For the first game of a match, a designated player – chosen at random by MTG ARENA during Swiss rounds, or the player ranked higher at the end of Swiss rounds during playoff matches – chooses either to play first or to play second.
After each game in a match, the loser of that game decides whether to play first in the next game. They may wait until after sideboarding to make the decision. If the previous game was a draw, the player who decided to play or draw at the beginning of the drawn game chooses.