STATISTICS 301

I must admit, if Deal or No Deal is on, I watch it. Usually with my business partners because we work late and it usually comes on while we're still at the office. All of us have business backgrounds with plenty of experience with numbers (obviously, since we are bankers) and statistics. However, we cannot agree on the statistics with regard to this show. It's been over 10 years since I took a stats class, and honestly - I was pretty much hammered that whole semester so to hell if I can really remember any of it. Maybe one of you can help with our argument. In example:

Position #1: When the contestant is down to 6 cases, including his/her own and there are 6 amounts of money still on the board (including the highest amount, for the sake of argument we'll say is $1,000,000), the show puts up the stat that there is a 1 in 6 chance that the contestant's case holds $1,000,000. This is correct.

Position #2: Given the same scenario, the stat of 1 in 6 chance is NOT correct because the case was originally chosen when there were actually 25 cases/amounts on the board. The odds cannot transcend the variable of time. AND the chosen case/amount was determined at the time it was chosen so therefore statistically speaking the chances of that case containing the $1,000,000 prize are much lower than the possibility of one of the other cases containing it.

We are deadlocked on this issue. Any genuises out there want to help settle this?

Anyone?
Anyone?
Bueller?

UPDATE: For the record, my position was position #1. My esteemed colleague seems to be coming around to admitting that he completely overanalyzed the issue. He still hasn't fully admitted he was wrong, but I expect he never will. That's alright though.