I've had plenty of open book exams where the prof knew you would fail if you grabbed the book for more than a second. It's pretty much the same as the exams where you get to write your own cheatsheet: if you need it too much you are screwed.
Cheat sheets have an extra bonus, they are a great way to trick students into studying without realizing it is studying. By giving them a limited size, the student has to consider all of what they know and decide which areas they are the weakest on that need to be included, which they then have to organize into a compact and quick to reference chart. It doesn't replace the more boring phases of studying, but it does create a one off that gets better engagement and is more personalized than a fillable study guide or example test.
I’ll say I’m a little mixed on this, depending on how tight your timings are. A benefit of open book, I think, is that you can ask some more offbeat questions confident that the students are able to lookup the details. The challenge comes in knowing that they fully grasp the theory so they know how to find the information if it’s not in their short term memory.
Maybe a simplified example might be a question that forces you to consider different data structures and choose the right one? A student may not have the experience to know off the top of their head but they have a reference they can skim to check. The trick would be setting it out such that a student that didn’t know the principles would completely miss this and not know what to look for. Like they would do nested loops instead of populating a hashmap, perhaps.
I remember this open book exam on graphs… one of the questions was “take this algorithm that’s in all books, invert the condition you’re optimizing for and write the new algorithm in pseudo code”. No I don’t remember which particular algorithm it was, it’s been a bit.
80% of my mates didn’t solve it. It was right there in any graph algo book.
It does not help you if you don’t understand the material. If the exam is done right at least.
The act of writing the cheat sheet is often enough to remember I find. It's yet another repetition of the material, just like doing labs and practice exams. And if you wrote the cheat sheet yourself, you also often know "where to look" for something specific, even if it's just to be sure you didn't remember something incorrectly and you really do only need to look at it for a few seconds.
So in my book (pun intended :P), allowing and actually encouraging a "cheat sheet" is a good thing. Open book is worse, as it's usually way too large and badly indexed. And who's gonna use an actual book in their actual job anyway?