This isn’t even related to the law of large numbers, which says that if you flip many coins you expect to get close to half heads and half tails. This is as opposed to flipping 1 coin, where you expect to always get either 100% heads or 100% tails.
I personally expected that P(AI) would drop-off roughly linearly as n increased, so this certainly seems counter-intuitive to me.
Isn’t it just the law of large numbers?
This isn’t even related to the law of large numbers, which says that if you flip many coins you expect to get close to half heads and half tails. This is as opposed to flipping 1 coin, where you expect to always get either 100% heads or 100% tails.
I personally expected that P(AI) would drop-off roughly linearly as n increased, so this certainly seems counter-intuitive to me.