Hey,
I was hoping someone could check my math regarding calculating probabilities when opening card packs for a collectible card game.
I'd like to think my method of calculating is correct (don't we all
), but I need to be sure.
The data below is simplified, but I just need to know if the general idea is correct.
Some info you need to know beforehand:
- A card pack always contains 5 cards.
- Each card can be one of four different rarities (common, rare, epic or legendary). The probabilities for these are as follows:
Calculations
Step 1: Calculate the percentage of missing cards (for each rarity seperately)
Here I simply divide the missing cards from user 'X' by the total available cards for each rarity.
Step 2: Calculate the probability of a new card being a missing card (for each rarity seperately)
Here I simply multiply the results from step 1 with the probability that a card has a specific rarity.
Step 3: Calculate the total probability of a new card being a missing card (of any rarity)
Simply add the percentages from the previous step together to obtain 5.75%.
Step 4: Calculate the total probability of a new card being a missing card when opening a card pack (5 cards)
So the final answer would be that there is a 25.63% chance that user 'X' would get a missing card if he/she opens a card pack.
If my calculations are correct, why does it seem like a relatively high number when taking into account this user already owns a lot of cards.
Not sure if this is useful, but in excel my main formula would be this:
1 - POWER((1 - SUMPRODUCT(<Results from step 2>, <Card rarity probabilites found at the top>)), 5)
P.S.: I do realise I'm ignoring the fact that, for example, card 1 in a card pack could be a missing card, thus reducing the probability for the other 4 cards. This is trivial to me, as I'm just interested in an approximation.
Any help is appreciated,
Best regards
I was hoping someone could check my math regarding calculating probabilities when opening card packs for a collectible card game.
I'd like to think my method of calculating is correct (don't we all
), but I need to be sure.The data below is simplified, but I just need to know if the general idea is correct.
Some info you need to know beforehand:
- A card pack always contains 5 cards.
- Each card can be one of four different rarities (common, rare, epic or legendary). The probabilities for these are as follows:
[*=1] Common: 72%
[*=1] Rare: 23%
[*=1] Epic: 4%
[*=1]Legendary: 1%
[*=1] Common: 100 cards total
[*=1] Rare: 70 cards total
[*=1] Epic: 35 cards total
[*=1]Legendary: 15 cards total
[*=1] Common: 1 card total
[*=1] Rare: 7 cards total
[*=1] Epic: 18 cards total
[*=1]Legendary: 10 cards total
Calculations
Step 1: Calculate the percentage of missing cards (for each rarity seperately)
Here I simply divide the missing cards from user 'X' by the total available cards for each rarity.
Common: 1/100 = 1%
Rare: 7/70 = 10%
Epic: 18/35 = 51.43%
Legendary: 10/15 = 66.67%
Rare: 7/70 = 10%
Epic: 18/35 = 51.43%
Legendary: 10/15 = 66.67%
Step 2: Calculate the probability of a new card being a missing card (for each rarity seperately)
Here I simply multiply the results from step 1 with the probability that a card has a specific rarity.
Common: 1% x 72% = 0.72%
Rare: 10% x 23% = 2.3%
Epic: 51.43% x 4% = 2.06%
Legendary: 66.67% x 1% = 0.67%
Rare: 10% x 23% = 2.3%
Epic: 51.43% x 4% = 2.06%
Legendary: 66.67% x 1% = 0.67%
Step 3: Calculate the total probability of a new card being a missing card (of any rarity)
Simply add the percentages from the previous step together to obtain 5.75%.
Step 4: Calculate the total probability of a new card being a missing card when opening a card pack (5 cards)
Step 4a: Calculating the probability that a card pack will not contain a missing card.
100% - 5.75% = 94.25% (This is the probability that a single card will be a duplicate.)
94.25% ^ 5 = 74.37% (This is the probability that all cards in a pack will be a duplicates.)
94.25% ^ 5 = 74.37% (This is the probability that all cards in a pack will be a duplicates.)
Step 4b: Calculating the probability that a card pack will contain a missing card.
100% - 74.37% = 25.63%
So the final answer would be that there is a 25.63% chance that user 'X' would get a missing card if he/she opens a card pack.
If my calculations are correct, why does it seem like a relatively high number when taking into account this user already owns a lot of cards.
Not sure if this is useful, but in excel my main formula would be this:
1 - POWER((1 - SUMPRODUCT(<Results from step 2>, <Card rarity probabilites found at the top>)), 5)
P.S.: I do realise I'm ignoring the fact that, for example, card 1 in a card pack could be a missing card, thus reducing the probability for the other 4 cards. This is trivial to me, as I'm just interested in an approximation.
Any help is appreciated,
Best regards