As we will see this will ensure that the contestant will win 1 out of 3 times.
Now, there are three possible games:
The Host then opens one of the other doors (which doesn't matter):
Since The Contestant does not switch doors when given the choice:
The Host then opens Door #3.
Since The Contestant does not switch doors when given the choice:
The Host then opens Door #2.
Since The Contestant does not switch doors when given the choice:
That is, in this case --if The Contestant does not change doors-- the chance of winning is 1/3.
As we will see this time, the contestant will win 2 out of 3 times.
As before, in this case there are three possible games:
The Host then opens one of the other doors (which doesn't matter):
The Contestant now switches to the remaining unopened door:
The resulting situation is:
The Host then opens Door #3.
The Contestant now switches to the remaining unopened door:
The resulting situation is:
The Host then opens Door #2.
The Contestant now switches to the remaining unopened door:
The resulting situation is:
That is, in this case --if the Contestant does change doors-- the chance of winning is 2/3.
This, then, is the final answer.
A Contestant who does not switch doors (i.e. who keeps the originally chosen door) has only a 1/3 chance of winning.
A Contestant who switches doors, however, has a 2/3 chance of winning.
In short, although it may contradict "common sense", The Contestant will double their chance of winning by switching doors.