# Numbers Don’t Lie

CoachLed
Posts:

**355**★★
I’ve speculated in the past about the drop rates of certain champs in different crystals but it wasn’t until this 5* featured that I decided to put pen to paper. What I found was astounding.

I have opened 3 5* featured crystals in the past few weeks and all of them have produced a 5* Thor Jane Foster. Assuming every champ has the same drop rate, the probability of pulling a TJF is 1/24. Here is where it gets interesting... Opening crystals are independent events. To find the probability of multiple independent events all occurring, you simply multiply their individual probabilities. So, the odds of getting a TJF is 1/24, multiply that by the probability of getting a second TJF on your next pull (1/24) and you get 1/576. That’s pretty unlikely but plausible. Now, take that probability and multiply it by the probability of getting a third consecutive TJF (1/24) and you get 1/13,824. That’s 0.007%. Again, that’s pretty unlikely but still plausible. I very well could be the unluckiest person in the whole MCOC community.

Here is where I find issue.... I have an alliance mate that has had similar luck. 3 5* Beasts in a row from 5* featured crystals. Again, independent events. The odds of my 3 TJF (1/13,824) multiplied by the odds of his 3 beasts (1/13,824) and you get 1/191,102,976!!!! That’s an astounding 0.000000523%. But it gets worse! Those are bad enough odds that this scenario can happen to two different people within the MCOC community for any given crystal, but when you take into account the fact that we are in the same group of 30 people out of the tens of thousands of people that play this game, the numbers really take a turn for the worse.

With all that being said, I can’t help but think that there are most likely similar stories out there where people have experienced this kind of luck. At some point we can’t just keep saying “that’s RNG for ya!” and we have to realize that maybe different champs are more likely to drop than others despite the assumption that they are all equal.

Anyways, rant over. Let me know what you all think. Maybe I’m off my rocker or maybe you agree with me. I’m interested to hear all sides.

I have opened 3 5* featured crystals in the past few weeks and all of them have produced a 5* Thor Jane Foster. Assuming every champ has the same drop rate, the probability of pulling a TJF is 1/24. Here is where it gets interesting... Opening crystals are independent events. To find the probability of multiple independent events all occurring, you simply multiply their individual probabilities. So, the odds of getting a TJF is 1/24, multiply that by the probability of getting a second TJF on your next pull (1/24) and you get 1/576. That’s pretty unlikely but plausible. Now, take that probability and multiply it by the probability of getting a third consecutive TJF (1/24) and you get 1/13,824. That’s 0.007%. Again, that’s pretty unlikely but still plausible. I very well could be the unluckiest person in the whole MCOC community.

Here is where I find issue.... I have an alliance mate that has had similar luck. 3 5* Beasts in a row from 5* featured crystals. Again, independent events. The odds of my 3 TJF (1/13,824) multiplied by the odds of his 3 beasts (1/13,824) and you get 1/191,102,976!!!! That’s an astounding 0.000000523%. But it gets worse! Those are bad enough odds that this scenario can happen to two different people within the MCOC community for any given crystal, but when you take into account the fact that we are in the same group of 30 people out of the tens of thousands of people that play this game, the numbers really take a turn for the worse.

With all that being said, I can’t help but think that there are most likely similar stories out there where people have experienced this kind of luck. At some point we can’t just keep saying “that’s RNG for ya!” and we have to realize that maybe different champs are more likely to drop than others despite the assumption that they are all equal.

Anyways, rant over. Let me know what you all think. Maybe I’m off my rocker or maybe you agree with me. I’m interested to hear all sides.

16

## Comments

399★★19,242GuardianSuppose I were to pull Hulk, Beast, and Archangel in that order from the featured crystal. What are the odds of that specific sequence happening? The same computation you did should still work: 1/24 * 1/24 * 1/24 = 1/13824. But you can do that for any sequence of champs. Is the conclusion that all possible openings are virtually impossible to happen?

In fact, all possible openings *are* very rare. If I pick any three champions at all and ask "how long would it be before you opened three crystals in a row that matched my picks" that would be a very long time: matching three picks in a row is extremely unlikely. But the catch is I'm picking three first, and then you're trying to match those picks. That's very hard. But if you open three crystals *something* has to happen. You're going to get three champs, of course. Now if you look at what you open and

after the facttry to determine how rare that was, this is a completely different situation. Now, you aren't actually looking for three Jane Fosters. You're looking for anything your pattern-matching brain will think is "significant."How many possibilities are "significant?" Well, look at your own post. You thought three Jane Fosters were significant. You thought three Beasts was significant. I'll bet you think three anything in a row is significant. What are the odds that if you open three crystals you'll get three champs identical? Well, there are twenty four possible ways that can happen: three Beasts, three Archangels, three Jane Fosters, etc. Twenty four different champs in the crystal, twenty four different ways to have all three identical.

So really, the odds of you seeing a "significant" set of three was actually 24 out of 13824, not 1 out of 13824. Which is one out of 524. It is the same number you get if you assume the first champ can be anything, and then the next two have to match it: 1/1 x 1/24 x 1/24.

Except: you've probably opened more than three featured crystals. I'll bet that most of those openings were not three identical champs in a row. So you didn't have one shot at landing on a one in 524 possibility, you've actually had many shots at that. The odds of you seeing this were actually N out of 524, where N is greater than one. What's more, there are people who post about getting two out of three being the same, which is even easier to happen. Your triple pull is just one out of many different possibilities that people consider "significant" and when you look at the odds of any of those things happening the odds are actually not all that bad.

And then, there's another error: the idea that since you're just a couple out of tens of thousands of players makes the odds worse. They actually make the odds better. Consider that tens of thousands of players don't post their pulls. Because while all pulls are equally (un)likely, most aren't interesting to human eyes. When someone pulls three different champs, they don't talk about it. Only those that actually see apparently significant to human eyes pulls actually posts about it. So what are the odds that out of tens of thousands of players two would be in the same alliance and both pull triples within a short window of time? Well, the odds of one player doing that is one in 524 as previously mentioned. What are the odds of two people in the same alliance of thirty people doing that. The odds are actually about one in 665.89 (math: (1/524)^2*(523/524)^28*30*29/2). In other words, one out of every 666 alliances that contain players who actively open featured crystals will have two people who both pull triples.

Out of thousands of alliances, the odds of this happening are actually very good. For any one player the odds are rare, but collectively out of all the many players and alliances, it is bound to happen multiple times. And we only hear about the rare time it happens, not the thousands of times it doesn't happen.

To put it another way, the odds of winning the Powerball lottery are astronomically low: one in 200 million+. So does that mean the Powerball lottery must have rigged the contest, because the winner couldn't possibly have won fairly and must have cheated? No, because there ultimately has to be a winner eventually (they keep going until someone wins). The odds of any one person winning are low, but the odds of a winner existing at all is eventually very high. So there's a difference between asking what are the odds of something happening to you, and asking what are the odds of something happening at all. You *saw* the rare occurrence first, then *retroactively* asked what the odds of that happening are. That's an alternate version of the significance problem.

7,371★★★★★598★★★1,962★★★★★399★★19,242Guardian173★★244★★There's def something weird going on with those Crystals.

4,292★★★★★399★★21,710★★★★★424★★Kabam: Lucky you!! Congratulations! You win the game, like you did as a sperm long time ago!! It's a miracle, right? Enjoy & dont need to thank us!!

🎊🎊🎊🎉🎉🎉💯💯💯

54★21,710★★★★★3,799★★★★★3★54★4,965★★★★★8,883★★★★★I offer this example only because I suspect the number of 6* pulls to be (and to have been) significantly less over time than 5* pulls. That may mean an extreme result like L100 Karnak is likelier than not because of a smaller sample size. Or maybe not.

I don’t think there’s any reasonable doubt that the drops are randomized. But I do wonder what “randomized” actually means sometimes to the game’s basic chance engine.

Dr. Zola

21,710★★★★★Do you have proof that code is enforced in the game?

173★★399★★This is an example that actually disproves your point but enforces your thoughts. Kabam should change the rng system to get better business like apple did.

21,710★★★★★173★★306★so I do not feel the Kabam guys have done such rigorous maths so as to design such a cunning way that some champs are to be thrown down at us more frequently than the rest of the champions. its more abt the randomness becoming a reoccurring event n not some casino styled treachery.

As I said before too that what u see in videos of end game players or players who spend regularly to buy champs, their pool or variety of possession of champions is due to their opportunity to have more chances to roll the dice or simply put as they are opening more crystals. The higher the no. of chances they are taking the greater the access to the probability of pulling a desirable champ. A player who can open only two 5 * crystals a month vs a player who will buy units n attempt those cavalier crystals @200 units a piece will obviously have higher chances to pull a desirable champ out of his many items.So the more u stake n gamble the more u will feel rewarded in the form of variety.This game is either for the patient guy or the impatient guy. A patient guy will just sit out like we sit out while fishing n bait the catch. An impatient guy will say forget fishing let's go buy the fish n eat it too.But at the end if the day target is to eat the fish. To eat it for free or buy it to savour its taste is our choice. Nothing else.