I've posed this question to a number of people and have gotten similar responses from all:

Warren Buffet thinks you a swell guy (or gal) and decides to give you $1 Million, but you have to consider a number of offers he may make. Everyone is agreeable to that.

Mr. Buffet offers to flip a coin for that $1 Million you're going to get. If you win, you get another $1 Million. If you lose, you don't get the first $1 Million. Do you accept that offer? Everyone declines.

Now Mr. Buffet offers to flip a coin again, but this time, if you win, you get another $2 Million (for a total of $3 Million), if you lose, you get nothing. Everyone still declines.

Now he offers $3 Million for a win. Everyone still declines.

I don't start seeing people saying they'd flip the coin until they're getting at least $5 Million for a winning flip. And I suspect in real life they wouldn't really flip that coin so soon.

Mathematically, turning down the even money flip is neutral; turning down the 2:1 flip is turning down another $500,000 of free money; turning down the 3:1 flip is turning down another $1 Million of free money; and so on. But everyone does it. I understand the math and I would turn down the offers too.

Clearly, people are valuing the 2nd, 3rd, 4th... $Million less than the first $Million. What is this principle? Is it utility? Something else?

Thanks.

(And for you game theory types, if Mr. Buffet even gets a whiff that you're holding out expecting even a better offer, you get nothing!)

I Googled "risk aversion study" and found this paper.

http://faculty.arts.ubc.ca/ftrebbi/research/bt1.pdf

In short, it (probably) is utility.

In your thought experiment above, the incomes of the participants should be noted. If these people were already multi-millionaires, I doubt they would decline the second offer, unless holding out for an even better deal.

Yes basically it is about the concept of diminishing marginal utility.

How much better off will you be with second million as opposed to losing all of the first million?

Change it from Buffet giving you $1000 instead and offering the coin flip for another $1000 and you are going to see a lot of folks taking that action.

Thanks guys. When I fully digest the info you provided, I'm sure I'll have some more questions and ideas.

OP, did you figure that out on your own or see it somewhere? if you came up with it on your own, i'm very impressed and 100% serious comment.

https://plato.stanford.edu/entries/p...-stpetersburg/

i always use an example of someone retired who has everything they need but is not rich. so $2MM net worth, including fully paid house... now that person would never flip for the $2MM net worth i.e. zero or $4MM after flip.

but as you've mentioned, that person would never flip for $10MM vs. zero.

and same idea, as you mentioned, about basic flip... a poor person would easily take the $1MM over 50% chance at $6MM - unless he has access to some sort of intermediary who will take the risk and pay some of the +EV to the poor person.

like i said, i always think of flipping for $1MM but you are absolutely right that most poor to middle class people wouldn't flip $1MM for $3-4MM.

pure entertainment but kerry packer - maybe world's #1 gambling whale - was dealing with a loud, obnoxious texan boasting he's worth $50MM. Kerry asked him "want to flip for it?"

I came up with the example myself, but it was based on bits and pieces of things I've heard and thought about over the years.

The main seed was how poker chips lose value in a multiple payout tournament the more you have (And I realize that this isn't based on the player's perception, but on a mathematically demonstrable model, although the utility concept would suggest the additional chips have even less value than the math suggests--as, for example, each dollar of prize money for 1st place at the main event is worth less than each dollar of prize money for 2nd. But the surprising concept was that they aren't worth "face" value, even though they were at the beginning, which would indeed surprise a lot of people).

Also, there was a game show a few years ago where the contestant had to pick suitcases and eliminate money amounts, hoping to wind up with the suitcase worth $1M. The "banker" would make offers to tempt the contestant to stop, but these offers didn't seem like a fair deal mathematically. But they did take advantage of the utility concept and put the contestants at a tough decision. On two different shows, a celebrity advisor essentially suggested the contestant stop and accept the offer, because the amount offered was life changing and any additional amount won by continuing wouldn't add that much to their life beyond that, but the life changing amount could easily be lost (I think most contestants would easily come to the same conclusion on their own, if not surrounded by the lights, cameras, audience, etc., which had them out of their comfort zone). One celebrity was poker player Annie Duke. The other (the surprising one) was our current President, Donald Trump.

As far as a rich person is concerned, I think the additional money is still worth less, but, also, losing the flip doesn't hurt nearly as much as it does a non-rich person. And the more a person is worth the less the additional money is worth to that person. And I realize someone's background and personality could cause this behavior to vary, even drastically.

But what if we talk really rich. Suppose Mr. Buffet made the 2:1 offer to Bill Gates? Mr. Gates might take him up on it a few times, but probably would quickly get bored. The amounts mean little to him, but his time is probably very precious to him. And this phenomenon probably is more significant the older a person is, as older folks value their time more (because they have less of it--the utility concept applied to time vis-à-vis age ). So a 70 year old Bill Gates might very well tell Mr. Buffet, "Go bother someone else with this silliness."

That is pretty much it George.

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