That reminds me that I finally need to start participating in lotto, just to have a skin in the game.
Not participating - zero chance of winning.
Participating - 1 in 30 million chance of winning 4m USD.
Not participating - zero chance of winning.
Participating - 1 in 30 million chance of winning 4m USD.
Which one comes up on top, expected value wise?
Example 1: you own the mafia 1 million dollar, pay tomorrow or die. You have absolutely no way to get the money before the deadline. You have some money though, and the winner of the lottery gets 1 million. Your expected value(in $) is negative, but the chance of surviving is no longer 0 if you play the lottery.
Example 2: you are a normal lower income person. You have no real chance of getting rich, or even comfortable. You can save the 4$, and maybe buy a slightly better TV every 3 years, but it will make no real difference in your life. Winning e.g 2 million on the other hand would lead to a qualitatively different (and better) life. Its not that 2 million is 2millon/4 times better than 4$, it is just incomparable. One leads to a completely different life.
Generally it is taken that money has diminishing marginal utility. This is even more salient for poor people, for whom the marginal value of $1 at their current wealth is vastly more than the value of $1 at the wealth of winning the lottery; i.e. playing the lottery is even worse, in terms of expected value, when you apply a reasonable utility function.
You're correct about your mafia example, but that's highly contrived. I contest that your second example does not show what you claim; that is exactly the sort of person who should not be playing the lottery.
A little money at a time changes life more per $ than a lot of money all at once.
You're better off spending your "lotto funds" on things like applying for jobs, personal networking, education, and other such things that have a random chance of increasing your wealth.