along with a non-random, or subset-restricted “exploit” distribution, though I didn’t really verify this