It certainly goes against instinctive logic, but the table below shows it clearly ( assumes you picked door 1 )

( its doors not ashtrays, and a car for kruger rand, and goat booby prize )

Door 1 Door 2 Door 3 result if switching result if staying

Car Goat Goat Goat Car

Goat Car Goat Car Goat

Goat Goat Car Car Goat

So you win twice as often if you switch.

If your first guess was right, you will lose by switching.

Or, if your first guess is wrong, you will always win if you switch, and always lose if you don't ( see table )