On average you get one legendary in 20 packs. That doesn't mean that the probably is 5 % for each pack. Your probabilities are wrong since the probability for 40 packs is 1.
On average you get one legendary in 20 packs. That doesn't mean that the probably is 5 % for each pack. Your probabilities are wrong since the probability for 40 packs is 1.
the "1 legendary per 20 packs" is not an official blue post statement, it's based on millions of opened packs (you can find those numbers if you google them).
It's definitely not a flat (and garuanteed) number: I consider myself rather unlucky while a RL mate is extremely lucky. I'm not even close to the "1 per 20" and my mate just had another 3 legendaries within 2 packs (and he had about 1 golden legendary per 10 packs so far in old gods).
opened 65 WoG packs so far and got only 1 legendary after 37 packs. on other days i got 2 legendaries in 1 pack so it all evens out i guess but 37 sounds pretty close to the pity timer of 40 packs which i am very happy they implemented.
oh, btw op, you got the maths wrong as you started calculating starting with wrong facts, the 5.37% probability per pack means that on average in 5.37% of cases a legendary was openend, it does not say anaything about starting value and increase of probability. in fact it is 100% for the 40th pack and average of 5% is calculated by the average percentages from 40 packs
You can't really use this as basis for calculus dude.
You can't look at the statistics per pack and then calculate the chance of getting a legendary, because you can get more than one.
Each pack gives 5 cards. Each card has it's own probability. Probability and statistics are two different things and you can't use probability to infer how something will react at a larger sample size. That is the job of statistics. What you're doing is getting statistical data and using probabilities with it to reach a conclusion, when the actual procedure is the opposite.
You would need to use the probability of each card in the pack being a legendary, not the pack itself. Because each pack can have more than one legendary, the probability of getting one in 20 packs is far greater.
The probability of getting AT LEAST 1 per pack is 5%, so you can't use that data to check how many you get at more than one pack, because at the first pack you could get 2 legendaries and this 5% does not account to that. Consider that you open 20 packs, you get 3 legendaries on one of them and 2 more on two different packs. Your math will say that 3 out of 20 packs resulted in a success ("have a legendary card"). Which is okay, but it DOES NOT relate to the probability of getting legendaries on 20 packs. Because it actually were 5 legendaries, so it should be 5/20 not 3/20. That's the mistake you're making.
You can't say that the probability of getting a legendary at 20 packs is 64% because the 5% is the chance of getting at least one in a pack. When you open pack number 7 and it comes with 3 legendaries, your formula counts it as just one.
Also don't forget that sample size is important. Statistical data cannot be trusted on small sample sizes. A good rule of thumb is that 300 is a large enough sample size for most things. You can't use 20 packs and count it as a good sample size or even expect it to behave to the probabilities you have. In the end it will even out when you get to that big sample size. Until then you can't really expect math to work out.
People get at that 1 legendary every 20 packs because at many studies realized, some with over thousands and thousands of packs opened, only 1% of the cards opened were legendaries. If every pack has 5 cards, on 20 packs you get 100 cards, 1% of it is indeed 1 legendary in 20 packs.
That's the statistical data, doesn't mean that the probability of getting one legendary in 20 packs is 100%. It only means that's what you should expect to get one by then. Probability lives in the realm of the theoretical. Statistics try to get something more concrete so we can make assumptions and take minimal risks.
Lastly, a remember: the distributions here have no memory, so each pack you open doesn't increase the chance of it showing up on the next one.
On average you get one legendary in 20 packs. That doesn't mean that the probably is 5 % for each pack. Your probabilities are wrong since the probability for 40 packs is 1.
The logic behind getting at least one legendary per 20 packs is:
5% chance of a legendary per pack. Multiply this by 20 packs and that gives 100%.
Clearly, the person who came up with this hasn't taken a course in probability.
The actual odds of at least 1 legendary in 20 packs is:
1- (19/20)^20=64.15%
For 30 packs, 1- (19/20)^30=78.54%
For 40 packs, 1- (19/20)^30=87.15%
My legendary count excluding adventure legendaries, dupes and old murk eye: 40
$$$ spent on this game: 0
Check out my card collection: http://www.hearthpwn.com/members/MCFUser175154/collection
On average you get one legendary in 20 packs. That doesn't mean that the probably is 5 % for each pack. Your probabilities are wrong since the probability for 40 packs is 1.
My legendary count excluding adventure legendaries, dupes and old murk eye: 40
$$$ spent on this game: 0
Check out my card collection: http://www.hearthpwn.com/members/MCFUser175154/collection
the "1 legendary per 20 packs" is not an official blue post statement, it's based on millions of opened packs (you can find those numbers if you google them).
It's definitely not a flat (and garuanteed) number: I consider myself rather unlucky while a RL mate is extremely lucky. I'm not even close to the "1 per 20" and my mate just had another 3 legendaries within 2 packs (and he had about 1 golden legendary per 10 packs so far in old gods).
Congrats, now flaunt your math skills to things that actually matters.
Also you clearly do not know how the legendary drop rate in the game works.
My legendary count excluding adventure legendaries, dupes and old murk eye: 40
$$$ spent on this game: 0
Check out my card collection: http://www.hearthpwn.com/members/MCFUser175154/collection
opened 65 WoG packs so far and got only 1 legendary after 37 packs. on other days i got 2 legendaries in 1 pack so it all evens out i guess but 37 sounds pretty close to the pity timer of 40 packs which i am very happy they implemented.
oh, btw op, you got the maths wrong as you started calculating starting with wrong facts, the 5.37% probability per pack means that on average in 5.37% of cases a legendary was openend, it does not say anaything about starting value and increase of probability. in fact it is 100% for the 40th pack and average of 5% is calculated by the average percentages from 40 packs
You can't really use this as basis for calculus dude.
You can't look at the statistics per pack and then calculate the chance of getting a legendary, because you can get more than one.
Each pack gives 5 cards. Each card has it's own probability. Probability and statistics are two different things and you can't use probability to infer how something will react at a larger sample size. That is the job of statistics. What you're doing is getting statistical data and using probabilities with it to reach a conclusion, when the actual procedure is the opposite.
You would need to use the probability of each card in the pack being a legendary, not the pack itself. Because each pack can have more than one legendary, the probability of getting one in 20 packs is far greater.
The probability of getting AT LEAST 1 per pack is 5%, so you can't use that data to check how many you get at more than one pack, because at the first pack you could get 2 legendaries and this 5% does not account to that. Consider that you open 20 packs, you get 3 legendaries on one of them and 2 more on two different packs. Your math will say that 3 out of 20 packs resulted in a success ("have a legendary card"). Which is okay, but it DOES NOT relate to the probability of getting legendaries on 20 packs. Because it actually were 5 legendaries, so it should be 5/20 not 3/20. That's the mistake you're making.
You can't say that the probability of getting a legendary at 20 packs is 64% because the 5% is the chance of getting at least one in a pack. When you open pack number 7 and it comes with 3 legendaries, your formula counts it as just one.
Also don't forget that sample size is important. Statistical data cannot be trusted on small sample sizes. A good rule of thumb is that 300 is a large enough sample size for most things. You can't use 20 packs and count it as a good sample size or even expect it to behave to the probabilities you have. In the end it will even out when you get to that big sample size. Until then you can't really expect math to work out.
People get at that 1 legendary every 20 packs because at many studies realized, some with over thousands and thousands of packs opened, only 1% of the cards opened were legendaries. If every pack has 5 cards, on 20 packs you get 100 cards, 1% of it is indeed 1 legendary in 20 packs.
That's the statistical data, doesn't mean that the probability of getting one legendary in 20 packs is 100%. It only means that's what you should expect to get one by then. Probability lives in the realm of the theoretical. Statistics try to get something more concrete so we can make assumptions and take minimal risks.
Lastly, a remember: the distributions here have no memory, so each pack you open doesn't increase the chance of it showing up on the next one.
Unless the next one is the 40th pack ^_~
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Weeeeell... There's no proof to that, right?
I mean... Statistically you should get 1 legendary after 40 packs anyway.
It might just be math doing it's thing, I'm not so sure there is a system in place for that.
I'm skeptical, but if it's there, cool. Better for everyone.
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