When Archaeomancer’s Map enters, search your library for up to two basic Plains cards, reveal them, put them into your hand, then shuffle.
Whenever a land an opponent controls enters, if that player controls more lands than you, you may put a land card from your hand onto the battlefield.
The last ability triggers only if that opponent controls more lands than you after the land enters the battlefield. The ability will check again as it tries to resolve. If that opponent doesn't still control more lands than you at that time, the ability won't resolve.
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.