Are the new Daily quests in Heroes of the Storm the same for all players?
Assuming that there 3 empty places for quests, will all players get the same 3 quests for 3 days?
Daily quests are not the same for everyone. The reason you might suspect this is the case is because there aren't many possible quests to get.
List of possible daily quests:
If the reason you are asking this is because you seem to get a lot of supports in your team on a day when you got a quest 'play as a support' you should also know that matchmaking system has some rules in group creation.
For further information, check the official site here.