> The question as stated does not permit such a choice by the host since if it were a choice, it had already been made. Whether the choice was already made by

> The question as stated does not permit such a choice by the host since if it were a choice, it had already been made. Whether the choice was already made by the host makes no difference, what matters is what information about the hidden state can be derived from that choice. Let's say the rules of the game are modified to sat that the host never offers a re-selection when you already have selected a door with a goat. Then if the host has offered you a re-selection you should definitely not take it because you already have the good prize. You know this because the re-selection offer provides information about what is behind the door you selected. In fact, any time your choice of door has amyy statistical effect on whether a re-selection is offered, then a re-selection offer (or lack) provides a small amount of information that modifies the expected value of choosing a new door. > This is like being presented with a nearly completed game of chess, asked if the loser can lose in 1 move and then arguing that the answer is more nuanced because there might have been other moves taken that produced a different end games It is absolutely nothing like that. That is not a question about statistics or probability.