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 extraordinary, sculpted, factory-made, preservative-riddled flawless beauty.

Locations

 * With the Automatron add-on installed, one can be found in a wall mounted Eat'o'tronic 3000 in the Mechanist's lair.
 * 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...
 * $$chance = \frac{ ( luck \times 2 ) + ( attempts \times 0.5 ) } {10}$$
 * ...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
 * ...so, even with a Luck of 10, there's still only a 2% chance of obtaining the pie on the first attempt. Regardless of Luck, a pie will always be dispensed after 2000 attempts.
 * Statistically speaking though, a pie should be dispensed in no more attempts than shown in the table below. Unless you've angered the RNG Gods.