Krama, it does NOT work like that because there is an UNLIMITED number of champions to be drawn from. I have 100 sacred shards, every hour I use ONE. The odds are exactly the same...6%. Nothing changes. There is always the exact percentage of Legos to voids to rares. If we use your logic then you are validating my argument that the draw IS rigged because with 200 shards I would have a 63% chance! You have the EXACT same chance no matter the number of shards.

You are mistaking probability with odds.

Please try reading an article like this. Maybe it will help: https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_confidence_intervals/BS704_Confidence_Intervals10.html

Oh, my dude, I definitely don't look foolish.

Lets go back to some basics about how percantages work so we can examine why the odds are the way they are. We can start with some dice rolls for you, since you are familiar with dice by working in a casino.

i

As you can see from the above graphic, we are examining the odds of rolling a 5 on a 6 sided die. Everyone would agree the chances of getting a 5 on a single roll is 1/6 or 0.167.

5/6 = Chance of rolling anything else

1/6 =Chance of rolling a 5

So how do we examine the odds of getting a 5 on one die, then picking up a second die and also getting a 5 when we roll it? Well, just like the previous die, the new die has a 1/6 (0.167) chance of rolling a 5.

But how do we calculate how often we should see BOTH die roll a 5? Well, since they are independent events, we take the probability of the first event and then basically combine that with the probability of the second. We do that combination with multiplication.

1/6 x 1/6 = 2.78%

So we take that 1/6 from the first roll and multiply it against that 1/6 from the second roll. 1/6 x 1/6 = 1/32. 1/32 is 2.78%. Our chances of rolling the first five then the second five is 2.78%.

Now lets expand that into Void Shard pulls for Raid, during no events, like you are pulling on. The odds of pulling a legendary champ is only 0.5. So we have on one side 99.5 percent chance to not pull a legendary with a void shard, and 0.5 percent chance to pull a legendary.

0.995 = Chance to get a Void Rare or Epic

0.005 = Chance to get a Legendary

So when we pull once we have only a small chance of getting a legendary. When we pull a second time, just like in the dice example, we have that same small chance again. On BOTH events, you have a 0.995 chance to get a Rare or Epic.

In our die example, we looked at two 1/6 chances, and figured out that it was a 2.78% chance to get that to happen twice in a row. In our Raid example, we are going to look at the chances of getting a Void Rare/Epic twice in a row.

0.995 x 0.995 = 0.990

When we pull two shards, we have a 99.0% chance to end up with only Rare or Epic champions after those two pulls.

Pulling three shards:

0.995 x 0.995 x 0.995 = 0.985  A 98.5% chance to end up with only Rares and Epics

Pulling four shards:

0.995 x 0.995 x 0.995 x 0.995 = 0.980  A 98.0% chance to end up with only Rares and Epics 

Now we keep doing this, in your case, until we get all the way out to 107 Void Shards, we express multipling something (lets call it Y) by itself X number of times like this: Yˣ

That means getting nothing but epics and rares during 107 Void pulls is expressed like this: 0.995¹⁰⁷ 

 0.995¹⁰⁷  = 0.584  This is a 58.4% chance we end up with nothing but Epics and Rares after pulling 107 shards

And if we have a 58.4% chance of only getting Rares and Epics, then 100-58.4 = 41.6, we have a 41.6% chance to pull at least one legendary over 107 Void shards.

So yeah, Krama rounded up to 42%. But that seems fairly appropriate given your initial post was about pulling 107 void shards and getting no legendaries, and the probabllity of that happening was 58.4%.

OMG you are all crazy, lol. NOTHING changes ok, nothing. I am a craps floor supervisor. I had this debate with a vice president of gaming 30 years ago. I said the odds of someone rolling a hard 10 (5 x 5) are 8 to one. Each individual roll is 8 to 1. Now, what are the odds of someone rollin a hard 10, 10 times in a row. He said they are the same as one roll. He was wrong and you are also. It is like  the exact same lottery numbers coming up 10 times in a row, not gonna happen right? Why? The odds/probability are worse. If I put 100 buckets of 100 golf balls in my back yard. Each bucket has 6 gold balls, the others don't matter. Ceteros paribus, what are the odds of you pulling one gold ball from one bucket, 6% then you get to draw again oh but wait, I put another ball back in the bucket what are the odds now, hmm 6%. We go through this 107 times. Everytime you draw I put the exact same golf ball back in the bucket, what are your odds of pulling a gold ball....6%. It doesn't matter whether you draw once or 1 million times the odds are exactly the same. The probability only comes into play when you draw a gold ball and say what is the probability of drawing another gold ball from another bucket or all 100 buckets, same argument as rolling a hard 10, ten times in a row. Each single individual draw for a sacred shard is EXACTLY the same odds as the previous one. The probabliity ONLY comes into play after you draw the first lego and try to get more, the odds stay the exact same but the probability goes down. Now, my argument is that out of 107 draws and getting skunked is not just unlucky with a 2x event. Something else is in play.

Your odds of getting a legendary from a sacred shard from your first pull is 6%. Your odds of getting a legendary from your 100th pull is 6%. Your odds of HAVING a legendary AFTER 100 PULLS is 99.8%.

WE ARE NOT SAYING THAT YOUR 100TH PULL WILL HAVE A 99.8% CHANCE OF GETTING A LEGENDARY.

WE ARE NOT SAYING THAT AFTER 100 PULLS, YOUR NEXT PULL WILL HAVE A 99.8% CHANCE OF GIVING YOU A LEGENDARY.

We are saying that AFTER THOSE 100 PULLS, 99.8% of the time you will have received a legendary FROM ONE OF THOSE 100 PULLS.

Sorry, I was speaking of Sacred shards, the odds of getting a lego with a void are .5% 1% on a 2x

Let's try this a different way. If 100 people pull 107 void shards on a 2x void weekend, 65 of those 100 people will have a legendary void champ after pulling those 100 voids, and 35 of those 100 will not. You were one of those 35.

Does that make more sense? 

What? The odds are the same 6%. You are twisting your odds and probability. 6% from each individual draw is 6% because the pool of champions is the same. Each draw is a single draw they are seperate.

Where do you guys get these numbers, all the draws are individual, no 65 no 35. With every draw if you draw a sacred the probability of drawing another goes down. Other than that you have a 6% chance on each draw, that's it, simple. 

Let's get 100 people and give them 107 voids. I will bet you 10k that 65 of those do not have a sacred after their draws. Bet? lol

Actually, I would bet that hardly any have a sacred. 

The probabliity ONLY comes into play after you draw the first lego and try to get more, the odds stay the exact same but the probability goes down. 

The lack of understanding you show here is really unfortunate. The fact you haven't looked back and reexamined your mathmatical conceptual misconceptions from a 30 year old conversation with a Vice President is troubling, but we're ONLY here to talk about math I guess, not the times people prevent their own upward mobility.

"Quinnie," my grandfather always used to say. "You have to watch out for people who know just enough to be dangerous." 

As I explained above, you pullled 107 shards and got only Epics and Rares. We did the math to see what the chances of that happening were, and it was 58%. I am not sure I can illustrate the concepts any differently for you, not in this medium, not without you visiting during office hours so we could get back to the basics and work through more problems.

The only person you are hurting by being wrong on this is yourself, but I did want to take the time to break down the reality of how this works for anyone else reading later. :)

Oh buy queenie, you are so smart. You are the one that is just smart enough to be dangerous. I will come to your office and we will do the golf ball and bucket test. If you are right I will give 10k if you are wrong you take your self out of the gene pool, right then. Deal?

I am not a math guy, I come from a family of attorneys. I was a history major with a minor in philosophy, but then I made a ton of money in real estate and the stock market. Easy math, buy low sell high. 6% on each individual draw is 6%. No change to the odds, and really no change to the probabiliy either. What If I use one shard evey decade?

No. Of course I wouldn't bet. Because there's a ton of other statistical stuff to add onto that equation, with respect to standard deviation, degrees of confidence, etc. I'm giving you an ultra simplistic scenario to try to help you understand how this stuff works.

However, yes, I can 100% guarantee you that *roughly* 65 of those people will have a legendary after those 100 draws, and *roughly* 35 will not. Will it end up being 62 and 38? Or 70 and 30? Or even 90 and 10? Sure, those are all possible.

Do that exact same run a thousand times, and you'll get closer and closer to the 65-35 result.

Here's a great way of visualizing it:

https://seeing-theory.brown.edu/basic-probability/index.html

Take a look at the "Expectation" one in particular. Note how the expected value from a dice roll is 3.5. Note how as you roll the dice more and more, you'll get closer and closer to that expected value of 3.5. This is exactly what we're trying to explain to you.

It really shows that you are not a math guy. 

You do not understand the concept, that we are actually showing you, that the odds of pulling a leggo from a sacred or an ancient remain the same. But we calculate the probability of having a leggo after pulling a number of shards. 

For a single draw, the odds remain the same....but if you pull 100 ancient shards, you will have 100 times the odds of 0.5 % to pull a leggo. The probability is higher since with the number of shards pulled, the probability will get higher. 

Simple example: 

Roll a six-sided die once. The odds to get a 6 on your roll are 16.7%

Roll a six sided die once again. The odds to get a 6 is 16.6% again. The probability to NOT get a 6 has been reduced. 

If you now roll the six-sided die 20 times, the probability that you do NOT have a 6 rolled on one of those rolls is (5/6 [odds of not getting a 6])°20 = 2,6 %

Neither of your or your family experiences and knowledge has anything to do with probability. I have a master degree in mechanical engineering...somehow I suspect that I know maths better than you do. 

You can also rant about our numbers being not correct...the point is, Krama was spot on with his numbers the first time. If you cannot distinguish between odds and probability, neither degree in history or philosophy will help you.

No, the dice roll does not change the odds, ever. I am an expert at what is known as game protection. With more rolls of the dice the true odds come into play. An individual may roll the dice for 2 hours, he/she may roll 5 hard 8's out of 10 rolls. But all that must be made up, which is basically what you are saying. My argument is that 65 out of 100 is wrong because void shards have only a 1% chance on 2x days for each individual draw. And each individual draw is just that...individual. No two draws are connected in any way. My shards and draws have nothing to do with yours or hers or anyone elses. Now from a corporate view I understand what you are trying to do. In the casino world we have what is called a "hold percentage" how much of that guests $100 will we hold, and typicall we want 85%. So we can bring in games that have a higher hold and we count the guests as one. BUT, how do we know when someone is cheating? Lots of ways actually, but winning a higher percentage than what they should be at for their buy in is big giveaway. This is called the Theoretical. So, my point is not hitting a sacred on a void, I understand I really do. Ther only reason I bought them again is because I had to, to get the sacreds. My problem is really with getting only 3 lego, from over 200 sacreds at 12%. And others going 5 for 5. I spend and they don't, kind of odd wouldn't you say?

For hoe long do you get highest chest of UNM ClanBoss and do not receive a Sacred shards? I experienced times of 2-3 weeks without a sacred shard...but it is important to note that you can only get them from the highest chests from NM or UNM CB-

The resort to "We'll bet and if you're wrong you'll kill yourself!!" is a bit dramatic, don't you think? And not necessary.

I am confident in my knowledge of very basic math. 

Kram, let's take a million people then, lol