Entertaining Myself While Watching Television

For the past two nights I've been watching Deal or No Deal. NBC's description of the show is so useless that I am forced to refer to Wikipedia.

I feel like I want to take notes during the show. Early in the game the bank's offer is substantially lower than the expected value, but later on it rises to be pretty close to expected value. I'm wondering at what point people will choose the deal over the case and also at what point would it become most advantageous to choose the deal over the case. What's nice about it is that after the person chooses, they quickly play out the rest of the game to answer "what if...." Which means more data. I'm pretty much convinced that this is not closely related to the Monty Hall problem, but since probability is so tricky, I'm unwilling to commit until I've thought it out carefully.

And then there's the issue of which dollar amount is in each case. It's unlikely that they use space noise or weather data to create a truly random permutation; instead someone is probably picking a permutation that looks like what we'd expect random to look like. Predicting high-probability locations of high and low dollar amounts might give the player an edge in the late-round deals.