The role of probability in solving the Monty Hall problem

[Fidel_Castronaut]

Even though mathematically, my odds have changed, in reality, they have not. because it is a two-step process with new information.  If the two doors left were randomly swapped (or not), this would then give me a true 50/50 on the second choice, but as the doors have not swapped, the 50/50, though it may seem to be better odds, will not change what is behind the door I picked.  The 50/50 will only apply if I change my mind, but because it is a 50/50 chance, I only have one choice, so it is not really 50/50.  Basically, I have a 50/50 chance of being right after door #3 is opened, but I do not have a 50/50 choice.

You have a greater chance of being correct if you swap. This is a fact that cannot be argued against. Or to put it another way, if you stick with your door, 100% of the time you will lose more often than you win.