I just played this for the first time. I picked case #1, which just so happened to have the $1M in it. This game is stupid easy.
Just now watched tonight’s DVRed episode.
5 cases left: EV 61K. Offer: 52K No deal.
4 cases left: EV 75K Offer 76K No deal!!!
He then hits the last large case and the offer goes to $50. His mathematical stupidity cost him $76,000.
Entertainment cost to me: priceless.
Really, they should do an American Express commercial for Deal or No Deal.
There are two reasonable ways:
1: Expected value - divide sum of remainding values by number of remaining suitcases
2: Median - the value of the “middle” suitcase if you rank the remaining suitcases by value (not sure what you do if there are an even number left).
Then apply a “discount” because the banker’s offer removes risk. Calculating in my head the discount seems to be about 40% in early rounds and moves towards 0% in later rounds.
I think you’ll find that there is no hard and fast algorithm being used. If Howie has any smarts at all he just may be doing it in his head and factoring in the momentum of the show.
I wouldn’t quite say that. He knew that the 76K was a big offer, but he really believed that he could do better, either by nabbing the 300K or picking a low-value case and driving that 76K offer upwards.
He wanted to gamble, and so passed up an offer that was 1,000 dollars better than random chance. That decision, at most, cost him the 1000 dollars. Pure luck deprived him of the rest. 