In hearthstone the odds of getting an epic card is said to be 1 in every 10 packs. One pack contain 5 cards so it's 1 every 50 cards. What are the odds of getting 4 epic cards when opening 4 packs (20 cards)? And why is it not the same to calculate the odds of getting an epic card in a single pack (10%) 4 times (0.1 x 0.1 x 0.1 x 0.1)?
First of all you open 1 epic card per 5 packs on average and not 10. So on each pack you have a more or less 20% chance to open an epic card.
Now I believe there is a pity counter for epic cards (just like there is one for legendaries), which pretty much guarantees that you get 1 epic card after opening 10 packs. I am not sure of the details, but I believe that they way pity timers are implemented, the odds of opening an epic card per pack are not constant but increase with every pack you open that doesn't contain one (and reach 100% when you reach the pity timer). If that's the case, then if you open an epic card in a pack, the odds that you open one in the immediately next pack should be less than 20% and 20% is only the long-run average over many packs
In hearthstone the odds of getting an epic card is said to be 1 in every 10 packs. One pack contain 5 cards so it's 1 every 50 cards. What are the odds of getting 4 epic cards when opening 4 packs (20 cards)? And why is it not the same to calculate the odds of getting an epic card in a single pack (10%) 4 times (0.1 x 0.1 x 0.1 x 0.1)?
Thank you in advance.
0,1^4 would be the probability for getting the exact same epic 4 times in a row. The probability for getting ANY epic in one of the packs is 0,1x4. So 0.1+0,1+.... but the numbers aren‘t quite right as SirJohn13 already said. But if you want an easy calculation for a rounded result, thats how to do it.
if you count in the other factors like the already mentioned pity timer it gets MUCH more complicated
This is a question of probabilities more than it is a question about Hearthstone.
Let's assume it is indeed 1 per 10 packs, as that makes calculations easier.
That would make the odds of a single card being epic 2%
Multiplying that (2%x2%x... etc) essentially multiplies fractions (2/100 x 2/100 etc) leading to a very small probability, because it calculates the chance of EVERY card being an epic.
Adding them (2/100 + 2/100 etc) would only be correct if the probabilities were exclusive, meaning if packs were not allowed to have more than one epic, and that would lead to 5 x 2% = 10%.
The way to calculate the chance of opening 4 epics in 4 packs (20 cards) with no additional rules is a bit more complicated. I would suggest you google binomial distribution.
In hearthstone the odds of getting an epic card is said to be 1 in every 10 packs. One pack contain 5 cards so it's 1 every 50 cards. What are the odds of getting 4 epic cards when opening 4 packs (20 cards)? And why is it not the same to calculate the odds of getting an epic card in a single pack (10%) 4 times (0.1 x 0.1 x 0.1 x 0.1)?
Thank you in advance.
First of all you open 1 epic card per 5 packs on average and not 10. So on each pack you have a more or less 20% chance to open an epic card.
Now I believe there is a pity counter for epic cards (just like there is one for legendaries), which pretty much guarantees that you get 1 epic card after opening 10 packs. I am not sure of the details, but I believe that they way pity timers are implemented, the odds of opening an epic card per pack are not constant but increase with every pack you open that doesn't contain one (and reach 100% when you reach the pity timer). If that's the case, then if you open an epic card in a pack, the odds that you open one in the immediately next pack should be less than 20% and 20% is only the long-run average over many packs
0,1^4 would be the probability for getting the exact same epic 4 times in a row. The probability for getting ANY epic in one of the packs is 0,1x4. So 0.1+0,1+.... but the numbers aren‘t quite right as SirJohn13 already said. But if you want an easy calculation for a rounded result, thats how to do it.
if you count in the other factors like the already mentioned pity timer it gets MUCH more complicated
This is a question of probabilities more than it is a question about Hearthstone.
Let's assume it is indeed 1 per 10 packs, as that makes calculations easier.
That would make the odds of a single card being epic 2%
Multiplying that (2%x2%x... etc) essentially multiplies fractions (2/100 x 2/100 etc) leading to a very small probability, because it calculates the chance of EVERY card being an epic.
Adding them (2/100 + 2/100 etc) would only be correct if the probabilities were exclusive, meaning if packs were not allowed to have more than one epic, and that would lead to 5 x 2% = 10%.
The way to calculate the chance of opening 4 epics in 4 packs (20 cards) with no additional rules is a bit more complicated. I would suggest you google binomial distribution.