Quote Originally Posted by Clavaat View Post
Therefore, farming for 15 minutes (another hyperbole on my part, I apologize), has the same odds as doing it for 5 hours. Your odds don't change based on the amount you do.
The difference in odds isn't because your odds improve, it's because you're doing multiple tries. The Gambler's Fallacy stems from the incorrect belief that if you've lost a bunch, then you're "due" for success. If you've flipped a coin nine times in a row and gotten tails, someone who falls for the Gambler's Fallacy believes that the next toss is more likely to be heads, because the odds of flipping ten tails in a row is only 1 in 1024. In reality, the odds of heads on the next toss is still just 1 in 2, just like any flip.

That doesn't apply here. Here, we are projecting odds of success. A person who plays for 15 minutes will have time to do maybe one or two FATEs. Someone who plays for five hours will have time to do more than a hundred. Someone who does two FATEs is less likely to get a drop than someone that does more than a hundred. The Gambler's Fallacy only applies on the individual attempt. If someone has done more than a hundred FATEs with no drop, and someone else has done one FATE with no drop, they both have an equal chance of getting a drop on the next FATE.

The reason the Gambler's Fallacy fails is because suckers who fall for it mistake past results as having the same odds as projected results. If you've flipped tails nine times, what are the odds that one of those flips is going to be tails? 1 in 1, obviously, because you've already flipped them. Multiply 1 in 1 together nine times, and you get... 1 in 1. Then multiply by 1 in 2, and you get 1 in 2. If you haven't started flipping, and you want to guess the odds of getting ten tails in a row, you multiply 1 in 2 by 1 in 2 by 1 in 2 etc, and wind up with a result of 1 in 1024.

tl;dr:

Believing someone who farms FATEs for 15 minutes in a single day is less likely to wind up with an atma than a person who farms for 5 hours in a single day is simple statistical mathematics. The Gambler's Fallacy has nothing to do with this.

Believing someone who has already farmed FATEs for 15 minutes is less likely to get an atma on the next FATE than someone who has already farmed for 5 hours, this is the Gambler's Fallacy.