I've done open-everything exams (just no collaboration) and my experience was that it didn't change the mean grade, but it did increase the standard deviation.

I've done open-everything exams (just no collaboration) and my experience was that it didn't change the mean grade, but it did increase the standard deviation. Students who were already mostly on top of the material could look things up and double-check their work, so their scores improved. Meanwhile, students who didn't really know what they needed to spent the whole time trying to find "the answer" in the book or online (and that's not the way programming tests work!), so in the end they either left the answer blank or put something totally nonsensical, copy-pasted off the internet. In a closed-book test, they would have at least tried to figure it out on their own, and maybe gotten a few partial-credit points.