Booster Pack Rates Explained

Larz70

     The rates in the booster packs above can be found by clicking on the % icon on the packs sold at the Vault.  As you can see from the note above the rates, the percentages refer to the odds of getting at particular rarity within the entire purchase.  For example, a mythic rate of 6.82% in a booster pack means you have exactly 6.82% or about 1 in 15 to get 1 or more mythics in the pack.  Because of the way the odds are presented, the rates won't add up to 100%.  The only time the rate will add up to 100% is if the pack contains exactly one card (like the old free single card booster pack).

     So what exactly are the odds for each rarity then and are they the same for all Packs?  The formula is simple and the answer is yes, they are all the same for all the packs.  The formula is Rarity Odds = 1 - ( (1-p)^(1/n) ) where p is the probability listed on the pack for that rarity and n is the number of cards in that pack.  Note that once the listed probability above reaches 100%, one can no longer back into the actual rarity odds.  Ok, so now I'm going to open up my calculator app and start computing....

M19 Booster Pack

• Common odds     = 1 - ( (1-.9797)^(1/5) ) = 0.5413
• Uncommon odds = 1 - ( (1-.9166)^(1/5) ) = 0.3915
• Rare odds            = 1 - ( (1-.2349)^(1/5) ) = 0.0521
• Mythic odds         = 1 - ( (1-.0682)^(1/5) ) = 0.014
• MP odds              = 1 - ( (1-.0050)^(1/5) ) = 0.0010

M19 Super Pack

• Common odds     = 1 - ( (1-.1)^(1/15) )       = 1
• Uncommon odds = 1 - ( (1-.9994)^(1/15) ) = 0.3902
• Rare odds            = 1 - ( (1-.5521)^(1/15) ) = 0.0521
• Mythic odds         = 1 - ( (1-.1910)^(1/15) ) = 0.014
• MP odds              = 1 - ( (1-.0149)^(1/15) ) = 0.0010

M19 Premium Pack

• Common odds     = 1 - ( (1-1)^(1/25) )        = 1
• Uncommon odds = 1 - ( (1-1)^(1/25) )        = 1
• Rare odds            = 1 - ( (1-.7377)^(1/25) ) = 0.0521
• Mythic odds         = 1 - ( (1-.2977)^(1/25) ) = 0.014
• MP odds              = 1 - ( (1-.0248)^(1/25) ) = 0.0010

     So you can see, they are the same.  For common and uncommon, it will be difficult to figure out exactly what the odds are but we can use the booster pack odds for both common and uncommon.

Common Odds     = 54.13%
Uncommon Odds = 39.15%
Rare Odds            =  5.21%
Mythic Odds         =  1.4%
MP Odds              =  0.1%
----------------------------------------
Total Odds            = 99.99%

     Didn't quite make 100% due to rounding, but if a single card M19 booster were to be made available, these will be the odds that are going to be displayed.

     But why stop here, lets calculate the rate of each single card, too.  M19 contains 60 common cards, 55 uncommon, 40 rare, 20 mythic and 10 masterpiece.  Assuming all the cards have equal chances of being picked:

Common Card Odds     = 54.13% / 60 = 0.9022%
Uncommon Card Odds = 39.15% / 55 = 0.7118%
Rare Card Odds            = 5.21% / 40   = 0.13025%
Mythic Card Odds         = 1.4% / 20      = 0.07%
MP Card Odds              = 0.1% / 10      = 0.01%

     Hmmm, nothing special. Common still has the highest rate and MP has the worst.  No surprise.

     In conclusion, whether you open one booster pack 5 times or a premium pack once, the odds will be the same.  However, premium packs are a better deal because of the bonus rare card and at a price of 320 crystals, you get 5 times more cards at only 4 times the price of a booster pack.

     I hope this clears up any mysteries behind the numbers provided by the game developers.  Let me know if you have any questions.

madwren

Thanks, Larz! Hopefully this will help illuminate how it works for others as well as it did for me.

DBJones

Thanks, this is a really good breakdown! There is a small error; in your conclusion you mentioned super packs once, near the beginning, when you seemed to mean premium packs.

Larz70

Good catch @DBJones and sorry for the late response.

Actually, what I wanted to say was the odds of opening 3 booster packs = 1 super pack and 5 booster packs = 1 premium pack but I must have typed too fast and shortened it to 3 booster packs = 1 premium pack ....  which was totally wrong!   

Thanks!