I happened to catch a new game show on TV last night called Deal or No Deal after seeing an incredibly long line of people queueing on the sidewalk for open auditions to be contestants on my way home from dinner. The show itself is incredibly boring, but the mechanics of the game are kind of interesting.
The game starts with 26 briefcases, each of which represents a dollar amount, running from one cent to one million dollars (or in the case of last night’s show, two million dollars). The game begins when the contestant picks one of the briefcases, which contains the amount of money they’re playing for. The contestant then chooses other briefcases to open, revealing amounts of money that they didn’t pick. Periodically the “banker” calls then and offers them money to stop playing, based on the amount of money still in play.
Once the person has picked their initial briefcase, they eliminate five or six other briefcases, then the first offer comes in. On last night’s show, contestants never eliminated the big dollar amounts in this first round, so with the person having a 1 in 20 chance (or maybe 1 in 19) of winning the big money, the bank offered something like $23,000 to buy them out. As they eliminated briefcases without revealing the top prize, the amount offered by the bank would go up. In one of the games, the person got to a point where there were four briefcases left and the two million dollar prize had not been revealed. They got a buyout offer of over $400,000, took it, and learned that their briefcase had $5 in it. Good choice.
What I haven’t figured out yet is whether the banker is trying to cheat people or whether the game is really just about tolerance of risk. In other words, are the offers fair given the amount of money left in play? If every offer is fair, then the only question is how much risk you’re willing to accept. Each time you open a briefcase, you chance removing a big amount of money from play and causing the banker to adjust your offer downward. On the other hand, removing a small amount will get you a higher offer. If some of the offers are unfair, then there’s math involved in determining whether or not to take the offer.
The game Web site doesn’t reveal how the offers are calculated, but the calculations I did in my head make it seem like the offers are fair, so the game is about a contestant’s willingness to gamble. (The odds are completely set, obviously.) I wonder how many of the players know that?