I have 18 semester hours of graduate level statistics.  That's enough coursework for a 2nd M.S. degree in statistics. You do not know WTF you are talking about. LOLOLOOLLOOLLL

You don't even know how to ask a question.  Put 12 apples in different basket?  What different basket?  How many basket's total?  If I have 100 apples and 2 baskets and put 12 in one and 88 in the second, then I have 88 in the second.  So what?  Is that your question?  It certainly isn't an example of statistics or odds.  Is this supposed to mean something other than you can count to 12, 88, and 100?  

LLOLLLLOOOOLOLLL!

The  odds  are  bad  my  friend.  Sorry  to  hear  about  your  mishap.  I  shared  your  pain  many  times  before,  i  just  want  to  collect  all  the  different  heroes  and  they  gave  me  a  failure  of  an  empowerment  system 

This complaint I understand.

They advertise the game as a Hero Collection game and it is everything but.......

I do not think people would download and play if they advertised as come manage your Energy and Shards and grind til your eyeballs bleed 😀

It should be an eye-opener, that even with the mercy system you only have the 100% chance of getting a leggo - if you didn't pull it before - on the 18th shard during a 2x event and on the 24th shard during no event (- hope I calculated it correctly). Anything can happen before these shards.

(Not complaining, just got to this revelation myself, thank you thread)

That is not correct.  You don't have a 100% chance on sacreds until th 59th shard, or on the 56th shard during a 2x event.

During normal times It's 6% through the 12th shard, than an additive 2% for each shard after that.  So 8% on the 13th, 10% on the 14th, etc., until you hit 100% on the 59th shard.

During 2 times events, only the base chance is doubled, that is the 6% goes to 12%.  Then it's still an additive 2% per shard.  So 14% on the 13th shard, 16% on the 14th shard, etc., until you reach 100% on the 56th shard.

I'm inclined to agree that the odds of pulling legendaries could stand to be a little higher.  But they do publish the odds, so they aren't being unfair about it.

Hmm, you're right... 

I tried to calculate with both the mercy system and with how much chance you have to not pull a leggo in a row but shouldn't have added up the chances. And should correct myself, as I wasn't calculating the chances from the shard, but the probability to get a leggo in a row of pulling shards.

Like the probability to get a leggo at the 12th shard if not before in a 2x is (1-0.88^12) and on the 13th shard I incorrectly added the 2% to that number (like 1-0.88^13+0.02) and so on...

So to correct it, it should read like 1-(0.88^12)*(0.88-0.02)*(0.88-0.04) at the 14th shard. Am I correct this time? 

With this, you get to the 99% probability at the 24th shard and the 100% on the 45th during a 2x event. But I reserve the right to be wrong again. 

Would appreciate the correction if needed :)

That might be correct, but it's also a bit misleading. While you're right that you can calculate the probability of an event occurring after X number of repetitions, it's misleading to think that if you had summoned 23 shards and didn't get a lego, that you have a 99% chance of getting one on the 24th.

I think you are aware of that, but I could easily see others not understanding. The 24th pull will have 20% more chance of pulling a lego, so on a 2x weekend that is 36%.

I totally agree that it sounds misleading. 

From the numbers, one lesson could be taken home: One can pull 44 shards without a leggo and that is the misfortune. Anything before that is just unlucky.

I don't think that's completly correct. But let me ask for clarification; Are you wanting to calculate the odd of getting AT LEAST ONE leggo, given the probability of getting a leggo at each independent event?  If so that is a simple calculation.

If you open 12 shards with a 12% chance of obtaing a legendary, the odd of at least one legendary are;

Odds of pulling a leggo from any single shard = 0.12

Odds of NOT pulling a leggo from any single shard = 1 - 0.12 = 0.88

Odds of not pulling a leggo from at least one of x (12) number of shards = 0.88^x = 0.88^12 = 0.216.

Odds of pulling at least one leggo from 12 shards with each independent event having a 0.12 odd of pulling a leggo = 1 - odds of no leggo = 1 - 0.216 = 0.784 or 78% chance of at least one leggo from 12 shards during a 2x event.  Pretty good odds.  If you do get a leggo it could be on the first, the twelth, or any other shard.  But 1 in 4 on average will not get a leggo, about 1 in 4 may get 2 or more leggos.

That part is pretty straight forward.  But there are a few complicatons.  First, are all 12 shards pulled during a 2x?  If so this should hold.  But if you pull 3 during no even, 2 during a 2x, 2 during a 10x, and the rest during a 2x, then the shards no longer have the same probability so the formula will not hold.

The bigger complicaction is the mercy system, once you begin adding 2% to the odds with each succesive event, the events are no longer independed.  You have the problem above compounded by lack of independence.  The formulas here are not straight forward and would require more time than I'm willing to put into it.

I agree the odds are slim.  I've kept track off all my shards for a little over a year now.  And I can say that the advertised mercy system has never failed, that it seldom if ever, in my experience, actually gets to the 100% chance of a leggo, and often I get more than expected, but other times less, and as far as I can determine, it averages out.  But yes, it is poor odds.

And unfortunately therein lies the problem. A combination of confirmation bias and selective reporting means you'll only see complaints from people who think they are unlucky, and those people will also far more often than not simply misremember.

This is compounded by the fact that people never remember the lucky moments - they ony remember the unlucky ones. For every time you pulled 30 shards before getting a lego, you'll have moments where you randomly pull one and get a lego on the "first" try.

Add to that if you pull a legendary. There is probaly on average about a 50% percent chance it will be one the puller subjectively think is bad and thus this pull will quickly be forgotten and the puller feel they pulled no legendary for a long time.

Sometimes you get 10 rares from 10 ancients, and sometimes it's like this:

i

Neither the legendary champs nore the epics are really top tier, but 3 epics and 2 legos from 10 ancients is still nice. I just want to post this pic to set a counterpart to all the cry-posts. 😭

True.  My very first shard I opened this year I pulled Soulguide.  I've only opened 22 so far and got Roxam 3rd from last.  I remember my first awesome luck maybe 2 years ago.  I opened 7 ancients and pulled Kymar and Roshcard.  Being able to look back leaves little doubt.

That's another good point. "My crappy leggos don't count!"

Why would you count the crappy Legos? 😁

Only S teir Legos are worth it 😋

You're right.  My next 2000 sacreds don't count no matter how many leggos I get, until I get Valk. Everything else is a corporate lie. lol

Plarium has for some reason decided to make void shards exceptionally rare. If you google Kizzle and void shards im pretty sure you can find a more in-depth analysis.

I play 3 accounts. 

My first account do ultra. nm. CB every day and finished both hard and normal DT last rotation. I think I got about 20 voids shards since last 2x void

My second account do NM CB every day and can only clear normal DT. That account got 10 voids shards since last rotation.

Each 2x rotation comes every six 6 weeks. That means the accounts can expect about 160 and 80 voids shards pr year. So if you only summon during 2x it is 1,6 legendary pr year and 0,8 legendary pr. year. Remember if you on average get 0,8 legendary pr. year out of a hundred people a good amount will have gotten no legendary after three years. (we are well into year 3 before mercy system triggers). I know this is not exact math and numbers can be off. But the point stand voids shard are very rare compared to the 0,5 chance of lego.

So Free to play I would not count on void shards. Think of them as non-exsisting and jump up from your chair IF you one day get a good void legendary. (Oh and only summon on 2x or maneater/Demytha 10x)