You - out of thousands of applicants - have been chosen to be the lucky participant in a televised game show.
You’ve made it to the final round, which consists of playing a probability-based machine game for a monetary jackpot.
For every 10% decrease in win likelihood, the jackpot goes up by an order of magnitude. What would you choose?
(Poll coming soon.)
Oh, and needless to say, you only get to play the machine once. No second spins.
This is also pre-tax income, so you might lose half of it in taxes.
And yes - before someone challenges the hypothetical - I know that $100 billion is a completely outlandish and impossible sum for a TV show to offer. 
I’ll go 50/50 on the life-changing sum.
I know, mathematically, how to calculate the “expected” amount for each tier…but in practice, 100 billion is not really much different from 10 billion, 1 billion, or even 100 million. They’re all “infinite” as far as my life-style would go, and so there’s no reason for me to choose any higher risk than the 40%.
However, I actually voted for the 80% chance at a measly $10,000 because I like the odds.
My vote also and consistent with a lot of the decision theory stuff that I read in grad school more years ago than I like to think about.
You could argue for the $1 million being life changing but depending on your age it is not a “liver comfortably without working” amount.
Like most so far I went for the middle. 50/50 chance of winning 50 million smackers? Can’t pass that up, though it would be smarter for me to go for the 70% chance of winning a 100 grand.
Pretty clear to me. In terms of expected outcome, the last option is “best”, but the utility of money does not increase linearly. As such, it seems to me it’s a balance of trying to get the highest chance at the lowest value that is life-changing. Thus, I think for most people, $100k would be great, maybe provide some limited relief, but it’s not fundamentally life-changing; you won’t be able to go back to school, pay off a house, retire, or whatever. A life-changing amount for most people probably lies around the $1M to $10M mark. So it seems to me that the answers should cluster there unless someone is either so desperately in debt they can’t risk even a slightly lower chance at fundamentallly changing their lives, or they are already rich enough that they need a whole lot more to make a real difference.
Ideally, I would pick some value between those two ideal values, as $1M is not quite what I’d like to have to really make a difference for me, but $10M is definitely more than I need. Ultimately, I went with 60% at $1M because it’s close enough to what I’d need that the extra lower chance isn’t worth it especially since I already have savings and don’t intend to just retire and have zero income. I’d still be willing to work (thought probably only part time at that point) but it would allow to to focus more on other endeavors that are more important to me that may or may not be monetized and, if so, may or may not be enough to support me on their own.
This thread makes me wonder about a lottery psychology: When people win or play such games, I think they are thinking more about what they missed out on than what they actually got.
So if someone chooses the 50% for $10 million option, he is thinking, if I chose a higher-probability option but got “only” $100,000, I would have missed out on nearly ten million dollars. He is not thinking, “By choosing a 50% probability, there’s a good chance I will not win anything.”
IMO **Blaster Master **nailed the logic.
But I picked the $10M choice since his $1M choice, though nice, won’t move my needle enough especially post-tax. The incremental utility of 10x that much dough is “worth” the decremental 10% in my estimation.
I’m fairly calm-natured and decent at money management (at the upper middle class tier), but I think the odds on screwing up my life (ref current thread http://boards.straightdope.com/sdmb/showthread.php?t=802181) would get uncomfortably high at the $100M & above level. Plus of course the ever-increasing chances of not even winning the OP’s game at that level.
So $10M is my sweet spot.
I said 1 million (60% chance). 100,000 would be just dandy - extremely helpful, but not life-changing in the long term. A slightly smaller chance for 1 million, where that WOULD be life-changing. Not “own palaces in 12 countries” kind wealth, but enough to pay down all our bills and put a LOT of extra money into retirement.