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."