Right, it would be simpler to just say “I flip a coin and keep it in my hand, and you guess heads or tails, but before I open my hand I ask if you want to chang

Right, it would be simpler to just say “I flip a coin and keep it in my hand, and you guess heads or tails, but before I open my hand I ask if you want to change your answer.” 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?