The story
From the idea of dividing up a pie fairly: one person cuts and the other chooses a slice.
Etymology from Wiktionary, CC BY-SA 4.0.
pie rule
Today it means: A rule used in certain strategy games for the purpose of fairness, where immediately after the first player's initial move the opposing player may optionally switch, taking over the first player's role and position for the rest of the game. Full definition →