I want to know the probability of opening Illidan Stormrage, Tinkmaster Overspark and two Nat Pagles out of 32 packs. That's a whole lot of useless legendaries right thurr. At least I turned them all into a TBK.
This can't be calculated unless you provide your % distribution of useless legendaries % of all legendaries useful legendaries % of all legendaries
These are unique, subjective % unique to you.
After that, we could use the transform ratio of useless legendaries -> useful legendaries 4 :1
@ pilleri: i dont really trust the reddit post. it arrives at similar conclusions on many things, but i see a lot of assumptions here and a lot of calculations where i dont see what it is based on. like the chances for a common/rare/epic/legendary to get advanced to the golden version.... no source, just educated guesswork. he uses a dataset of 1143 expert packs, assembled from youtube.
i use this dataset: http://www.4shared.com/web/preview/pdf/mCdvUh9Wce i like that the dataset is huge, and that no assumptions are being made. all they did is to look for forum posts or youtube videos where people share their expert pack opening experience, and most time has been spent on making sure these smaller datasets are not fake and not duplicates. and so the author managed to get a decent dataset that covers a whopping 11359 expert packs. and all the small datasets that he used are linked as sources, and you can still check them. the author did not bother to make assumptions on how the "1 rare or better per card pack" works, or how the golden cards are implemented, all he does is to give us the averages of the huge dataset he assembled.
there are some contradictions between the reddit post and the numbers from the huge dataset. the reddit post got :"3.67 commons are in a pack, on average, 1.33 rares or better are in a pack, on average". the big dataset arrived at 3.50 versus 1.50 for that. the reddit post claims that legendarys contribute more dust than the other raritys. the big dataset shows that non-golden rares, epics and legendarys contribute averages of 21.4, 21.4 and 21.6 dust per pack, so its the same. for golden rares, epics and legendarys the averages are 6.85, 6.16 and 8.88, these numbers might also be the same in reality, because we know that there are only 63 golden legendarys in the dataset.
i have to say i trust the big dataset more. but the final conclusions are quite close. average dust value 107 versus 108-109, golden legendary every 180 or 188 packs, both agree that you get a legendary every 19 packs.
the data is good. we have big datasets that are in close agreement on many important stats. since i started playing, it always bothered me that there is no large dataset and that we dont know for sure what the odds for the expert packs are. it seems like this problem is now solved.
I looked at this card originally and I thought, you know, it's a card, and you play this card. The card will be that card that you play so you're playing a card. So, it is one thing to play a card. If you're opponent doesn't really have any cards, the card will screw up the card pretty hard, and that means it's a pretty good card.
there are some contradictions between the reddit post and the numbers from the huge dataset. the reddit post got :"3.67 commons are in a pack, on average, 1.33 rares or better are in a pack, on average". the big dataset arrived at 3.50 versus 1.50 for that. the reddit post claims that legendarys contribute more dust than the other raritys. the big dataset shows that non-golden rares, epics and legendarys contribute averages of 21.4, 21.4 and 21.6 dust per pack, so its the same. for golden rares, epics and legendarys the averages are 6.85, 6.16 and 8.88, these numbers might also be the same in reality, because we know that there are only 63 golden legendarys in the dataset.
I agree that a larger data set is better, and that the OP is generally more valid and sound than the reddit post.
However, most of the numbers you used in the comparison are incorrect. Meaning that you have chosen to use figures which can not be meaningfully compared. Let me illustrate.
As I said before, in the reddit post commons = C + G.C rares = R + G.R epics = E + G.E legendaries = L + G.L
Now, to get some comparable values:
in the OP data, the rate of commons = C + G.C is not 3.50. This is C only. Therefore, the rate of commons in the OP is C + GC = 3.50 + 0.0735 = 3.5735 per pack. This value is comparable with the reddit post (3.67 per pack).
the rate of rare or better is therefore 5 - commons = 5 - 3.5735 = 1.4265 per pack. This value is comparable with reddit (1.33 per pack).
From here, we can see that the 30.48 of legendaries is larger than the epics, rares or commons. This is in line with what the reddit poster argued: legendaries (L + G.L) contribute more to expected dust amount than any other rarity.
In reddit, commons = C + G.C = 3.67232 * 5.9 = 21.67 rares = R + G.R = 1.32768 * 19.2 = 25.49 epics = E + G.E = 1.32768 * 19.2 = 25.49 legendaries = L + G.L = 1.32768 * 20.8 = 27.62
27.62 is a larger figure than any of the others. So both reddit and the OP agree that legendaries contribute more than commons, rares or epics.
Now, to calculate the dust per pack using comparable formulas:
reddit: (3.67232)(5.9) + [1.32768](19.2 + 19.2 + 20.8) NOTE: the reddit poster had f'd up his own dust calculation, see bold, which certainly does not add credibility to his claims. = (3.67232)(5.9) + [1.32768](19.2 + 19.2 + 20.8) = 21.67 + (25.49 + 25.49 + 27.62) = 21.67 + 78.60 = 100.27 = 100 dust per pack (rounded down)
Next, evaluating the reddit poster's theory about golden card ratios.
versus OP: G.C:C = 1.47 : (70 + 1.47) = 1.47 : 71.47 = 0.020568 <- very close to the reddit assumption of 0.02 G.R:R = 1.37 : (21.4 + 1.37) = 1.37 : 22.77 = 0.060167 <- 0.06 is significantly different from the reddit assumption of 0.05 G.E:E = 0.308 : (4.28 + 0.308) = 0.308 : 4.588 = 0.067131 <- very close to the reddit assumption of 0.0667 G.L:L = 0.111 : (1.08 + 0.111) = 0.111 : 1.191 = 0.093199 <- 0.7 % units off from the reddit estimate of 0.10. However, gold legendaries are so rare that I guess this difference can be due to natural variance.
From here, we can see that the OP data set actually confirms the following ratios from reddit: Common: 1 in 50 is gold (2%) Epic: 1 in 15 is gold (6.67%)
Potentially confirms (as the MythBusters say, "plausible") Legendary: 1 in 10is gold(10%)
But invalidates Rare: 1 in 20is gold (5%) -> In reality, 6% is gold (1 in 16.67)
Much of the reddit calculations seem to be based on this assumption: "We would therefore expect the [non-golden] rare:epic:legendary ratio to be (20/25):(4/25):(1/25) = 20:4:1 which it is!
The OP has the following ratios for non-golden rare:epic:legendary = 21.4 : 4.28 : 1.08
Comparisons:
reddit: epic to rare = 4:20 = 20.0% legendary to epic = 1:4 = 25.0% legendary to rare = 1:20 = 5%
OP: epic to rare = 4.28 : 21.4 = 20.0% legendary to epic = 1.08 : 4.28 = 0.25233 = 25.2%, IMO "close enough" to 25% legendary to rare = 1.08 : 21.4 = 0.050467 = 5.04%, IMO "close enough" to 5%
tl;dr Based on the OP, rare:epic:legendary ratio = 20:4:1 (confirms reddit) Common: 1 in 50 is gold (2%) (confirms reddit) Rare: 6% is gold (1 in 16.67) (reddit incorrectly assumed 1:20 = 5%) Epic: 1 in 15 is gold (6.67%) (confirms reddit) Legendary: 9.3% is gold (reddit assumed that 1 in 10 is gold (10%), which is quite close since golden legendaries have a lot of variance)
1 in 19/20 packs should have a legend? Well that sucks. I've only hit 4 legends so far in about 140-150 packs: 2x King Krush, then a tink, then a Gromash. Here's hoping the next 140-150 fall in line with the expected stats!
I once pulled a Golden Onyxia and a Golden Gorehowl from the same pack with some other rare (that didn't seem important to me at the time) as well. ( I DE'd the Golden Onyxia for a Leeroy, and still have the Gold Gorehowl.) Can someone calculate what percentage chance that was? I'm thinking that will never happen again. (on a happy note, I let my Four Year Old, click those cards open for me...she was so happy about how excited I got.)
My seven-year-old actually plays with me frequently. He has learned my card pack opening ritual, which starts in the top-right, and then bottom-left, top, bottom-right and top-left. At first, we just hover over the cards, then we click on the common ones first, then increase in rarity. It is fun to watch him open his own packs on the iPad the same way. He got his first legendary (probably about 25 packs in) and it was Malygos. On a side note, he is already level 18 this season and is currently on a win streak lol. It's amazing how even a seven-year-old can grasp the concepts of the game and do well in the higher ranks.
My seven-year-old actually plays with me frequently. He has learned my card pack opening ritual, which starts in the top-right, and then bottom-left, top, bottom-right and top-left. At first, we just hover over the cards, then we click on the common ones first, then increase in rarity. It is fun to watch him open his own packs on the iPad the same way. He got his first legendary (probably about 25 packs in) and it was Malygos. On a side note, he is already level 18 this season and is currently on a win streak lol. It's amazing how even a seven-year-old can grasp the concepts of the game and do well in the higher ranks.
This can't be calculated unless you provide your % distribution of
useless legendaries % of all legendaries
useful legendaries % of all legendaries
These are unique, subjective % unique to you.
After that, we could use the transform ratio of
useless legendaries -> useful legendaries
4 :1
@ pilleri: i dont really trust the reddit post. it arrives at similar conclusions on many things, but i see a lot of assumptions here and a lot of calculations where i dont see what it is based on. like the chances for a common/rare/epic/legendary to get advanced to the golden version.... no source, just educated guesswork. he uses a dataset of 1143 expert packs, assembled from youtube.
i use this dataset: http://www.4shared.com/web/preview/pdf/mCdvUh9Wce i like that the dataset is huge, and that no assumptions are being made. all they did is to look for forum posts or youtube videos where people share their expert pack opening experience, and most time has been spent on making sure these smaller datasets are not fake and not duplicates. and so the author managed to get a decent dataset that covers a whopping 11359 expert packs. and all the small datasets that he used are linked as sources, and you can still check them. the author did not bother to make assumptions on how the "1 rare or better per card pack" works, or how the golden cards are implemented, all he does is to give us the averages of the huge dataset he assembled.
there are some contradictions between the reddit post and the numbers from the huge dataset. the reddit post got :"3.67 commons are in a pack, on average, 1.33 rares or better are in a pack, on average". the big dataset arrived at 3.50 versus 1.50 for that. the reddit post claims that legendarys contribute more dust than the other raritys. the big dataset shows that non-golden rares, epics and legendarys contribute averages of 21.4, 21.4 and 21.6 dust per pack, so its the same. for golden rares, epics and legendarys the averages are 6.85, 6.16 and 8.88, these numbers might also be the same in reality, because we know that there are only 63 golden legendarys in the dataset.
i have to say i trust the big dataset more. but the final conclusions are quite close. average dust value 107 versus 108-109, golden legendary every 180 or 188 packs, both agree that you get a legendary every 19 packs.
the data is good. we have big datasets that are in close agreement on many important stats. since i started playing, it always bothered me that there is no large dataset and that we dont know for sure what the odds for the expert packs are. it seems like this problem is now solved.
Link not valid.
I looked at this card originally and I thought, you know, it's a card, and you play this card. The card will be that card that you play so you're playing a card. So, it is one thing to play a card. If you're opponent doesn't really have any cards, the card will screw up the card pretty hard, and that means it's a pretty good card.
I agree that a larger data set is better, and that the OP is generally more valid and sound than the reddit post.
However, most of the numbers you used in the comparison are incorrect. Meaning that you have chosen to use figures which can not be meaningfully compared. Let me illustrate.
As I said before, in the reddit post
commons = C + G.C
rares = R + G.R
epics = E + G.E
legendaries = L + G.L
Now, to get some comparable values:
in the OP data, the rate of commons = C + G.C is not 3.50. This is C only. Therefore, the rate of commons in the OP is C + GC = 3.50 + 0.0735 = 3.5735 per pack. This value is comparable with the reddit post (3.67 per pack).
the rate of rare or better is therefore 5 - commons = 5 - 3.5735 = 1.4265 per pack. This value is comparable with reddit (1.33 per pack).
In the OP,
commons = C + G.C = 3.50 * 5 + 0.0735 * 50 = 17.5 + 3.675 = 21.175
rares = R + G.R = 1.07 * 20 + 0.0685 * 100 = 21.4 + 6.85 = 28.25
epics = E + G.E = 0.214 * 100 + 0.0154 * 400 = 21.4 + 6.16 = 27.56
legendaries = L + G.L = 0.054 * 400 + 0.00555 * 1600 = 21.6 + 8.88 = 30.48
From here, we can see that the 30.48 of legendaries is larger than the epics, rares or commons. This is in line with what the reddit poster argued: legendaries (L + G.L) contribute more to expected dust amount than any other rarity.
In reddit,
commons = C + G.C = 3.67232 * 5.9 = 21.67
rares = R + G.R = 1.32768 * 19.2 = 25.49
epics = E + G.E = 1.32768 * 19.2 = 25.49
legendaries = L + G.L = 1.32768 * 20.8 = 27.62
27.62 is a larger figure than any of the others. So both reddit and the OP agree that legendaries contribute more than commons, rares or epics.
Now, to calculate the dust per pack using comparable formulas:
OP:
21.67 + (28.25 + 27.56 + 30.48)
= 21.67 + 86.29
= 107.96
= 108 dust per pack (rounded up)
reddit:
(3.67232)(5.9) + [1.32768](19.2 + 19.2 + 20.8)
NOTE: the reddit poster had f'd up his own dust calculation, see bold, which certainly does not add credibility to his claims.
= (3.67232)(5.9) + [1.32768](19.2 + 19.2 + 20.8)
= 21.67 + (25.49 + 25.49 + 27.62)
= 21.67 + 78.60
= 100.27
= 100 dust per pack (rounded down)
Next, evaluating the reddit poster's theory about golden card ratios.
reddit:
G.C:C = 1:50 = 2%
G.R:R = 1:20 = 5%
G.E:E = 1:15 = 6.67%
G.L:L = 1:10 = 10%
versus OP:
G.C:C = 1.47 : (70 + 1.47) = 1.47 : 71.47 = 0.020568 <- very close to the reddit assumption of 0.02
G.R:R = 1.37 : (21.4 + 1.37) = 1.37 : 22.77 = 0.060167 <- 0.06 is significantly different from the reddit assumption of 0.05
G.E:E = 0.308 : (4.28 + 0.308) = 0.308 : 4.588 = 0.067131 <- very close to the reddit assumption of 0.0667
G.L:L = 0.111 : (1.08 + 0.111) = 0.111 : 1.191 = 0.093199 <- 0.7 % units off from the reddit estimate of 0.10. However, gold legendaries are so rare that I guess this difference can be due to natural variance.
From here, we can see that the OP data set actually confirms the following ratios from reddit:
Common: 1 in 50 is gold (2%)
Epic: 1 in 15 is gold (6.67%)
Potentially confirms (as the MythBusters say, "plausible")
Legendary: 1 in 10 is gold (10%)
But invalidates
Rare: 1 in 20 is gold (5%)
-> In reality, 6% is gold (1 in 16.67)
Much of the reddit calculations seem to be based on this assumption:
"We would therefore expect the [non-golden] rare:epic:legendary ratio to be (20/25):(4/25):(1/25) = 20:4:1 which it is!
The OP has the following ratios for non-golden rare:epic:legendary = 21.4 : 4.28 : 1.08
Comparisons:
reddit:
epic to rare = 4:20 = 20.0%
legendary to epic = 1:4 = 25.0%
legendary to rare = 1:20 = 5%
OP:
epic to rare = 4.28 : 21.4 = 20.0%
legendary to epic = 1.08 : 4.28 = 0.25233 = 25.2%, IMO "close enough" to 25%
legendary to rare = 1.08 : 21.4 = 0.050467 = 5.04%, IMO "close enough" to 5%
tl;dr
Based on the OP,
rare:epic:legendary ratio = 20:4:1 (confirms reddit)
Common: 1 in 50 is gold (2%) (confirms reddit)
Rare: 6% is gold (1 in 16.67) (reddit incorrectly assumed 1:20 = 5%)
Epic: 1 in 15 is gold (6.67%) (confirms reddit)
Legendary: 9.3% is gold (reddit assumed that 1 in 10 is gold (10%), which is quite close since golden legendaries have a lot of variance)
1 in 19/20 packs should have a legend? Well that sucks. I've only hit 4 legends so far in about 140-150 packs: 2x King Krush, then a tink, then a Gromash. Here's hoping the next 140-150 fall in line with the expected stats!
Holy interruptus Batman!
My seven-year-old actually plays with me frequently. He has learned my card pack opening ritual, which starts in the top-right, and then bottom-left, top, bottom-right and top-left. At first, we just hover over the cards, then we click on the common ones first, then increase in rarity. It is fun to watch him open his own packs on the iPad the same way. He got his first legendary (probably about 25 packs in) and it was Malygos. On a side note, he is already level 18 this season and is currently on a win streak lol. It's amazing how even a seven-year-old can grasp the concepts of the game and do well in the higher ranks.
Best of luck to him :)
-0,12%
I have opened more than 20 packs, 30 or 40 to leave a legendary. They run every almost 2 month D: