The lottery. Honestly it bugs me a bit that I don't know the right way to model it - because so often people will slate it for having a terrible expected return (E[X]), but.. some very high percentage of us here could play every single week without noticing it (negligible downside), and yet winning however slim the chance would be somewhat life changing - even if it wouldn't make you quit work it'd be a nice windfall…
Opportunity costs make the lottery a poor option. If you could only invest money in the lottery and nothing else, sure, it's better than no chance of multiplying your income. But if you invest in an index fund, there's a very high chance of getting a 15-30% return on investment, versus a near-guaranteed amount of just losing the money spent on the lottery. It may not seem like a lot each ticket, but the costs add up…
In exchange, I get extremely unlikely but extremely massive 'asymmetric upside'.
As I said, I don't do it, but sometimes I think actually it would be the rational thing to do. (What stops me is the thought: why stop at one ticket? how many tickets is the correct amount? clearly I don't know the appropriate way to model it (simply massive variance?) so I'll leave it alone. But it does bug me sometimes.)