What type of mental games could I play with my border collie?

10-15 min of obedience training per night

hide the treat

make a maze of furniture to see if he can figure out how to get around it.

Just teach him as many tricks and commands as you can- I've heard of a few pet collies who knew a couple of hundred tricks. Try making up more complicated ones, like asking the dog to get a bottle of water from the fridge and close it after him, or giving more than one command in sequence (eg go up the stairs and sit). You could think of stuff that would be useful to you, as they generally like being useful, and you could teach him to fetch different named objects (eg fetch a pen, fetch a tissue).

Jobs like Agility and Obedience are great. You work as a team and get a workout, especially Agility. You can teach him to identify his toys and training, which is what I'm doing right now with my dog.

Hide treats/toys and teach a "Find it" command.

Get a book on tricks, and teach a new one every week.

Go for walks, but practice sit/down/stays, with increasing diversions, etc.

Basically, don;t get stuck in a routine with your dog!

Agility training. You can create your own. There are websites everywhere for this. You have the perfect dog for it.

hide and seek is fun to teach your dog. It makes him use him nose to find your scent and other kinds of scents