- something rotten in Denmark?

Player Experience Side:
We agree it can feel bad, regardless of the math.

~

Math Side:
The point is the math (and the tests I ran with the random data) shows that what happened is not actually uncommon or lacking in mathematical explanation as you claimed.

Can you provide mathematical proof that what you experienced is extraordinary?

Basically, you keep making the mistake that such small sample size matters when it doesn't as well as confounding the difference between dependent and independent events. The smaller the sample, the more likely you don't get the expected distribution - this doesn't make your outcome "improbable." And each pack opened is an independent event - one result doesn't affect the others, but humans think in terms of streaks and patterns.

In fact, all of this makes your outcome inevitable rather than improbable - you are just looking at it as the significant event, when it is simply part of a spectrum. Your insistence at cherry picking ONLY the data that you believe proves your point is part of the problem.

This is why studies often talk about sample sizes and confidence intervals and such things - because these are vitally important in determining whether a particular set of data is statistically significant.

I also think one of the key things I want to talk about next is dependent vs independent events, as I think that might help in this discussion given that one of the specific key arguments being made is that the specific sequence of events is what is concerning, so I will write something later today maybe, but the key is to understand that independent events don't care about patterns/sequences.

 

So to discuss Dependent vs Independent, we should start with the basic coin flipping.

Heads: 50%
Tails: 50%

(Caveat: A real coin is not actually 50%, it's close but not quite, however for the purposes of this we'll just say it is but if you are interested in that sort of thing you can look this up.)

So, if I have thrown 4 Heads in a row, what's the chance of me getting another Heads?

HHHH?

50%.

If I have thrown 2 Heads and 2 Tails?

HHTT?

Still 50%.

In fact, it doesn't matter how many times I have thrown what, the next flip is STILL 50%.

HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH HHHHH ?

50%.

This is because each coin flip is INDEPENDENT from the last, and its probability does not change based on previous results.

The thing with INDEPENDENT event with coin flips is that the chances of each specific sequence is the same as any other sequence.

HHHHH
TTTTTT
HTHTH

To calculate the probability of independent events, you simply multiply the % chance of each individual event together:

0.5 x 0.5 x 0.5 x 0.5 x 0.5

So all have the same chance of occurring:
3.125%

No matter how likely or unlikely a sequence of coin flips "looks," it has the SAME chance of occurring.

~

On the other hand, if the events were DEPENDENT, we'd have a different story.

Let's say we have 10 cards, 5 with Heads and 5 with Tails written on them, shuffled them and then dealt 5 cards from that deck.

What happens then?

Each time you dealt a Heads, you DECREASE the likelihood of the next card being Heads and increases the chance of the next one being Tails, since one has been REMOVED from the deck!

So HHHHH will have the following probability:
5/10 x 4/9 x 3/8 x 2/7 x 1/6
0.5 x 0.44 x 0.375 x 0.29 x 0.17

Or 0.41%.

Compared to HTHTH which has
5/10 x 5/9 x 4/8 x 4/7 x 3/6
0.5 x 0.56 x 0.5 x 0.57 x 0.5

Or 4%.

So if the events were DEPENDENT, then the probability changes dramatically depending on what kind of sequence it is.

~

But Pox Packs, with 10% EXO chance, isn't a coin flip, is INDEPENDENT and isn't 50/50, so how do we think about that? Coming up next!

 

To consider the Pox packs, let's consider the case of 9 Rares and 1 Exotic, in this sequence:

RRRRX
RRRRR

This matches up with our human expectation of 1 out of 10. I don't think anyone would suggest that this sequence is "improbable," right?

It should have a high chance occurring? But this specific sequence actually only has a probability of just 3.8% chance of occurring. Why is this? What about the other 96.2%?

The thing we have to realize is, there are 10 different ways we can get an X into these 10 packs.

XRRRR
RRRRR

RXRRR
RRRRR

RRXRR
RRRRR

etc.

Each of these have the same 3.8% chance of occurring. So as a result, the probability that you get exactly 1 Exotic out of 10 packs is 38% (3.8 x 10) - because there are 10 different ways you can get there.

~

It doesn't matter how much we expand this. We can look at 2 Exotics after 18 Rares:

RRRRR
RRRRR

RRRRR
RRRXX

And our human brain sees that and thinks, "that must be rare!" and it is true, the specific sequence is rare, but it is not any rarer than any other sequence that produces the exact same number of Exotics along with the exact same number of Rares.

It has the same chance as

RRRRX
RRRRR

RRRRR
RRRRX

Or

RRRRR
RRXRR

RRXRR
RRRRR

You can put the Exotics anywhere in the order.

~

If you are not convinced, you can also think about it this way:

Let's say you have 20 packs of physical cards. Because they are physical, you know the probabilities cannot be altered. If they have an Exotic, they have one, and that's not going to change no matter what happens.

So let's say you open these packs, and the first 18 had Rares, and the final 2 had Exotics. You might say, "How weird!"

But now imagine if you put the cards back into their respective packs and sealed them back up.

And then shuffled the packs and opened them all again.

We know there will still be exactly 2 Exotics out of those 20 packs.

The probability here has not changed, it is still exactly 10% of the packs will have Exotic, but the sequence is almost certainly different.

The key is that the order in which you open the packs has NO EFFECT WHATSOEVER on the overall probabilities here. Those remain exactly the same no matter what method you decide to open the packs.

 

Fun with Probabilities

 

We agree on this. I have said this 3 or 4 times already.

I don't know why you keep trying to make it sound like I disagree with you on this.

I am just disagreeing with you continuing to claim that what you experienced is extraordinary.

You claim to have experienced some "outlier" which I disagree with:

No, you weren't.

It doesn't. If you actually understood the math you would not still make this point. What you experienced was normal. It isn't a good user experience, but it isn't some unlikely event either.

 

First, there absolutely is.

That's the whole point of math and probability theory - to help us understand and describe our experiences in a way that isn't just our minds tricking us. At the same time, it could also be that the math tells you that, "hey, your feelings about your anecdotal experience is absolutely correct, it is actually a systemic problem that affects many people and can be addressed!" essentially substantiating the experience and validating it.

So I absolutely don't understand how you can write this sentence - so my only conclusion is that you meant something else. Maybe you meant to say invalidate rather than substantiate.

If you meant invalidate, then sure, we agree there, but I think even in that scenario the math understand the experience, and is relevant to discuss.

Second, no, it isn't our only disconnect. Because throughout this conversation you have repeatedly made the claim that what you experienced is out of the ordinary and cannot be explained. In fact, you originally claimed that not getting anything in 27 packs is "more than an outlier" or how you replied to @Thbigchief by saying sample size doesn't matter. These are things I cannot abide

Though I will admit in a recent reply you did at least write:

So perhaps you no longer think you experienced some outlier event (or worse, claiming that you experienced 4 of them in a row).

~

First, what you experienced IS, in fact, statistically irrelevant, that's the whole point I've been making! If I had found that you went, say, 100 packs without an Exotic instead, then it'd be statistically relevant and require further investigation from the programming standpoint to see if it was just an outlier (see, THAT would be an outlier) or if there's a systemic problem.

But this doesn't mean it isn't relevant at all from a user experience perspective. As I have said several times now, just because something isn't relevant from the math perspective doesn't mean it isn't relevant at all. It totally is a relevant problem. But considering that we already have a plan for this exact problem, it's obvious we are not just dismissing it.

Maybe part of the problem is you keep using the wrong words/terms. You claim to be arguing from a user experience perspective (which I have agreed with numerous times), but continually claim math/statistical backing for what you are saying (which is what I am arguing against).

For example, the following terms all have very specific meanings in regards to statistics and probability theory:

• outlier
• statistically significant/relevant
• sample size

So when I hear you say "outlier" to describe events that don't qualify, I take issue with that.

But maybe when you say "outlier" you don't mean outlier in the statistical sense, but it's hard to know for sure since you also claimed to have used probability math to "prove" you were an outlier (though you really proved no such thing).

In short:

1. People getting unlucky on RNG is NORMAL and EXPECTED
   • because randomness is streaky, not evenly distributed
   • someone being unlucky doesn't automatically make them an outlier
2. Being unlucky on RNG can be a negative experience
   • there are actually cases where it is actually helpful to the user experience to be unlucky with RNG, but that's a different topic
3. This can be mitigated by design/rigging
   • This is something the game previously addressed by introducing Boxes with the guaranteed EXO;
   • In addition, the Shard system was also introduced to mitigate the impact of not getting what you want from packs and give greater freedom/autonomy to players in terms of rune acquisition
   • Additionally, we already discussed the pack adjustments (for which I linked an entire discussion thread which also explains why it is being done)

Also, just to be complete with the thought:

1. People getting lucky on RNG is also NORMAL and EXPECTED
   • because randomness is streaky, not evenly distributed
   • someone being lucky doesn't automatically make them an outlier
2. Being lucky on RNG can be a positive experience
   • there are actually cases where it is actually detrimental to the user experience to be lucky with RNG, but that's a different topic
3. This is partly why Gambling in general and by extension why the Blind Repeat model often works quite well

 

Functionally, aren't you just describing the shard system?

Also, by doing this, you just make it slightly less likely to be unlucky, but you can still be unlucky, so it doesn't really solve the problem, does it?

 

As I have said, we don't disagree that there's something to be improved potentially.

I do take issue, once again, with your phrasing and terminology here... because I am not even fully sure what your sentence says. "Correlation?" Between what? "Marginal Incremental Adjustments?" What does that mean? And what adjustments? You realize that Correlation and Marginal are both specific technical terms, right? Do you mean to use them here or did you mean something else? If we are talking more "layman" usage, then Marginal Incremental just seems redundant - but since you used them both it suggests you did that on purpose...

~

That said, we can speculate based on context and assume you are talking mitigating the bad luck streaks in some way.

Let's establish some base line stuff:

First, we have already addressed this address in the most major way possible - guaranteed EXO in the boxes as I mentioned. In addition, the Shard system introduced in the last couple years ALSO help by allowing you to sacrifice unwanted runes to get what you want instead.

Second, individual pack sales account (outside of mid-terms, but those are a different structure) for very little of the game's fulfillment process. It doesn't mean it doesn't happen at all - but they are rare relative to box sales.

Third, new players overwhelming also buy boxes, and this is a problem because they have to save to buy a box (not 4-7 weeks though I am not sure how you arrived at that number, but long enough).

So what are the goals of the new pack structure then? As I said in the other Pack Update thread:

For new players specifically, this combined with the editable decks from the start eases them into deckbuilding and allows them to immediately start using runes they acquire.

In addition, the second phase of the pack updates to introduce the Pity Meter which guarantees an EXO in the next pack should have a greater, more consistent and more transparent impact than other things like increasing rates for sacrificing runes as you suggest.