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# Deal or No Deal Revisited

1 June 2008

Back in November of 2006 I wrote an article about Howie Mandell's show Deal or No Deal. In it I gave examples to show that the show's producers appear to give very low offers early on and then increase them as more and more cases are opened. Then in February 25th of this year they offered a special show that included thirteen million-dollar cases. This meant that the player had a 50-50 chance of selecting one of the million dollar cases as his case. I speculated that in such a game the offers would be generous. Boy, was I wrong.

Here were the amounts in the cases.

 Amount Amount 1 cent 1 Million 1 1 Million 5 1 Million 10 1 Million 25 1 Million 50 1 Million 75 1 Million 100 1 Million 200 1 Million 300 1 Million 400 1 Million 500 1 Million 750 1 Million

The player chose case #5 as his case. His first six selections eliminated the \$10, \$25, \$300, \$400, and two of the million-dollar cases. If you average the values of the remaining cases, the figure is \$550,084.05 so this would be a fair offer. What was actually offered was \$242,000.00. On the fourth pass the player eliminated the 1 cent, \$5, and \$75 cases and the offer was \$435,000.00, the highest during the game. In fact here is how the game proceeded. I'll list the fair offer and the actual offer at each pass and the percentage difference between the two.

 Pass Fair Offer Actual Offer Percentage 1 550,084.05 242,000.00 44.00% 2 533,442.00 211,000.00 39.55% 3 545,530.00 277,000.00 50.78% 4 750,106.25 435,000.00 57.94% 5 611,808.33 366,000.00 54.89% 6 750,212.50 298,000.00 39.72% 7 666,950.00 273,000.00 40.93% 8 504,425.00 209,000.00 41.76%

At this point there were only two cases left; one containing \$750 and one containing one million dollars. My recollection is that the player didn't take the deal. Case #5 contained \$750.

I'll leave it to you to figure out what the above table says about the producer's motivations. Whether or not the so called Banker knows the distribution of the amounts in each box before the game begins is unknown to me but I believe the above table does suggest an answer. I'll have to leave it at that. See you next month.

Don Catlin can be reached at 711cat@comcast.net

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Donald Catlin

Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers
Donald Catlin
Don Catlin is a retired professor of mathematics and statistics from the University of Massachusetts. His original research area was in Stochastic Estimation applied to submarine navigation problems but has spent the last several years doing gaming analysis for gaming developers and writing about gaming. He is the author of The Lottery Book, The Truth Behind the Numbers published by Bonus books.

#### Books by Donald Catlin:

Lottery Book: The Truth Behind the Numbers