**Mastery Loadouts**
Due to issues related to the release of Mastery Loadouts, the "free swap" period will be extended.
The new end date will be May 1st.
Due to issues related to the release of Mastery Loadouts, the "free swap" period will be extended.
The new end date will be May 1st.
Comments
The game doesn't calculate that, any more than dice calculate anything at all. But there is still a calculable probability of, say, rolling sevens ten times in a row. What I think youi're getting confused about is the fact that probability encapsulates a measure of unknown stochastic information. In other words, before you open any crystals the odds of opening six science in a row is (1/6)^6. But after you open one and you discover it is science, the odds of opening six in a row is (1/6)^5, because you only need five science openings in a row to make six. The first one has already happened, so its probability of happening is now 100%.
There's a saying in statistics, which is paraphrased as "the odds of history happening is always 100%." History has already happened, so the odds of history happening any other way are zero.
It is also important to note that people often calculate the wrong probability numbers for reasons related to this. For example, when someone opens six science gems they ask what the odds of opening six science in a row are. But they are generally failing to account for the fact that the noteworthy thing here is six identical in a row, not six science in a row. Had they opened six cosmic, they would have been saying the same thing. The odds of pulling six identical in a row is (1/6)^5, not (1/6)^6, because the first one can literally be anything: it is the other five that have to match it.
If you don't account for this principle you get to nonsensical results. For example, if I open one science, one skill, one cosmic, another science, a tech, and another cosmic, what are the odds of that happening in precisely that way? It is the same calculation as calculating the odds of pulling six science in a row: (1/6)^6. In other words, the odds of that exact sequence happening are identical to the odds of opening six science in a row. The reason why this is counter-intuitive is because the first sequence isn't "interesting" so no one talks about it. This is sometimes known as significance bias in statistics, and is really the Fundamental Counting Principle in disguise.
Another thing people don't fully account for is the fact that when we calculate the odds of pulling six identical gems in a row as (1/6)^5, which is one in 7776, we sometimes jump to the conclusion that one in 7776 players will see this. But that's not entirely true, because individual players don't have only one shot at this. If a player opens seven crystals and the first one is cosmic and the next six are science, they will only remember the six in a row. They won't remember or care about the first one not being science. But while the odds of seeing six identical class openings in a row out of exactly six openings is one in 7776, the odds of seeing six science in a row out of seven openings is about one in 4241. As the number of openings increases the odds of seeing six science in a row also increases (it is about one in 3255 for eight openings). The more crystals you open, and for that matter the more crystals all players open, the more likely it is you'll see this sequence, and it doesn't take 7776x6 openings for the odds to become likely.
Besides, for the little amount of people there is a high probability they will come and complain about them being unlucky. The average majority will not be heard, because their pulls aren't outstanding in any way.
P.S.: Please pardon any miscalculations from my side, especially the 10^6/1296, it is a rough estimate from top of my head.
Also it was quite funny that you called out dna3000 on maths... you had already lost by that point