Ongoing World Events are only discarded once no players are affected by the event.
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Does a new World Event card replace the current one?
If the current World Event does not say it is ongoing, then yes, it gets replaced. If it is ongoing, then it would not get replaced. There can be multiple ongoing World Event cards in play at the same time.
Do I have to use a specific world event card even if it seems broken / overpowered / too harsh?
While the World Event cards are designed to add a bit of chaos to the game to force the players to think outside the box, Quodd Heroes is designed to be modular. Feel free to take out certain cards or even remove the entire deck if that’s the way your group would enjoy playing the game!