So it really depends on if Carmine views Bob as a bigger threat than Bill, which he might. If he does, there is a world where it makes sense for Bill to keep Bob even though it reduces his chance of winning FIC. However, I'm speaking as someone with little confidence in my own challenge ability so that shapes my perspective. Bill's odds of winning FIC outright are probably good enough for it to be the right move just to cut Bob. I think cutting Bob is probably the right call.
The point you raise about Carmine is interesting, because maybe this is a hot take, but I do think there is a chance Carmine beats Bob at FTC but much less chance he beats Bill. Bob is exactly the kind of finalist I could see a Jury not wanting to reward. With that said, I do think Bob probably wins, but the Jury might be kind of looking for reasons not to give him the win if that makes sense.
However, clearly Carmine's best path is to go with Crystal, and that's as close as he can get to a 50-50 chance of winning if he can make it happen. So he needs to decide if either he or Crystal pulling off a fluke challenge win next round is so unlikely that it's worth risking it with Bob or if he'd rather take whatever their combined odds of winning the final challenge are.
