When's the cut off for events to reach their min player requirement? Also will Gen Con purge these or do we have to ask for them to be removed?

There is no deadline, and they don't purge them unless the EO asks to cancel the event.  People can show up at events with generics and fill the slots.

Or they can buy those unsold tickets at the show. 

It's only once everyone sits down at the table that minimum players becomes an issue. If you simply can't run your game with the number of people that have shown up, talk to your hall or hotel HQ and say that it can't be played, and they'll take care of the players who were at the table. 

Remember, even if your game sold out in the first hour of ticketing, players might not show up when the time comes. 

The expectation is that the event organizer will wait until the event is scheduled to start to determine if the minimum number of players has been met, both to accommodate any tickets that have been sold and to allow walk-up players a chance to participate.

There are exceptions, of course - usually when expensive materials need to be purchased in advance - but in general we encourage event organizers to do what they can to accommodate the players that show up in a way that will still satisfy them.

And no, there is never any automated purge. If an event needs to be canceled, the event organizer needs to explicitly request it.

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Derek Guder
Senior Event & Program Manager
Gen Con LLC