This is hardly a gripping concept: N rounds of random numbers, then N bribes to give up. Those bribes are related, of course, to the briefcases that haven't been opened: the possible values that the contestant could walk away with from just taking the briefcase. The banker, of course, almost never offers a fair shake, and why would he? It's to the station's advantage to only give offers below the mathematical average. But it can be to the contestant's advantage to take it, because the station and the contestant are playing very different games. From a statistician's point of view, this actually can be interesting, but most people are not statisticians. The contestant is playing the game one-trial; the Banker is playing the game many times. The Banker can wait for the Law of Averages. The contestant only gets one chance, and is best served by taking an offer above the median, even if it's below the mean.
Deal or No Deal is, however, extremely entertaining television.
The show can be interesting for someone majoring in Psychology, or for that matter just trying to learn about humans (like a lot of the nonhuman sort reading this journal), to watch poorly-planned risk-taking behavior under social pressure; people will make big mistakes when people with no particular vested interest in any particular outcome of the game encourage them to. And it can be amusing to watch how people will be happy with what they get even once they're totally screwed: when a game came down to $1 vs. $5, two of the three lowest values in the game, the woman who decided not to accept the bank's high-stakes offer of $2 was absolutely thrilled when she turned out to be holding the $5. (Enjoy your sandwich, ma'am.) If she had taken the offer one turn before, she would have left the game with $80,000. (Then she opened the 300K and that was that.) She was happy about winning less than one tenth of one percent of what she could have had if she quit the game one turn earlier. And to be honest, I think that's a good thing: there's nothing to be gained by her regretting it and being upset, since she can't play again.
It is not the psychoanalysis aspect that interests most people, however. It is probably due to the fact that there is something inherently interesting about the idea of people being offered "push this button to get a life-changing sum of money" several times in one hour, and then not do it. Consider the idea: someone who makes under $14,000 a year was offered $180,000 for pressing a button and did not do it. (Note that this turned out to be a good call; he left the game when offered $202,000.) Furthermore, his wife, his campaign manager (he is the mayor of Brunswick, Georgia), and his constituents were all rooting for him not to press the button. There was a lot of pro-button support for the $200K, but his campaign manager was telling him "no"- despite him having only one very large value left on the board, with a maximum of $50,000 left if he opened the $500,000 and the possibility of only $300 if he did not quit. Those were the only three values on the board. I don't know about you, but if I was mayor of a city and my campaign manager told me to take a 1 in 3 chance of losing $202,000 for a shot at twice that, I would be looking for a new campaign manager. This was also interesting because it was the first time on Deal or No Deal- in the USA, that is, as it's popular in many countries and this is just the most recent one- in which the Banker actually offered a sum greater than the mathematical average of the amounts left on the board. (Board total was $550,300; the board would have to be $606,000 for the Bank to not expect to lose money on the offer.)
I don't beleive that either of those factors alone, however, are enough to make the show worth watching. It is the antics of the host of the show, Howie Mandell, who actually makes it entertaining.
Consider the situation. This is only the second game show I've seen where switching hosts would destroy the show. (The first is, of course, Win Ben Stein's Money, and it should be immediately obvious why nobody except Ben Stein can reasonably be expected to host it.) The show is, in my opinion, worth spending the time watching, because and primarily because the host is entertaining. It's the host who made this really intrinsically boring idea and made it a lot of fun to watch: his diving catch for the briefcase when the contestant knocked it off the platform, his recovery when the contestant's excited jumping and hooting knocked the telephone off the table and revealed it for the cheaply-made prop it was with the faceplate off and the battery out ("We'll get a telephone repairman, you watch these commercials"), and his willingness to do whatever frequently-inane luck ritual the contestant suggests. It's not all Howie- a lot of it is what the show gives him to work with. The producers don't mind giving out large sums of money if they don't have to do it very often, and a very effective way of doing that is to stretch out the show- which has included Howie running up the stairs to argue with the Banker after a particularly lousy offer for one of the more amusing breaks from the protocol of the show.
There's a lot more to the performance than that, but it's difficult to describe- it's worth spending the hour to watch it at least once. The show is, in and of itself, entirely inane (although probably not as inane as America's Funniest Home
But the actual conclusion to draw from this is what marketers have known for a very long time: good presentation can make even a really lousy idea really interesting.