Before going to uni, Pointless was my favourite gameshow, but it’s a bit serious to be watching with your flatmates, especially if not everyone is too keen on gameshows. I find The Chase and Who Wants to be a Millionaire have the same problem – they focus too much on the questions rather than being funny. If you care about the game it's fun but if you don’t, it can be a bit boring.
The time and day these shows are shown is important as well because if your accommodation is like mine, we can only watch live TV, so anything on a Friday or Saturday night, like The Wheel with Michael McIntyre, wasn’t really an option as most of us had plans. Similarly, games that run across the week are also not a great option as it requires commitment from your group, this makes shows like Richard Osman’s House of Games not a great option either.
In my experience, the best game shows to watch with your flatmates, especially as you get to know each other, is something like 8 Out of 10 Cats Does Countdown. It’s funny but there are lots of different comedians so normally there's something for everyone to enjoy - you don’t need to know anything about the show to start watching it, everyone can play along with all the rounds and it’s easy to make up your own drinking games too (if you’re that way inclined)! You can also leave for a night out and talk all the way through as it tends not to be a game you get too invested in. There are a few games that fall into this category: Taskmaster, Total Wipeout (when it’s replayed), Would I lie to You, etc.
Of course this is just what I found with my flatmates last year and, to be honest, we started out by watching the Queens funeral as that was the day after we all moved in and everything was closed (I think whatever you watch is probably going to be better than that)! Good luck freshers, and anyone else moving in with people they’ve never met before, and happy quizzing!