One encounter per turn

The offense gets a single encounter on their turn, whether or not they win it and whether or not they make a successful deal. Fantasy Flight offers this in the core rulebook as a variant. The printed rule gives the offense a second encounter after a win or a deal, so a player on a run can take two while the table takes one; limiting it to one evens out how many turns each player actually gets across a game. Nothing else about the encounter changes.