Imagine you have a bag with 999 red rocks and one blue rock. your goal is to reach into the bag blindly and pick the blue rock. You reach into the bag and take out a rock but you arn't allowed to see what color it is. There is now 999 rocks in the bag and one in you hand. Someone take 998 rocks that arn't blue out of the bag so there is only one rock left in the bag. You can either pick the rock in the bag or the one in your hand. You always take the rock in the bag, 999/1000 times that rock with be the blue rock.

Here is why. When you pick a rock for the first time (when their are 999 red an 1 blue in the bag) your odd of picking the red rock are 999/1000. If you pick a red rock, there will be 998 red rocks and one blue rock left in the bag. So if they get rid of 998 rocks from the bag that arn't blue, it will only leave the blue rock. And when you which you will get the blue rock.

The only way you can lose by switching is the 1 out of 1000 times that you pick the blue rock out of the bag on the first time.

The monty hall problem is basically the game thing except there are 2 red rocks (bad doors) and 1 blue rock (good door). As long as their are more bad doors than good you should always switch.