and so far none of them have made sense to me.
It is a counter-intuitive probability theory argument, like the Monty Haul question. i have found that when I look carefully at that sort of problem after awhile it makes sense. So for example with Monty Haul, you start out with a 1/3 chance for each of 3 choices. You choose one of them. Monty is obligated to show you one of the other choices that fails. There's always at least one of them that fails so he can do that. When he does, it doesn't improve the chance that your choice is correct. So the remaining choice is 2/3 likely to be correct. If Monty chose one of the other possibilities at random and if it was the correct one then he just told you so, then you'd do just as well by choosing either of the remaining choices, unless you had already lost.
I haven't seen any description of this problem that actually describes the probability argument coherently. I could go to old questions and ask in comments for a real answer. Or I could answer an old question, saying that I didn't actually have an answer but none of the existing answers did what I wanted either. It looks to me like a new question is appropriate, unless an existing question that I have overlooked inspired a good answer.
Here is how the problem looks to me. A good answer does not depend on reading how I misunderstood it, maybe you can make a good explanation without needing to understand why I didn't understand others.
QM predicts probability distributions of outcomes, given probability distributions of inputs. When there's no known way to measure inputs as more than probability distributions, this is the best we can do.
Some people want to think that there might be deterministic equations that describe what really happens on a subatomic level, but we can't yet collect the data that would reveal them. Others want to think that it's all just probabilities and there's nothing else but probabilities. At first sight with no way to measure anything else, we can't tell whether there IS anything else -- and it doesn't much matter until we can measure it.
However, Bell's Theorem and various similar things say that deterministic models must fail if they accept "locality". The central concept appears to go like this:
Suppose there are two particles a and b that are separated by some distance. They can't immediately affect each other, not until light can get from one to the other. Any attempt at explaining their behavior will have a limit on how much correlation there can be between them. But QM shows that in some particular circumstances their behavior has MORE correlation than any reasonable explanation can possibly allow. Therefore there can be no explanation. All we can do is apply QM to get correct probability distributions.
What I'm looking for is a descriptive probability story. Perhaps with game show contestants locked into their soundproof boxes where they can't communicate with each other. What is it that happens that can't fit a reasonable story, that's analogous to the events that QM describes that similarly can't fit a reasonable story.