The intentions of the host pass you information that you can use to choose the correct door. The information is this: "There's a 2/3 chance I was forced to reve

The intentions of the host pass you information that you can use to choose the correct door. The information is this: "There's a 2/3 chance I was forced to reveal this door; ergo, there's a 2/3 chance the other door is the correct one." If the host is choosing randomly, no information is passed. With regards to your last paragraph, the odds of the host picking wrong are either 1/2 or 0 depending on the intentions of the host. I'm a tiny bit annoyed that you think you're pointing out a "flaw" in my logic when you missed something so simple, but whatever. If you don't like my explanation, direct your attention to the OP's link to Wikipedia, where there are many more variations and explanations that you might like.