This forums is for questions, answers, and discussion about First Edition rules, formats, and expansions.
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By winterflames (Derek Marlar)
 - Delta Quadrant
 -  
#562725
So tomorrow the Bigs (a label for indicating my older 2 children) and I are going to do a Box Break of Mirror Mirror packs. Actually a box and a half. We plan to put the stuff we open up on my ebay after we open them and the vids and sales should all go live one week from tomorrow. But I have a question about the numbers and I recall that several of you guys are number crunchers.

How many packs/boxes/cases do I have to open to ensure a high likelihood of acquiring a Full Set?
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By Armus (Brian Sykes)
 - The Center of the Galaxy
 -  
Goateed
Community Contributor
1E American National Second Runner-Up 2020
#562731
winterflames wrote: Wed Sep 22, 2021 3:19 pm So tomorrow the Bigs (a label for indicating my older 2 children) and I are going to do a Box Break of Mirror Mirror packs. Actually a box and a half. We plan to put the stuff we open up on my ebay after we open them and the vids and sales should all go live one week from tomorrow. But I have a question about the numbers and I recall that several of you guys are number crunchers.

How many packs/boxes/cases do I have to open to ensure a high likelihood of acquiring a Full Set?
With 50 R and one UR, you can do it in 2, but most likely 3. If FOS is playing hard to get you may need 4.
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By winterflames (Derek Marlar)
 - Delta Quadrant
 -  
#562734
Cool. I have 2 First Officer Spock's in my collection so if he is the holdout I can pinch hit and go for broke.

I probably just murdered that sports allusion there...
 
 - Alpha Quadrant
 -  
#562747
I think you guys are waaaaaay off.

You're discounting the chances of duplicates in truly random packs, a variation of the birthday problem. Also you're ignoring the R+, which Decipher claims was "33% more rare than rare." It's funny, they say that Mirror, Mirror included "a handful of Rare+ cards (33% more rare than rare), and a distribution of Rare, Uncommon and Common cards, similar to other Star Trek CCG sets." And by "a handful," they meant "more than the number of rares." There are 30 R+ cards and 20 R cards. Some handful!

I don't know what the exact distribution was, but people throw around 121 cards on a sheet as a number. If the rare sheet had them all, and if there's 1 UR on the sheet, 60 R+s (2 copies of each) and 60 Rs (3 copies of each), then you're chances of completing a full set are about 0.0001% in 3 boxes (30 packs a box is 90 packs). If you don't care about the UR, then your chances climb to 0.0005%.

I could be wrong about the R+ distribution on the sheets. Let's be generous and say there are 50 rares, all equally likely to be in a pack, no R+s, and we don't care about an Ultra-Rare. Then your chances of getting a complete set rise to about 0.0009%, with 3 boxes or 90 packs. To have a 90% chance of getting a full set of 50 rares, you'd need to open around 300 packs, which is 10 boxes. That's the birthday problem for you.

All of this is assuming that commons and uncommons aren't an issue of course.

I'm also assuming that the packs are truly random, rather than being correlated. In other words, if two neighboring packs in the same box are likelier to have their rare cards have also been neighbors on the same print sheet, then the math goes out the window entirely. It depends on whether or not Decipher shuffled the cards or shuffled the packs before packing the boxes.

I know this assumption was not the case in at least one high profile case for one game (Magic?), where people could figure out which pack in the box to purchase from the store to pick out the super-valuable rare, if they knew what one of the other packs already contained, based on that pack's location.
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By Armus (Brian Sykes)
 - The Center of the Galaxy
 -  
Goateed
Community Contributor
1E American National Second Runner-Up 2020
#562748
DISCO Rox No More wrote: Wed Sep 22, 2021 7:23 pm I think you guys are waaaaaay off.

You're discounting the chances of duplicates in truly random packs, a variation of the birthday problem. Also you're ignoring the R+, which Decipher claims was "33% more rare than rare." It's funny, they say that Mirror, Mirror included "a handful of Rare+ cards (33% more rare than rare), and a distribution of Rare, Uncommon and Common cards, similar to other Star Trek CCG sets." And by "a handful," they meant "more than the number of rares." There are 30 R+ cards and 20 R cards. Some handful!

I don't know what the exact distribution was, but people throw around 121 cards on a sheet as a number. If the rare sheet had them all, and if there's 1 UR on the sheet, 60 R+s (2 copies of each) and 60 Rs (3 copies of each), then you're chances of completing a full set are about 0.0001% in 3 boxes (30 packs a box is 90 packs). If you don't care about the UR, then your chances climb to 0.0005%.

I could be wrong about the R+ distribution on the sheets. Let's be generous and say there are 50 rares, all equally likely to be in a pack, no R+s, and we don't care about an Ultra-Rare. Then your chances of getting a complete set rise to about 0.0009%, with 3 boxes or 90 packs. To have a 90% chance of getting a full set of 50 rares, you'd need to open around 300 packs, which is 10 boxes. That's the birthday problem for you.

All of this is assuming that commons and uncommons aren't an issue of course.

I'm also assuming that the packs are truly random, rather than being correlated. In other words, if two neighboring packs in the same box are likelier to have their rare cards have also been neighbors on the same print sheet, then the math goes out the window entirely. It depends on whether or not Decipher shuffled the cards or shuffled the packs before packing the boxes.

I know this assumption was not the case in at least one high profile case for one game (Magic?), where people could figure out which pack in the box to purchase from the store to pick out the super-valuable rare, if they knew what one of the other packs already contained, based on that pack's location.
If it's 4 random boxes sure. I just opened 4 boxes in a case last year. In every box I got a complete uncommon set, 2-3 complete common sets, and over 4 boxes I got a complete set including FOS.

All that to say, there's some pretty strong correlation at the box and case level such that doing a normal distribution doesn't lead to great results - it's not that random.
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By winterflames (Derek Marlar)
 - Delta Quadrant
 -  
#562951
We opened 44 packs. We are short, I believe, 8 cards from a full set, all R & R+. But we got First Officer Spock. We did not receive any of the Mr. Ferengi. I still haven't even seen a physical Marlena. Captain Bashir failed to show up. We did get some duplicate Rares.
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By Armus (Brian Sykes)
 - The Center of the Galaxy
 -  
Goateed
Community Contributor
1E American National Second Runner-Up 2020
#562952
winterflames wrote: Sat Sep 25, 2021 9:45 am We opened 44 packs. We are short, I believe, 8 cards from a full set, all R & R+. But we got First Officer Spock. We did not receive any of the Mr. Ferengi. I still haven't even seen a physical Marlena. Captain Bashir failed to show up. We did get some duplicate Rares.
PM me your list of missing cards. Odds are I got you covered. :cheersL:
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By Keiimaster (Mathew McCalpin)
 - Delta Quadrant
 -  
1E The Neutral Zone Regional Participant 2021
#563050
Armus wrote: Sat Sep 25, 2021 10:08 am
winterflames wrote: Sat Sep 25, 2021 9:45 am We opened 44 packs. We are short, I believe, 8 cards from a full set, all R & R+. But we got First Officer Spock. We did not receive any of the Mr. Ferengi. I still haven't even seen a physical Marlena. Captain Bashir failed to show up. We did get some duplicate Rares.
PM me your list of missing cards. Odds are I got you covered. :cheersL:
I also have extras....and an unopened box.
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By winterflames (Derek Marlar)
 - Delta Quadrant
 -  
#563057
Just so we are clear, this was for a YouTube video. I am not a completionist collector. The cards we opened are going on Ebay either in Common/Uncommon sets, as individual rares, or as Learn To Play Vs. Decks, depending on circumstances.

As far as my personal collection, I am only missing Mr. Rom and Marlena. Who I will likely just print if I want to put them in a deck.

I do appreciate the willingness of you Traders to help out though.
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