Hey there!
So, he can be a little tricky on the first time, but I will tell you the secret. He'll always strikes on the third night. Which means you can tell Petra to watch a location twice (which will eliminate it from the pool for that attempt)
The first attempt he could be in 5 places, and you can eliminate 2 (by telling Petra to watch them each night), and then you have a one in 3 chance.
The second attempt, Petra eliminates one of them herself. You can eliminate 2 again, so you're now a 50/50 chance.
And if you're massively unlucky, during the final sequence Petra eliminates 2 of them herself as she gets to know your intruder. If you tell Petra to eliminate 2 locations, you know exactly where he's going (there's even a special variation when Petra straight up tells you she knows where he's going to be).
Cheers!