Whether it's worth picking up a $20 bill depends on
The odds for #2 and #3 are pretty high compared to the odds of similar activities when playing the market. The odds of #1 vary depending on how well travelled the place is but are generally a lot higher than for whether you're the first person to notice an opportunity in the market.
Of course, #1 is also affected by how many people use this entire chain of reasoning and conclude it;'s not worth picking up the bill, but the other factors are so important that this hardly matters.
The way I see it, in practical terms, it's always worth picking up. I've picked up a number of fake bills. I keep them. It's better than leaving them to torment each successive person who picks it up until someone else does it instead.
Another month, another rationality quotes thread. The rules are: