PartyGames is a game mode which is made of 6 randomly selected minigames. So every round is unique.
In PartyGames, the player who has collected the most stars after completing the 6 minigames wins. The better your placement in each mini game, the more stars you'll get. All stars obtained by the placing are added together. Note that as PartyGames goes on, more and more stars are awarded. So you still have a chance to win the PartyGames even though you didn't do so well in the first rounds.