I have no idea what point you're trying to make. I am aware the selection process is different. If you understand the argument now but you're just splitting hairs about whether it's similar to Monty Hall, fine let's agree to disagree. If you don't understand the argument and are trying to use the dissimilarity to Monty Hall as a counterargument then I don't think I can help you any further.

This is not coherent as written:

  If I flip a dime and a quarter, and tell you that one of them is heads, do you have increased chance of knowing if either particular one is heads? This is more liar's dice than it is monty hall.