The Keymaster perk in Skyrim is mathematically useless

I recently reverse-engineered the formula behind the pickpocket success rate in Skyrim. One of the Pickpocket perks in the game is called "Keymaster", which makes pickpocketing keys "almost always works", and which which I described as "maybe the most worthless perk in the game". Now that we have the formula, we can prove that it's mathematically useless.