Suppose their was a lottery designed as follows:
- With probability
you win ten million dollars. - It costs
dollars to buy a ticket.
Do you want to buy a ticket?
The expected net profit from buying a lottery ticket is
It is my understanding that in trading, high variance positive EV trades are a common thing, and the prevailing wisdom is that you should take them, and that your natural inclination to be risk averse is wrong.
Thoughts on this:
If you have a very large bank of money, and are going to be repeatedly engaging in trades like this many times, then you can probably prove mathematically that it’s not actually risky within the larger context to take the trade. You’re fairly unlikely to go broke before gaining a bunch of money. Of course the parameters matter. For the lottery ticket as stated, you’d need to have at least 9 million dollars you’re willing to risk before you even expect to win once.
My brain is incapable of visualizing large numbers, so my utility function for money is sub-linear. That is, it’s hard for me to really feel like 9 million dollars and 10 million dollars are different amounts.
Now, from a selfish perspective I think grading 10 million and 9 million dollars as providing roughly equal amounts of utility actually makes a lot of sense. What do I need money for?
But my utility function has terms for the well-being of other people as well. Terms for others in my utility function