> And the reason it matters is because people start spouting woo about how the host's knowledge or intentions are what mattered, when that isn't true at all. K

> And the reason it matters is because people start spouting woo about how the host's knowledge or intentions are what mattered, when that isn't true at all. Knowledge and intentions don't matter? They most certainly do. Imagine a third version of the problem (I'm afraid I don't have a good name for it) where the host actively tries to lure you away from the correct answer, and only opens an empty box if you've picked the correct box. Now, if you pick a box and the host opens an empty box, you should absolutely not switch, because the remaining box has 0% of being the right one. Knowledge and intentions matter. The real problem happens when you don't know what strategy the host is using.