Original Video Here -
https://youtu.be/RBf1s4TassI
I watched VSauce2 today and their video about an infinite money paradox. Basically that if any given risk/reward system had a potential infinite outcome, no matter how unlikely, the expected value would also go to infinity. While this is true, we certainly wouldn't spent a near infinite amount of money to play a game that would mostly likely gain us just a few dollars. The video a bit overdramatozes this and plays it off as "humans as not just followers of the strict numbers" idea. I think it's a bit misleading.I think we as humans just have misconceptions about probabilities than run deep.
Despite the expected value going off to infinity, could you make an argument for the Median result being something modest like $4? Since half of all games end after the first flip, would it be safe to say the median value is either 2 or 4, without even running a sample size, or does the median require a list of results to exist?
This ties in with the TCG a bit with the drop weight of Tier 12 cards - despite being in a wholly non-infinite expected value. I've calculated expected values left and right and I don't think they tell the full story, considering the absolute rarity of the top prize. Wouldn't an expected median value be more telling? It seems more practical and less theoretical than an expected value.
It's like calculating a return on investment for lottery winnings when the chances of YOU winning are astronomical. This whole misconception between median expected value and average expected value is probably behind why people even play lotteries to begin with. I'm sure psychology plays a role here, but maybe we've just not been generally trained to look at these situations through the right lens, and has applications in practical decision making.
If there's something I'm missing here, please enlighten me, I'd love to know more about this kind of stuff - it facinates me. Something about his video though struck me as a misconception and it inspired me to make this thread.