How many Battlefields does a tournament legal 2v2 deck need?

In a tournament-legal 2v2 (Magma Chamber) deck, each player must register exactly 3 battlefields, all with unique names (Rule 402.1, Rule 484.4.a). Additionally, partners cannot include the same battlefield name across both decks (patch notes clarification for 2v2). During setup, the three players who are not going first each randomly select one of their three battlefields to use; the first-turn player's battlefields are not used at all (Rule 484.5.a–b).