Yet Another Comment Not Answering Your Question ….
Let’s assume you have a one in a million chance of winning the lottery. Despite the poor chance, you pay five dollars to enter, and you win a large sum of money. Was playing the lottery the right choice?
A lot depends on whether this “large sum of money” is more or less than five million dollars.
Even with positive expected value, you may be better off passing up the bet depending on your tolerance for variance and the local shape of your utility-of-money function.
Yet Another Comment Not Answering Your Question ….
A lot depends on whether this “large sum of money” is more or less than five million dollars.
I guess that in most ordinary situations the utility of $5M isn’t anywhere near 1M times the utility of $5.
Even with positive expected value, you may be better off passing up the bet depending on your tolerance for variance and the local shape of your utility-of-money function.