4.6 gets rounded to 5. Thats just common math rule when only whole numbers are possible.
Its good everyone is pointing out that your result is just around average. Because it shows to everyone how bad the average value is. Thx to everyone for helping in pointing this out.
But we are still lucky,because it could have been much worse.
An argument you will hear increasingly often from politicians in the next few years.
Not in this case. You cant get .6 of a card, so it gets rounded down to 4.
I messed up on a variable in my previous reply and deleted it.
Anyways this is what I am talking about, I am not disputing that 4.6 in 92 is the average, I am talking about 3 in 91 being below average, which I donât know why you are disputing with me about when it is very clearly much below average.
Also, since this is bothering me. Ignoring the first guaranteed legendary does not create a âfake crisis,â but rather highlights the expectation of additional legendaries through regular probability. The argument hinges on understanding that the total expected legendaries, considering all packs, should be viewed in context of both pity guarantees and the probability drop rate. Anyways, hereâs the calculation now:
Thus, within 91 packs:
P(X=1)=(911)â (0.05)1â (0.95)90
Breaking this down:
So: [ P(X=1) = 91 \cdot 0.05 \cdot 0.007 \approx 0.03185 ]
The probability of opening exactly 1 additional legendary card in the remaining 91 packs, given the 40-pack pity timer and regular 5% drop rate, is approximately 3.2%.
Therefore, the probability of opening exactly 3 more legendary cards (totaling 4 legendaries including the one from the first pack) in the remaining 91 packs is around 3.2%.
In a group of 100 people, approximately 3 to 4 people would open exactly 3 more legendary cards in 91 packs under these conditions.
The fact that you had a legendary on your first pack makes you lucky. Most wonât have that luck. Afterwards you were a bit unlucky, but still OK.
But thatâs not at all how averages work.
Four or five is the most common answer, with five being fractionally more likely, but four being nearly as common.
You donât round an average like this because it will set false expectations.
They could have gotten two, so this is actually correct.
It also could have been much better⌠but it wasnât this time⌠which is how random works.
Because youâre not reflecting accurate information and cherry picking your answer.
Include all your packs, not just the ones that make you seem right.
That said, you didnât open 120 packs, which is three pity times so youâre ahead of where you could have been.
Your result is average no matter how much it makes you mad.
And you got three in 90, which is exactly what you should have gotten, but really itâs four in your total packs which is, again, absolutely normal.
What a joke.
So you got super lucky and got one on the first open, but want to ignore that.
The pity time was 3 in 120, so youâre ahead of that curve not behind it.
No, we donât. You just need this to be a thing so you can cry that you were ripped off, but you werenât.
This is just ridiculous and not how it works. With this formula you will have a small chance for every value you put in.
This is absolutely ridiculous and wrong. Itâs not how the drop rate works and it ignores the fact that you got four in 92 to cherry pick your point.
You have no point other than to cry about your âbad luckâ thatâs not actually bad.
So you were lucky and pulled a Legendary in your first pack and are upset that RNG âbalancedâ itself out and in the end got the the average like you were supposed to? no wonder Carnivore argues with you about RNG so much you clearly donât understand it
How is 3 in 91 average? You keep saying this over and over but have not once used any data to back up your answer, and I have shown multiple times now that 3 in 91 is below average. You keep referencing 4.6 being the average in 92 so surely you can also use your brain and apply that same calculation to 3 in 91 but you keep just saying 3 is average in 91. Furthermore I played multiple tavern brawls yesterday and it actually went to 3 in 113 packs before I opened a 4th legendary there.
You cannot just separate 3/91 from 4/92, the way probability works you should calculate the frequency between legendaries as well, not just the total pulled. With your logic it is like saying
âI played sunset volley and 5 shots hit the 1 minion on board as well as 5 shots hitting face, which is what is the average outcome with 1 minion on the board,â
but you disregard that in that scenario 5 shots in a row could have hit face on a 50/50 and then 5 shots in a row could hit the minion which is statistically only a 1/1024 chance for that exact outcome. Your logic just looks at the whole fraction and disregards the intricacies of probability within the repetition itself.
This is why you calculate for the exact outcome in the scenario given the data available and not the average outcome. Calculating an exact outcome given these parameters indeed indicates 3-91, given 2 legendaries being guaranteed in 91 packs is far below average probability. On average in 91 packs you would open 4.5 legendaries or in 910 packs you would open 45, not 30.
But you are doing exactly that because you have to for your example to work.
And you donât understand how that works? Blizzard has told us you should pull one legendary every twenty packs on average. You have 92 tries divided by the average is 4.6⌠you have four legendaries⌠you hit the average which will either be four or five legendaries⌠you got four. Nothing to see here.
Your entire calculation is wrong, though, because the chance to pull a legendary card in your packs is not static.
The pity timer may have dropped your legendary in the very next pack you open and then, again, this whole discussion is moot because your back at the average or ahead of it with FIVE legendaries in 93 packs.
Youâve got your knickers in a twist because you think blizzard owes you one more yellow card, and thatâs just sad.
I think I just showed you right above this how itâs actually you doing this.
I meant that you cannot disregard one in favor of the other, not that you cannot separate them as 2 different probabilities. You are disregarding one for the other, when it is much more complex than just looking at the total. Which is what I was trying to show you with the example of Sunset Volley where the total of 5 hitting each target is statistically average, but the repetition probability is where things gets very unlikely. It is always more complicated than just looking at the total and disregarding the other details like you do
No, dude, I am not. I am including it because it has to be.
The average includes all packs opened of a given type. That first ten lego is part of that twenty pack average. You leaving it out makes the whole thing wrong.
No, thatâs not what this is about. You are here ignorning that the first five hit the minion and complaining about bad rng/low probability because the next five hit the face - completely ignoring those first five.
You mean like ignoring that the probability to have a legendary in your pack changes over time? That itâs a dynamic effect that increases that chance the longer youâve gone without a legendary pull? Because thatâs not in your calculation.
Without knowing exactly which packs in the middle had legos, itâs hard to understand much about your pulls. Did you get two in first twenty and then none in 39 so that youâre right on the pity time in this next pack?
Edit: Wait⌠are you the same dude who thinks youâre not pay to play if you only spend $10 a month? Because this discussion reeks of that sort of failed logic bad justification for an horrible take.
Once again, Iâm probably not gonna read everything in this topic, including your replies to stgange posts â thus Iâm sorry if I missed something meaningful (by the way, the maths in your post doesnât look very readable to me, sorry; even if you used LaTeX notation everywhere, thatâd probably be easier for me to understand). Nevertheless, lemme point out something related to the substance of the matter:
I donât get it.
If you wanna account for pity timers (good point, I havenât thought much of it), you probably gotta use conditional probabilities. For example:
P(X legendaries) = P(hitting 0 pity timers) * P (X leg. | 0 pity timers) + P(hitting 1 pity timer) * P (X leg. | 1 pity timer) + P(2 pity timers) * P (X leg. | 2 pity timers) + âŚ
Admittedly, it might get cumbersome, but it looks like a proper rigorous way to account for pity timers to me. Am I missing something?
Apart from this little problem, thereâs another non-mathematical aspect where I think youâre making another mistake (the first one being that âstepping of the same rakeâ with those packs, as discussed above) â I hope you donât mind my pointing it out. Namely, youâve chosen to embark on conversations with very strange characters (persons or chatbots, I dunno) seemingly producing nothing but meaningless âword saladâ (because banana phlegm, farthing flymumâŚ) of supposedly inflammatory (?) nature â and in large quantities at that. I donât think this is going to take you anywhere if you wanna discuss your results or calculations (those forum âpunditsâ also tend to have a zero mathematical aptitude, as well as an intellectual one in general â why, not even something in the department of common sense and decency, it would seem⌠but I digress a bit). Youâre your own man, of course, but please donât tell me I didnât warn you 
if this topic results in ten more pages of:
Maragibo, safluses!
Hergling flur dianomomo.
Coconut⌠boot⌠kahoogling.
Ah, cowda hericken zar zar.
Last expansion they changed the guaranteed drop rate for Signature legendary from 1 in 181 to 1 in 361. This coincides with the drop rate overall going to 0.6%. They did this to match the drop rate for a Golden Legendary from a pack odds.
Apparently before this change a Signature legendary had exactly the same odds to be in a pack as a regular legendary except it was calculated each time for each common within a pack. Thatâs why so many more legendary signature cards were dropping from packs. It was apparently never supposed to be like this.
That makes it significantly harder to finish a whole set now versus how much easier it was when signatures first went live.
Hearthstone is a gacha collecting card game. You think you deserve more.
I wasnât factoring in pity timers in my previous calculation, where I said that the average is 4.6.
First, my assumptions:
Source for assumptions: https://hearthstone.fandom.com/wiki/Card_pack_statistics
If those above assumptions hold, then the average number of Legendaries in your first 92 packs of an expansion is about 5.97, with a min-max range of 5.57 to 6.27. So basically an average of six. In 91 packs after youâve already gotten your first Legendary, the average for additional Legendaries is about 5.39, with a min-max range of 4.96 to 5.71; therefore, opening that Legendary in the first pack doesnât really take the expectation higher than 6 total, because the 10 pack pity timer is gone.
Where?
Are you trying to âreinventâ the binomial distribution, btw?
Ugh, if youâve gotta cite a wiki, why not use the current, as opposed to the outdated, one? Replace that fandom.com with wiki.gg, and there you go.
So if your shelling out that much dough, it behooves you to buy golden packs. Just straight up golden packs, at a large amount will net you more dust than the equivalent amount (4 times more) of regular packs. If nothing else my understanding the pity timer for a legendary is ten packs with golden packs and 40 for regular packs, so you should at least buy ten golden packs, or maybe eleven to be sure, then do whatever you want with the rest of the money.
The most Iâve spent on this game is 15 dollars way back when classic was standard, so I canât say I know the feeling. But any low roll when you spend that much money feels bad man.
Iâm pretty sure there are countries that ban Hearthstone because buying packs is effectively gambling.
Itâs around 0,26%
Which is crazy, because that happens to me all the time, although not while buying packs, ofc, since I would never do that.
I actually have no idea why youâre complaining. If you were really unlucky you would only have the minimum 3 legendaries. You got 4. Since playing on this account since November 2021 Iâve hit the pity timer a lot. It can happen. Just like the fact that I got lucky ones and got a signature and a legendary in 1 pack.
remove the 0, or the % sign.
Its a 1 in 4 chance, which is (un)shockingly common. it happens 1 time out of 4!
Ive opened 15-20 packs from the brawl and somehow i got 3 legendaries off of that xD
None of them that i want to use but still pretty lucky rolls for me so far