In an Archenemy game, these methods aren’t used to determine who takes the first turn. Rather, the archenemy takes the first turn.
April 17, 2020 · Ikoria
If a player wishes to reveal a card with a companion ability that they own from outside the game, they may do so after setting aside their sideboard. A player may reveal no more than one card this way, and may do so only if their deck fulfills the condition of that card’s companion ability. (See rule 702.138, “Companion.”)
April 27, 2018 · Dominaria
In a Commander game, each player puts their commander from their deck face up into the command zone before shuffling. See rule 903.6.
September 30, 2011 · Innistrad
In a Commander game, each player puts his or her commander from his or her deck face up into the command zone before shuffling. See rule 903.6.