3 ms·

0.000000000000001 chance - cost $0 0.000000033333333 chance - cost $4 Which one comes up on top, expected value wise?

Epa095 4y ago
Your evaluation of the price might not scale linearly with the money amount, making it a fault to focus to much on the expected value. 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.
- dkbrk 4y ago
  You're not wrong in principle that you could have a utility function with positive expected value for playing the lottery, but that's misleading. 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.
- lupire 4y ago
  If you are poor, winning a large windfall is likely to harm you. You'll get a lot of attention from dangerous and desperate people, draining the EV at best. 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.

Your evaluation of the price might not scale linearly with the money amount, making it a fault to focus to much on the expected value. 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.

dkbrk 4y ago
You're not wrong in principle that you could have a utility function with positive expected value for playing the lottery, but that's misleading. 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.
lupire 4y ago
If you are poor, winning a large windfall is likely to harm you. You'll get a lot of attention from dangerous and desperate people, draining the EV at best. 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.