Deal or No-Deal

I happened to watch this program called "Deal aa - No Deal aa" in Sun TV today, for the first time.  It is celebrating its 100th show next week, is an extra info!

This is a game show purely based on random numbers.  The contestant is given with 26 boxes worth values ranging from Re 1 to Rs 50,00,000.  Out of that, the contestant has to select one box and keep it aside, the one marked as his box for him to be taken home.  Now he opens the remaining boxes in various rounds in order to know the  value of the box that he had selected and kept aside for him.  In Round 1, he opens 6 boxes and gets to know what all those 6 values that he cannot take home. In Round 2 - five boxes, Round 3 - four boxes, Round 4 - three boxes and so on. At the end of each round he is offered a particular value which he can choose to take, ditch his marked box and quit the game. Or, he can proceed to next round and get to open more boxes.  The offer price at the end of each round increases or decreases based on the values in the hidden boxes (including the one marked for the contestant, and kept aside)

It is a pure fun game, not much knowledge or creativity required on part of contestant, except to answer some very basic GK type questions at the end of each round, to continue the game.

One interesting thing is the offer price at the end of each round.  The Offer price is not the expected value of the hidden boxes.  It is some percentage (<100) of the expected value. It starts as low as 8% in the episode that I saw today and went up to 74% at the end of round 5.  This gives a natural inclination (though, he may be unaware of this fact) for the contestant to go for the further rounds in the initial stages and to restrict himself in the later stages of the game, which is a good design!

This spreadsheet gives a detailed analysis of the same.  For any episode, the expected value of the game is Rs 3.95 lacs and the offer value will be lesser than that in the further rounds. Further, the game designer previously knows what is there in the marked box which was chosen first.  So, accordingly he can play around with the offer price. 

Deal or No Deal?  Not-So-Fair Deal!