Perfectly Preserved Pie (Fallout 4)

The perfectly preserved pie is a consumable item in Fallout 4.

Characteristics
The pie's most significant difference from many other foodstuffs found throughout the wasteland is its preservative-filled nature, lacking any radiation 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 Sole Survivor's Luck, even if the Port-A-Diner is operated by a companion
 * 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 Sole Survivor 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. Another factor adding to the time is the ammount of time it takes to grab and dispense a pie. It takes 19-20 seconds for the machine to reset and be able to be interacted with.

Depending on the Sole Survivor'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. In any case, it should not take anywhere near 2000 attempts.

Perfectly preserved pie locations

 * One can be found in a wall mounted Eat-o-tronic in the Mechanist's lair.
 * Two slices of pie can be found on the counter in Cappy's Cafe, not contained within a Port-A-Diner.
 * One can be found above the entrance to Fizztop Mountain, only accessible by dropping from a beam above.