Whenever you attack, surveil X, where X is the number of opponents being attacked.
At the beginning of each end step, if three or more cards were put into your graveyard from anywhere other than the battlefield this turn, draw a card.
The value of X is determined only once, as Dimir Strandcatcher's second ability resolves. If a player leaves the game after the ability triggers but before it resolves, they won't be counted when the ability resolves.