What are the odds of that happening?!
Priyansh7
Member Posts: 446 ★★
Just popped open 2 Cavalier Underground Crystals using the shards and got back to back 5 Star Mordo!
I could've gotten 3 or 4 stars lol! Nothing too special about the champ as long as I know unless you guys know anything. Did he ever get a rework? Anyone ever popped the same rarity champ back to back?
I could've gotten 3 or 4 stars lol! Nothing too special about the champ as long as I know unless you guys know anything. Did he ever get a rework? Anyone ever popped the same rarity champ back to back?
7
Comments
The reason for that is it doesn't matter who you from the first crystal, that is the independent outcome. What we really care about is the second crystal because we want it to match what we got from the first crystal.
https://stattrek.com/online-calculator/binomial
If you are assuming there are 250 different champions in a crystal (this does not match the Cavalier crystals mentioned by the OP but let's set that aside for now) then the odds of pulling two of the same champ in a row are one in 250, not one in 250x250= 62500 (or 0.002%). There's two ways to look at it.
The first one is to note that if you open two crystals in a row and are looking for a dup, it doesn't matter what the first crystal drops. Whatever it is, the second one has to match. But the first one can be literally anything. The odds of the first crystal dropping anything at all are 100%. The odds of the second crystal matching it are one in 250. So the odds of a dup are one in 250.
The second is to resort to first principles, which in the statistical case means counting possibilities. There are 250x250 = 62500 possible ways for two crystals, each with 250 different champs, to open, 250 possibilities for the first crystal, and 250 for the second crystal. Out of all those possibilities, how many are dups? It isn't one, obviously. It could be Mordo, Mordo, but it could also be Drax, Drax. There are 250 possibilities that result in dups, one for each champion in the crystal. So the odds of seeing a dup are 250 out of 62500, or one in 250.
A lot of times when people see something uncommon happen they think it is far rarer than it actually is. This is probably the most common reason for that incorrect estimation.
The odds of pulling a 5* champ is 16%. So the odds of pulling two 5s in a row from two crystals is 0.16 x 0.16 = 0.0256, or about 2.56%, or about one in every 39 openings, assuming you always open two crystals. Unusual, but not super uncommon.
The odds of both being the same champion when it happens is about one in 250 or so, which thus happens about once every 9750 openings. Which is very uncommon, but across all the Cavalier crystal openings that players make I would guess that at least 10% of the player population has seen this at least once.
One in ten thousand openings seems super rare, but one in ten players seems less so.
"The probability of pulling the same champ from two consecutive basic crystals is approximately 0.00002."
"The probability of pulling Mordo from two consecutive basic crystals is approximately 0.00002."
But yes, the probability of pulling Mordo twice, or any other specific champion twice, is 0.02%.
However, this actually touches on a very important non-trivial non-semantic problem in probability, namely the problem of proper accounting of significance. Someone opens a bunch of crystals, and sees Mordo twice in a row. So they come to the forums and says "the odds of pulling Mordo are one in 62500, this is almost astronomically low, something must be up."
However, the problem here is that the odds of pulling *any* two champs are the same one in 62500. The odds of pulling Mordo followed by Havok are one in 62500. The odds of pulling Storm followed by Beast are one in 62500. So why can't someone open two crystals, see whatever pops out, and then come to the forums and claim that no matter what they saw, the odds against it were very low? Why can't I open five crystals, see Hercules, Magento, Moondragon, Archangel, and Void, and say the odds against seeing that specific sequence of champions is one in 250x250x250x250x250 = 976,562,500,000. Why isn't that so astronomically rare that I can claim I just won the lottery?
Because every sequence is equally likely, or equally rare, but human beings don't treat all sequences equally. The odds of seeing Hercules, Magento, Moondragon, Archangel, and Void in exactly that order are *exactly the same* as the odds of seeing Hercules, Hercules, Hercules, Hercules, Hercules. There is no difference in odds. But we humans see nothing in the sequence Hercules, Magento, Moondragon, Archangel, and Void but we see something in the sequence Hercules, Hercules, Hercules, Hercules, Hercules. We *notice* it; we consider it noteworthy.
When someone sees two Mordos in a row, they are almost never specifically looking for Mordo. Their brains just detected the interesting pattern of two identical champs in a row. So when calculating the odds of the player seeing that, it is important to note what the "that" actually is. Their brains detected a dup, and reported on the dup. It could have been any dup, so the odds of them seeing what they saw should be calculated that way.
Now, if a player goes on stream and says "let's see how long it takes me to see a Mordo dup" then that's different. The odds of them seeing that are in fact one in 62500 (actually, it is a bit more complex than that due to how sequences work, but we'll set that one aside here). But if they then see a Kingpin dup, they should just ignore it. If they say "well, I was looking for a Mordo dup but here's a Kingpin dup and that is just as rare so I have still seen a one in 62500 event" then that is cheating. The odds of them seeing that drop to one in 250, because it is clear they were lying when they said they were looking for a Mordo dup, they were actually looking for any dup and would claim success on any dup, so that's how the odds should be calculated.
This, this, and a million times this. I've ben trying to say this for along time in posts like this, but with far less mathematical precision as DNA.
( i should have opened gem first lol )