Quote Originally Posted by L-D-Omlette View Post
What he is referring to is the odds of certain events occurring in succession. If you flip a coin you have 50% chance of it being heads. If you flip it twice, you still have 50% chance of it being heads for that particular flip, however, since the odds of it being heads twice in a row is 25%, you are more likely to see tails on the second flip.

From a mathematical standpoint, lets assume that Atma drops at 2.5%. For any given FATE you have 1/40 odds of getting a drop. Two FATEs in a row would be 1/160, or .00625 percent. But, we are more interested in what our odds are each subsequent failure. So, first fate: 39/40 that we won't see a drop, or 97.5%. Two FATEs in a row: 1521/1600, or ~95%. Notice that the odds of NOT seeing a drop decreased on the second instance. In order to get odds in your favor, you need to fail 28 times in a row. Then the odds of failure are ~49%. At 100 failures in a row, your odds are ~8% that you won't get the drop.

Does this mean that you will get it at number 100? Absolutely not, just that you are more likely to. No matter how many you do, there is always that opportunity to not get the drop. Even a .00000001% chance is still a chance.

There is another assumption at work with this type of calculation in that we believe that the chances of getting an Atma are equal for each FATE. There very well could be other factors at play here, it depends on how they seed the RNG for these items.
You're referring to frequentist/empirical probability there. But classical probability states that each individual event has the same chance of occuring, always. Which is what I assume what the system is built upon. Saying that "to get odds in your favor" you need to fail 28 times in a row is stupid, plenty of people have gone WAY over 200 consecutive FATEs without a single atma drop; and please don't tell me that these people have NOT gotten their Atma (with an 8% chance of failure, which is constantly decreasing according to empirical probability) 100 FATEs after the first hundred.

I'm just going assume that the Atma drop works this way: You have a certain chance (say 5%) of getting an Atma after finishing a fate with gold rating. If you got it, then that means that the 5% worked in your favor. If you didn't, then that means that the 95% chance of failure made you not get the drop. Also, previously completed FATEs, with unsuccessful results, DON'T affect in any way your overall chance of getting an Atma drop in the future.