Keep in mind we're talking about two different problems here. Monty Hall and Monty Fall (I hadn't heard of that name before, but let's stick to it). The differe

Keep in mind we're talking about two different problems here. Monty Hall and Monty Fall (I hadn't heard of that name before, but let's stick to it). The difference between these two problems is subtle and yet dramatic, because whether or not the host knows which box is empty and is therefore guaranteed to open an empty box, or doesn't know and is therefore lucky to open an empty box, makes the difference between whether the remaining box has a chance of 2/3 or 1/2. These are the valid answers to the two problems. It's not clear to me what you think I'm ignoring, but if you can make that clear, perhaps I can explain my meaning a bit better.