That gives you the expected value if you played the game an infinite amount of times, but you only play once so that makes it interesting. The offer seems to range from about 40% of the EV in early rounds to over 100% in some cases (heh heh) near the end.
I don’t think it is at all simple, especially where there is a large difference between the mean and the median values of what is left. Economics dopers: is there a term for the expected value of the median?
My question on that show is: does the Banker know which case has the grand prize?
Based on statements I recall, no. Only the two independent auditor guys know.
That’s about right. Or to put it in even simpler terms if someone had two cases and one had $1 and one had $10 and they offered you the option of opening a case or taking $5 which one would you choose? Most people would risk it and open a case. How about $1/$100 cases and an offer of $50? $1/10,000 and an offer of $5,000? $1/$100K and an offer of $50K? Or the big $1/$1million or an offer of $500K??
There’s not too much to calculate when the odds are basically 50/50 it’s more a question of how much your willing to personally gamble. In the $1/$1million with an offer of $500K what’s a dumb decision? What’s a smart decision? Does that change if the offer is $450K instead? How about $550K? It’s all a personal choice.
Actually, if you’re already worth millions, you would be a fool to try to add to it by squealing and jiggling on a TV game show. 
What if I’m willing to risk all for a chance to punch Howie Mandell in the face?
I did the expected value deal at one point and the offer was lower than that but still in the ballpark.
I hate the part when they say “What would you have opened?” “And then which?” Just open the contestant’s case, darn it!
When the guy styled just like Howie was on, :eek: The thumb ring freaked me out exponentially