[Cobra]

This is known as the Monty Hall trick. You should switch cards all the time. During your first pick you lost 2/3 the time and won 1/3. After the dealer removes the other card you are left with the following. If you don't switch you will win 1/3 time and lose 2/3.(The same as before). If you switch you will win 2/3 the time and lose 1/3. Obviously this is over many hands.