The difference between this game and the Monty Hall is that Monty never offers you to take the average of all the prizes combined. Big difference.
It would be the same if Monty did this:
You pick a door. He shows you a goat behind a door you didn’t pick. The other doors contain a goat & a car. Now, he gives you the option of taking a bicycle.
That’s a big difference.
I haven’t watched the show, but it sounds kind of interesting.
Rarely is it stupid to take the bank or not because they have it high enough to make it interesting.
A coworker was telling me about a case where a guy had a
10,000
300000
400000
500000
and they offered him about 250000. He said, “the guy should have taken it. What an idiot.”
But, of course. First of all, his expected value was about 300,000. But, he also knows that the offer would decrease to about 190,000 (should be 230000) even if he chose the 500,000 briefcase. It would stay about the same if he chose the 300000 or 400000 and would rise to probably 350000 if he eliminated the 10,0000.
A lot of factors go into that decision, not the least of which is a person’s view of the utility of the difference.
For instance, mathematically speaking a guy on “who wants to be a millionaire” should ALWAYS guess when he has 64K and has done a 50/50. He loses 32 or wins 61 on a coin flip. But, if he owes $45,000 to his bookie, that’s a whole other thing to consider beyond the numbers.
From what I’ve heard, it sounds like they’re not offering you exact expected value. The online game definitely doesn’t and from the descriptions I’ve heard, they don’t on TV either.