What are the odds of this
Aceymcoc
Member Posts: 195 ★★
I’m genuinely curious what the odds of this happening are there two basic six stars 
49
Aceymcoc
Member Posts: 195 ★★
Aceymcoc
Member Posts: 195 ★★
Aceymcoc
Member Posts: 195 ★★
Comments
The first event had already happened when you asked the question. Therefore, it’s the odds of pulling any one champion.
Now if you asked before opening the odds of getting him twice in a row, the probability is 1.6E-5 which is absolutely minuscule.
3 in a row🥵...then we are up to over 1/15M...our national lottery has 1/4.5M on 7 numbers...top prize about $2M per round.
So you can take comfort in the fact that the chance of a 3d Cyclops next time, is terribly small 🫣
However, this is important, and something even professionals get wrong sometimes. The odds of pulling Blue Cyclops followed by Blue Cyclops is one in 48400. But the odds of pulling Blue Cyclops followed by Rogue is also one in 48400. The odds of pulling Hulkbuster followed by Archangel is one in 48400. The odds of pulling any specific champion followed by another specific champion is exactly the same: one in 48400.
That's because there are exactly 48400 possible combinations of two champs, and the odds of any one of those sequences coming up are identical. Let's simplify and consider the case of a crystal with just three champs in it: A, B, and C. There are three possibilities if you open one crystal:
A
B
C
The odds of each of those coming up are equal and identical, so the odds of pulling A or B or C are the same: one in three. Three possibilities, one chance for each. What if you open two crystals? There are now nine possibilities:
AA
AB
AC
BA
BB
BC
CA
CB
CC
Now, what are the odds of pulling A twice in a row? One in nine. There are nine possibilities, in exactly one of them you pull A twice, so the odds are one in nine. But what are the odds of pulling A followed by C? Still one in nine. AC is no more and no less likely than AA. There's nothing special, statistically, about pulling A twice in a row.
We only *think* AA is special because it is a dup, and we think dups are rare. Which they are. If you look again, there are three ways to get a dup: AA, BB, and CC. That's three possibilities out of nine. So dups happen one time in three, while non-dups happen two times in three. So if you only care about whether your crystal dups or not, then dups are rare compared to everything else.
But notice: dups happen one time in three. One specific dup, AA, happens one time in nine. If you compare dups to non-dups, dups are not common. But if you compare the specific sequence AA compared to all other sequences, it *isn't* rare. It happens one in nine, just like all other sequences.
The fact that AA "seems" special is only in people's heads. It *looks* special, because dups seems special. But, and this is the punchline: dups are special, specific dups are not special.
That's hard to wrap one's mind around. But think about it this way. Suppose *before* I were to open crystals I were to call my two openings. Suppose I call Winter Soldier and then Iceman, and then I get WS and Iceman in that order. That would seem to be extremely lucky. It is extremely difficult to call your openings like that, because as I said there are 48400 possible openings. To land on the bullseye is a one in 48400 shot. That's true no matter what those two are. It is just as hard to call your openings if it is two different champs than if it is two identical champs, because it is equally hard to get it right twice in a row.
This is sometimes referred to as the postdiction problem in statistics. The rarity of an event or sequence of events has to be calculated before they are observed, with only the information you have before they are observed. If you attempt to calculate the odds of an event happening after it happens, you run into the question of what context that rarity should be judged against. What were you expecting, verses what you got. If you *call* Blue Cyclops twice in a row and then get it, the odds of that happening are one in 48400. But if you open first, see two Blue Cyclops, and then ask how rare that is, are you asking "what are the odds of Blue Cyclops and Blue Cyclops" or are you asking what are the odds of two identical champs coming up. Are you noticing two Cyclops, or just two dups and you'd notice just as much if it was two of any other champ.
The odds of Blue Cyclops followed by Blue Cyclops is one in 48400. But the odds of you coming here to post about a duplicate champ is one in 220, because you'd still be here if it was two Rogues, or two Hulkbusters, or two Agent Venoms. Out of the 48400 possibilities, there are 220 in which you'd be here asking what are the odds of that, because what you noticed was a dup. The odds of a dup are 220 out of 48400, or one in 220.
Dr. Zola
People need to write this down because most clearly do not understand it. I’ve been saying this for a while, albeit with far less authority.
This is part of what I was getting at in my previous post. If someone insists that two Cyclops is one in 48400 and astronomically rare, then two Nightcrawlers is uninteresting. It *isn't* two Cyclops, because we defined interesting to specifically be two Cyclops. But if we decide that two NCs are just as interesting and notable, then it is obvious we did not think the OP's pull was interesting because it was two Cyclops, but rather because it was any dup, just like yours. And the odds of the OP getting a dup and you getting a dup are both one in 220.
That's *per dual opening*. If there are lots of players opening lots of crystals, the odds that someone somewhere will see this becomes very high, because when the odds are one in 220 and you have thousands of players opening dozens of crystals aiming at a one in 220 bullseye, a lot of them will end up hitting it.
Dr. Zola
What are the odds of that
My mini account, pulled 6* Hulk, the 5* Hulk…
I do this stuff for a job