Game Show Switching (Monty Hall Problem)

The Resident Jew and I always talk about how, if you don't switch your case on deal or no deal at the end of the game, you're the biggest sucker in the world.  This situation reverts back to the Monty Hall Problem.  Most of the time people believe lady luck is on their side and that they picked the winning case and in some 'cases' they did, but the odds are not in their favor.  At all.

Let me just give you a quick rundown of the situation.  You have a choice between 25 cases at the start of the game.  One of them has $1,000,000 in it, the others have lower quantities and the lowest case has $.01.  So right off the bat, you have a 4% chance of picking the case with the Million Dollars in it, and the field has a 96% chance of containing the million dollar case.
The object of the game is to pick cases that have low numbers in them so your case is worth a higher value.  There is a banker and offers being made throughout the game, but that doesn't matter right now.  What does matter is when you get down to decide between your case and the case left on the board, you always switch.  You exchange cases every damn time and twice on Sundays.  Why might you ask?
Because as you recall, your initial pick has a 4% chance of being the ideal case.  After removal of 23 cases there are 2 values left.  One is presumably higher valued than the other (For this example well pretend its $500,000).  So your case has a 4% chance of having the $500,000 value, and the field has a 96% chance.  Even though we have removed 23 other cases, your chance of picking the $500,000 case was still 4% when you chose.  Now the case that is still sitting in play has a 96% chance of being the higher valued case.  I really don't care what your gut is telling you.  It doesn't matter if 4 is your lucky number, if 4 is the number of boobs you touched or the amount of kids you want to have.  Switch your case, don't be a Neanderthal.  Be a rational human.

If you are confused, please watch this clip.  It is from the movie 21.  It will explain it all to you in two minutes.