To Mrrzy's problem:

One third of the time you have originally picked the desired prize. If you switch, you lose.

One third of the time you have originally picked Ass A. The MC, who knows what's behind each door, will show you the other ass. If you switch to the other door, you win.

One third of the time you have originally picked Ass B. Again, if you switch, you win.

Two thirds of the time you will improve your choice if you switch after being shown one of the asses.