The standard formulation of Newcomb's problem has always bothered me, because it seemed like a weird hypothetical designed to make people give the wrong answer. When I first saw it, my immediate response was that I would two-box, because really, I just don't believe in this "perfect predictor" Omega. And while it may be true that Newcomblike problems are the norm, most real situations are not so clear cut. It can be quite hard to demonstrate why causal decision theory is inadequate, let alone build up an intuition about it. In fact, the closest I've seen to a real-world example that made intuitive sense is Narrative Breadcrumbs vs Grizzly Bear, which still requires a fair amount of suspension of disbelief.
So, here I'd like to propose a thought experiment that would (more or less*) also work as an actual experiment.
A psychologist contacts you and asks you to sign up for an experiment in exchange for a payment. You agree to participate and sign all the forms. The psychologist tells you: "I am going to administer a polygraph (lie detector) test in which I ask whether you are going to sit in our waiting room for ten minutes after we finish the experiment. I won't tell you whether you passed, but I will give you some money in a sealed envelope, which you may open once you leave the building. If you say yes, and you pass the test, it will be $200. If you say no, or you fail the test, it will be $10. Then we are done, and you may either sit in the waiting room or leave. Please feel no obligation to stay, as the results are equally useful to us either way. The polygraph test is not perfect, but has so far been 90% accurate in predicting whether people stay or leave; 90% of the people who stay for ten minutes get $200, and 90% of those who leave immediately get $10."
You say you'll stay. You get your envelope. Do you leave the building right away, or sit in the waiting room first?
Does the answer change if you are allowed to open the envelope before deciding?
*I don't know if polygraphs are accurate enough to make this test work in the real world or not.