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Over the past week I watched most of two episodes of the game show "Deal Or No Deal." Putting aside that the whole thing is silly and a monument to greed, the dynamics of the show are intriguing. It's more interesting as a statistics problem and study of human nature than it is as an actual game.
The real game of course is to get enough people to watch so that sponsors will buy enough advertising to keep the game profitable for the producers and the network. Beyond that it's a fairly simple give-away game. A number (26, I believe) of cash prize amounts ranging from pathetic to very hansom are randomly placed in an equal number of numbered briefcases (ie. assigned random numbers). A list of the prize amounts is placed on a glittery, glowy board so the prizes can be removed dramatically as the game takes them from play. The contestant picks one case containing an unknown prize amount to be set aside as the case belonging to the player. Then there is a 'cast off' period during which about 6 cases are picked by the contestant and the amounts in them revealed. At the end of this period the is a 'dramatic' phone call from a figure hidden in shadows (or so the audience is told) to tell the host what to offer the contestant. Basically the contestant chooses to accept the cash offer and go home or keep playing trying for a better offer, which may possibly lead to playing to the end and risking opening the case they originally chose to set aside and taking home the prize in it. As each offer is rejected there is another period of picking cases/prizes to eliminate followed by another offer. To make a long explanation shorter, if the contestant gets lucky and picks cases with low prizes to reveal, the chance that the case set aside contains a good prize increases, so the offers go up. If the contest is unlucky and picks cases with very high numbers inside, the odds go the other way and the offers go way down.
The game is both honest and rigged at the same time. In terms of statistics most of the 26 prizes are far below the mean prize value. So that to start with, the chances of picking an average prize in the case set aside are low, no better than 3 in ten. (As opposed to the mean prize amount, the median prizes available would be enough to cover the hotel bills of the contestants and friends, but not much more.) But, in terms of making the game exciting, it also works as the game progresses, because the odds on each selection of throwing out a low valued prize are higher than throwing out a high prize, because there are more of them to start with. I didn't sit and figure out the math for each offer but it seemed that they were always below, not at, the mean value of the remaining prizes, so if you knew the odds there was always a small incentive to play on. As it progresses, the game becomes a balance between the growing or shrinking odds of getting a bigger prize/offer and the greed of the player and her/his friends helping with suggestions about what to do. Much of the presentation of the game is about stalling to keep building tension. Obviously too, the faster the game goes the more money that gets given away compared to the commercials sold.
Since the game is a straight give-away, there surely is some skill in picking the contestants. The first offer given the contestants, though far below the mean prize value is a substantial amount of money, and statistically likely to be far more than the value in the case that was set aside. There is nothing to stop anyone from accepting the first offer and gloating all the way to the bank. No matter what is in the stupid case, it's all profit. Watching the game proceed it's easy enough for anyone with or without a background in statistics to see the offers generally trend upward, whether we notice it's because there are more low numbers to throw out of the game or not. But still, there is a point in the game when the offer becomes larger than all, but a very few remaining prize amounts. At this point anyone who knows a little about statistics like me, would probably bailout take the loot and gloat all the way to... Someone with a better knowledge of statistics could probably successfully squeeze much more out of the game than I'd settle for. But, who cares. It's a give-away, so free money. The trick I think is to pick players who like gambling, not ones who can puzzle out the statistics and take the show for whatever. Also there seems to be a consistent thread with the contestants I saw, that they all really needed a large amount of money, so that winning one of the smaller substantial prizes would not be nearly as attractive as it would be to those of us who'd just like to pay off the credit card bill or buy something cool. They need players who will take the amounts in play personally. People like me who'd see it all as free money would be bad. People who see the offer drop after some bad picks and get desperate to 'win' it back are better contestants, both in terms of how much they will cost the show on average and in terms of the entertainment they provide begging the gods of luck for each case opened to be a low amount.
I don't find 'Deal Or No Deal' particularly fun the watch as a game. It's a bunch of random numbers floating by punctuated by watching greedy people get richer or walk away with very little. There is some small joy as in playing solitaire, over comparing how I'd play compared to the contestants. But, even after as little as I saw, as a show based heavily on statistics, it does become predictable fairly quickly. Still as a study in human nature, I wouldn't mind watching bits and pieces of it while waiting for others better shows to start. I wouldn't say that about every show of that ilk.
The real game of course is to get enough people to watch so that sponsors will buy enough advertising to keep the game profitable for the producers and the network. Beyond that it's a fairly simple give-away game. A number (26, I believe) of cash prize amounts ranging from pathetic to very hansom are randomly placed in an equal number of numbered briefcases (ie. assigned random numbers). A list of the prize amounts is placed on a glittery, glowy board so the prizes can be removed dramatically as the game takes them from play. The contestant picks one case containing an unknown prize amount to be set aside as the case belonging to the player. Then there is a 'cast off' period during which about 6 cases are picked by the contestant and the amounts in them revealed. At the end of this period the is a 'dramatic' phone call from a figure hidden in shadows (or so the audience is told) to tell the host what to offer the contestant. Basically the contestant chooses to accept the cash offer and go home or keep playing trying for a better offer, which may possibly lead to playing to the end and risking opening the case they originally chose to set aside and taking home the prize in it. As each offer is rejected there is another period of picking cases/prizes to eliminate followed by another offer. To make a long explanation shorter, if the contestant gets lucky and picks cases with low prizes to reveal, the chance that the case set aside contains a good prize increases, so the offers go up. If the contest is unlucky and picks cases with very high numbers inside, the odds go the other way and the offers go way down.
The game is both honest and rigged at the same time. In terms of statistics most of the 26 prizes are far below the mean prize value. So that to start with, the chances of picking an average prize in the case set aside are low, no better than 3 in ten. (As opposed to the mean prize amount, the median prizes available would be enough to cover the hotel bills of the contestants and friends, but not much more.) But, in terms of making the game exciting, it also works as the game progresses, because the odds on each selection of throwing out a low valued prize are higher than throwing out a high prize, because there are more of them to start with. I didn't sit and figure out the math for each offer but it seemed that they were always below, not at, the mean value of the remaining prizes, so if you knew the odds there was always a small incentive to play on. As it progresses, the game becomes a balance between the growing or shrinking odds of getting a bigger prize/offer and the greed of the player and her/his friends helping with suggestions about what to do. Much of the presentation of the game is about stalling to keep building tension. Obviously too, the faster the game goes the more money that gets given away compared to the commercials sold.
Since the game is a straight give-away, there surely is some skill in picking the contestants. The first offer given the contestants, though far below the mean prize value is a substantial amount of money, and statistically likely to be far more than the value in the case that was set aside. There is nothing to stop anyone from accepting the first offer and gloating all the way to the bank. No matter what is in the stupid case, it's all profit. Watching the game proceed it's easy enough for anyone with or without a background in statistics to see the offers generally trend upward, whether we notice it's because there are more low numbers to throw out of the game or not. But still, there is a point in the game when the offer becomes larger than all, but a very few remaining prize amounts. At this point anyone who knows a little about statistics like me, would probably bailout take the loot and gloat all the way to... Someone with a better knowledge of statistics could probably successfully squeeze much more out of the game than I'd settle for. But, who cares. It's a give-away, so free money. The trick I think is to pick players who like gambling, not ones who can puzzle out the statistics and take the show for whatever. Also there seems to be a consistent thread with the contestants I saw, that they all really needed a large amount of money, so that winning one of the smaller substantial prizes would not be nearly as attractive as it would be to those of us who'd just like to pay off the credit card bill or buy something cool. They need players who will take the amounts in play personally. People like me who'd see it all as free money would be bad. People who see the offer drop after some bad picks and get desperate to 'win' it back are better contestants, both in terms of how much they will cost the show on average and in terms of the entertainment they provide begging the gods of luck for each case opened to be a low amount.
I don't find 'Deal Or No Deal' particularly fun the watch as a game. It's a bunch of random numbers floating by punctuated by watching greedy people get richer or walk away with very little. There is some small joy as in playing solitaire, over comparing how I'd play compared to the contestants. But, even after as little as I saw, as a show based heavily on statistics, it does become predictable fairly quickly. Still as a study in human nature, I wouldn't mind watching bits and pieces of it while waiting for others better shows to start. I wouldn't say that about every show of that ilk.
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