The experiment seems flawed because they might think the experimenter knows the right choice and tries to lead them to the wrong answer. If you're only interested in studying regret, I wouldn't let the experimenter know the right cup.
It’s the exact same probability but with less extraneous factors that can confuse people. It also makes it plainly obvious that switching makes no difference to your likelihood, and takes away any interpretation of “why” people don’t switch in the first experiment: because it doesn’t make any difference so what’s the point?