Skyrim

The costliest effect in the bottle is in charge. It names the result, and if it is a harmful one the mortar hands you a poison no matter what else is in there. Each card outlines the effect responsible.

cost = floor( baseCost × max(magnitude^1.1, 1) × (duration/10)^1.1 )

Aloe Vera Leaves and Butterfly Wing share Restore Health and Damage Magicka; Damage Magicka costs 7.37 against 2.94, so that is a poison with a Restore Health passenger. It runs the other way too — Abecean Longfin with Small Antlers carries Weakness to Poison and is still a potion, because Fortify Restoration is worth more than twice as much.

Your alchemy is deliberately not in that formula, and that is exact rather than a shortcut. Skill, gear and Fortify Alchemy all put the same M^1.1 in front of every effect’s cost, and a common factor cannot change which one is largest. Perks are out for a better reason: the game leaves them out too, which is what stops Benefactor from silently converting a poison into a potion.

Resist Magic, Weakness to Poison and Weakness to Magic all cost exactly 7.1774. Nothing documents what the game does with a tie, so the 65 mixtures where one decides the bottle read Potion or poison rather than a guess.

mag = BaseMag × 4 × (1 + Skill/200) × (1 + Gear/100)
            × (1 + Alchemist/100) × (1 + Benefactor/100) × (1 + Seeker/100)

mag       = floor( BaseMag × skillMult × (1 + Enchanter) × (1 + categoryPerk) × (1 + Sorcery) )
skillMult = 1 + x(x − 0.14) / 3.4
x         = Skill × (1 + potion/100) / 100

The loop. A Fortify Restoration potion boosts every Fortify <Skill> enchantment you are wearing while it runs, because those enchantments are internally school-of-Restoration. Not the ones in your pack, and it does not matter which pieces or in what order you put them on — if it is on your body it reads base × (1 + the live boost). And because you never wait for the potion to expire, one is always live, which is what makes it compound: the potion you drink is scaled by the one already running.

brewed = round( 0.6 × (1 + wear × 25% × (1 + x)) )
takes  = brewed > the last potion’s own magnitude
piece  = 25% × (1 + x)
x      = brewed × (1 + x)          only if it takes

So a round offers exactly one choice: how many pieces you have on while you brew. With growth this violent, that brake is the only reason landing on an exact number is possible at all.

Whether a round takes at all is bottle against bottle. Two potions of the same effect do not stack, and the new one only supersedes the old if its own magnitude beats the old one’s — not the boost you are walking around with. Which means brewing with nothing on always makes the same bare 60% potion, so it can only ever be the opening move.

Measured in game — four 25% pieces, plain ingredients, all four worn every round:

observed        modelled
  100% gear →     120%        120.0%
  220% gear →     422%        422.4%
  522% gear →   1,948%      1,948.6%
2,049% gear →  26,405%     26,405.8%
cash out   →    3,991%      3,990.9% Fortify Enchanting
               9,831%       9,831%   placed

The enchanting step is the soft one. A second run cashed out at a measured 887% potion against a modelled 887.4, and placed 587% against a modelled 585.3.

The soul gem is the finest control there is. On apparel the gem scales the magnitude directly — the engine’s term is soulCharges / 3000, so a common soul places exactly a third of a grand one. Since the set of reachable numbers is discrete and lumpy, five gems give five overlapping copies of it, and that turns targets with no landing into comfortable ones:

target   grand soul only        best gem
  200%   no landing             200.70   0.30 inside   Greater
  300%   no landing             300.55   0.45 inside   Greater
  400%   400.82, 0.18 inside    400.40   0.40 inside   Petty
  600%   no landing             600.42   0.42 inside   Petty
 1000%   no landing            1000.48   0.48 inside   Common
 1500%   no landing            1500.52   0.48 inside   Lesser

It applies to the final enchantment only — the Fortify Alchemy gear you wear is whatever you made it.

One thing this deliberately does not cover: waiting. Let the potion lapse between rounds and the boost stops compounding. The potions still climb, just geometrically rather than explosively — 120% → 192% → 235% → 261% → 277% → 286% → … converging on 300%, off gear that settles at 4 × 100%. Mind which number is which: what converges on a hard 36.6% is the enchantment you can place off that settled set, not the potion series. Waiting also brings back per-piece history, because a value written while a potion was up sticks after it expires. That is a different, slower routine.

Two ways this is wrong for you. If you run the Unofficial Patch none of it works: USSEP takes the Fortify effects out of the Restoration school and separately turns the enchanting potion into a flat multiplier. And the last digit of any enchantment is soft, for the reason in that formula’s legend. Everything upstream of the enchanting step is exact.

A flat +10% is a flat +10%. But the Fortify Enchanting potion scales your skill inside a quadratic, so it is worth a couple of points on a bare character and hundreds on a looped one. Anything that adds skill points rather than a percentage lands in that same privileged spot, which is why it matters whether Ahzidal’s Genius is +10% or +10 skill — and nobody seems to know.

The fair loop is most of it, and it is no glitch: brew the best Fortify Enchanting potion you can, place better Fortify Alchemy gear with it, and that gear brews a better potion. It converges, which is exactly what makes it fair. On five slots it does not — each pass makes better gear than the last, forever, still with no Restoration glitch involved.

Both Seeker boons compound, and Sorcery wins. Shadows is inside the loop, so it brews a better potion; Sorcery boosts every enchantment you place, including the Fortify Alchemy gear the loop is building, so it compounds too — and by more. You can only hold one, and the module enforces that.

One playthrough, every faction, and the character still has to hold together. Everything above is downstream of that.

Coherent beats optimal. A Nord who fights for the Empire and then kills the Emperor is not a build, it is a spreadsheet.

The ceiling is vanilla. No Restoration glitch anywhere in it — the two sections above show the working for the parts that look like they need one.

How the slider knows. Raising a skill from S to S+1 banks S+1 character XP; a level costs 75 + 25L; one perk comes with each. Nord starting skills are 15, plus the racial +5 on One-Handed, Block, Smithing, Light Armor and Speech. Only Speech and Lockpicking are counted as incidental drift, so the level it reports is a floor — every other skill you happen to raise, every trainer and every skill book only adds perks.

Two things it does not settle. Extra Effect costs two points rather than one, because Insightful only reaches it through Corpus Enchanter. And the boots in the base plan, the shield and the boots’ second slot under Extra Effect are genuinely undecided — the doll draws them as empty sockets instead of guessing.