What are some other gameshows one could nerd out about? I'll start:

An obvious one is the traitors, but I dunno if there's much you can do with this one as the contestants rarely gain much concrete information.

"Deal or no deal" / "let's make a deal" would have interesting game theory approaches - probably has a lot of parallels with Monty Hall?

Countdown (UK) - solving the maths puzzles on here using integer programming would be cool

"Let's Make a Deal" was hosted by Monty Hall and is literally the Monty Hall problem.