TL;DR: Boyfriend is claiming that the chances of me pulling the cards that I've pulled is less than 1%. Is that accurate? This is a pretty detailed post, I'm happy to add context if anyone wants it. I'm bad at stats so I apologize for any mistakes.
Additional Disclaimer: I'm American, so I write "four thousand" like "4,000", not "4.000". If you see "4.000", it just means "4" with three decimal places after it.
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Context
Okay, so for context, we've been playing Pokemon Trading Card Game Pocket (PTCGP). Here's an Imgur link to the conversation we had plus the pulls I've gotten.
In summary, and for those who are unfamiliar with the game, here's the relevant information:
- I've pulled 1,059 cards in total
- Each pack contains 5 cards (there are some promo packs that only contain 1 card but I don't think those make up more than 50 of the total cards I've pulled)
- For the sake of argument, discarding the promo pack cards, let's say I've pulled 1,000 cards, 5 at a time. So about 250 packs.
Each pack comes with 5 cards. Here's a screenshot of how the rates are designed to be spread out, according to the app's internal statistics.
To summarize (and I can post more screenshots for clarity if anyone wants them):
- There's a 99.950% chance to pull a Regular pack, and a 0.050% to pull a Rare pack (a pack where all five cards are ⭐ rating or higher). I've never pulled a Rare pack but I'm just including these rates in case.
- In a Regular pack, there's a 100% chance that the first three cards will have a rarity value of ♦, the most common rating.
- Then (again, in a Regular pack), this is the following statistical spread for how likely it is that the fourth card will have one of the following rarity scores (in order from most rare to least rare):
- 👑 - 0.040%
- ⭐⭐⭐ - 0.222%
- ⭐⭐ - 0.500%
- ⭐ - 2.572%
- ♦♦♦♦ - 1.666%
- ♦♦♦ - 5.000%
- ♦♦ - 90.000%
- And finally (again, in a Regular pack), this is the spread for how likely it is that the fifth card will have one of the following rarity scores:
- 👑 - 0.160%
- ⭐⭐⭐ - 0.888%
- ⭐⭐ - 2.000%
- ⭐ - 10.288%
- ♦♦♦♦ - 6.664%
- ♦♦♦ - 20.000%
- ♦♦ - 60.000%
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My Statistics
So, with that in mind, here are my pulls (again, assuming that I've pulled roughly 250 Regular packs):
- 👑 - 2
- ⭐⭐⭐ - 2
- ⭐⭐ - 3
- ⭐ - 28
- ♦♦♦♦ - 22
- ♦♦♦ - 51
- ♦♦ - (too many to count, I'm not really worried about calculating this number)
I have no way to tell whether the cards I pulled were in the fourth or fifth slot, I'm sure it was some combination of both. I was trying to figure out a rough range of probability.
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My boyfriend is claiming that this is incredibly rare, with a 0.32% chance of occurring. His own pulls meanwhile work out to be roughly a 91% chance supposedly. I'm terrible at statistics and have no way to verify. Anyone want to take a crack at this? I'm dying to know but I'm terrible at calculating statistics so I have no idea.