Perfectly Preserved Pie (Fallout 76)

Perfectly preserved pie is a consumable item in Fallout 76.

Characteristics
The pie's most significant difference from many other foodstuffs found throughout Appalachia is its preservative-filled nature when compared to most other pre-War foodstuffs.

Obtaining
The perfectly preserved pie can be obtained from any Port-A-Diner, with a small chance of dispensing. Obtaining the pie on any particular attempt is determined by the formula...
 * $$chance = \frac{ ( luck \times 4 ) + attempts} {20}$$
 * ...where...
 * chance: the percentage chance of obtaining the pie
 * luck: the Vault Dweller's Luck
 * attempts: the number of previous attempts made to obtain the pie

...thus, even with a Luck of 10, there is still only a 2% chance of obtaining the pie on the first attempt.

By cumulative probabilities, a player character with Luck 5 has a 50% chance of obtaining the pie within the first 36 attempts. Luck 10 reduces that to 26 attempts, while Luck 1 doesn't reach those odds until 49 attempts. Depending on the player character's Luck, it takes between 75 and 105 attempts to reach a 95% chance of getting the pie, and 109 to 140 attempts to reach a 99.5% chance of getting the pie.