The reason Step  needs explanation is because it needs explanation I gave the explanation You will notice that the explanation refers to our ignorance of the hosts door opening procedure Till then we had only made use of our ignorance of the cars location Till then we had only obtained a simple solution A chance of winning by switching given we chose door    Step  strengthens this to a conditional solution B chance of winning given we chose door  and the host opened door    Statements A and B are different They mean something different Dont you realise that