Hi everyone,

After seeing a discussion in the trading card server about the chances of pulling certain numbers of cards, I decided to brush up on math skills and write a little text based tool to determine how lucky you are when it comes to card draws. All you have to do is enter the number of cards you own for each rarity and the program will tell you your odds of getting that amount or fewer of the rarity as well as that amount or more of it. For results to be accurate, you must include ALL cards, including duplicates. If you only care about certain rarities, you can enter the correct number for those rarities only and just ensure that the total sum of cards regardless of rarity adds to the sum of your entire collection. Using my collection as an example, the use of the program is as follows:

LINK TO THE TOOL: https://www.online-python.com/LFvw9BcxKM (Last updated 2022-04-05)

To use the tool, click the run button first and then enter your values as shown below, pressing enter after submitting your number for each prompt.

# of Hall of Fame cards:
1
# of Diamond cards:
2
# of Ruby cards:
1
# of Logo cards:
3
# of Gold cards:
8
# of Silver cards:
37
# of Bronze cards:
50

After drawing  102  total cards

98.951 % chance of getting  1 or fewer  hall of fame  cards
14.197 % chance of getting  1 or more  hall of fame  cards

84.005 % chance of getting  2 or fewer  diamond  cards
40.109 % chance of getting  2 or more  diamond  cards

8.163 % chance of getting  1 or fewer  ruby  cards
98.445 % chance of getting  1 or more  ruby  cards

32.135 % chance of getting  3 or fewer  logo  cards
84.262 % chance of getting  3 or more  logo  cards

2.306 % chance of getting  8 or fewer  gold  cards
98.998 % chance of getting  8 or more  gold  cards

93.001 % chance of getting  37 or fewer  silver  cards
10.255 % chance of getting  37 or more  silver  cards

82.015 % chance of getting  50 or fewer  bronze  cards
23.643 % chance of getting  50 or more  bronze  cards


When looking at these results, I focus on a different number depending if I want to know how lucky or unlucky I got.

For example, I feel like getting 1 hall of fame card this early was fairly lucky, so I look at the second line of text where it tells me there was only a 14.197% chance of having 1 or more hall of fame card at this point.

On the other hand, I feel like getting only 8 golds was fairly unlucky, so I look at the first line of text where it tells me there was only a 2.306% chance of having 8 or fewer gold cards at this point.

For common cards it's the opposite. I would rather not have 37 silver cards in my collection, so I look at the second row to see that there was only a 10.255% chance of having so many silvers by now.

There really isn't anything useful you can do with this information, but if you're anything like me then you'll enjoy the process of seeing these numbers while on your gambling addiction journey.

Just like my chances of getting 3 or more logo cards, my confidence in the correctness of this math is around 85% so if you're someone who is super smart and knows what they're doing I'd love to hear if you agree with my methods.

Enjoy!

600 words + 50 lines of code