Booster Pack Probability Math Question

[Drunken Hairdresser]

Hi All

Looking for a math legend to figure this out.

(and no, this is NOT my homework) :P

What is the probability of rolling the same foil card from unpacking two consecutive booster packs for a 5 card set.

My thought was ...

foil drops are 1% chance for any drops

Booster pack gives you 3 chances, which is slightly less than 3% (lets say its 3% to make it easy)

3 / 100, however there are 5 foil cards

5/3 * 100 = 166

5 foils out of 166 cards

The events are independent so:

1 / 166 on the first draw x 1 / 165 on the second draw * 100

= 0.00365%

Is this correct ?

or should it be 5 / 166 on the first draw ? = 0.018% , or something else ??

been a long time since i did math :P

[HereIsPlenty]

What I do know is I recently got 2 foils from the one booster. Rawr.

[cSg|mc-Hotsauce]

Take out the fact that there are 5 FOILs. That doesn't matter. Why not? Duplicates.

[GuRu Asaki]

If it helps at all...

I am not sure if you are referring to this math twards all Games in your Library,
or only a Certain Category, or something of Games...

What I do know is, not all Games come with Foils, so there is that to also consider
in your Math Statistics...

But i've myself gone through like a pretty good list of Games on STEAM, & have
only gotten 1 Foil Card from any of them... & that Foil came from Square Enix's
Tomb Raider Game...

You also gotta factor in that some Games give you a set Standard Cards, with
a Foil Card...

Meaning, the Foil Card Drop for those Games won't count twards this Math at all...


It really just depends on which Games you buy really, I don't think it matters, though...
I think that it takes way too long to get Cards for any Foils to drop, & they are just too
Rare to even bother hunting for them....


I'm just lucky I can even cover any of my Trading Card Games with a Wallpaper
& Emotes, & such at all, lone enough have to deal with Foils, & Ultra Rares...

A 1ngle STEAM Wallpaper & a 1ngle Emote just isn't worth my time hunting for these...




But good luck with your Theory, though... =D

[HereIsPlenty]

I am not sure why you posted this. I appreciate that you have 10 years service. As far as I am aware, all games that have trading cards have foil ones. With some games, they do not yet list the foil card for a specific slot on the Market as nobody has put one on Market but Steam database still holds them. In some cases (more than you would think) the Steam Exchange site will not list a badge but this is because, again, no one who has made the badge has shared the image.

You are steam level 24. You have made one game badge, level 1. That is not a wealth of experience on this subject, I am afraid.

[Lokiator]

You're opening two booster packs, so getting six cards in total. The set contains five cards.

There's a 1/100 chance of getting a foil with any one particular card of those six.
There's a 5/100 (1/100 x 5) chance of getting a second foil from the other five draws.
There's a 1/5 chance that the second foil will be for the same card in the set as the first one.

So 1/100 x 5/100 x 1/5 = 1/10,000 (or a 0.01%) chance of getting the same foil twice from opening two booster packs.

[HereIsPlenty]

I will not pretend to be good enough at maths to argue that properly. I do see different ways you could express the problem and am not sure they give the same %.

Regardless its gosh-darned* unlikely but completely unimportant.

[Lokiator]

True. You could also go with the following option:

3/100 chance of getting a foil in the first booster pack
3/100 chance of getting a foil in the second booster pack
1/5 chance that they're the same foil

For 3/100 x 3/100 x 1/5 = 1.8 / 10,000 or 0.018% chance of getting the same foil twice.

Either option makes sense at first glance, but it depends on whether you're treating the problem as six 1% events or two 3% events. You are correct though, it's not going to happen often and it's definitely unimportant. :P

[CycLoNeShadow]

Foil cards drop:

1. 1 card (10 Apr 2019) - Unpacked 7 BP
   
2. 3 cards (11 Apr 2019) - Unpacked 7 BP
   
3. 1 card (13 Apr 2019) - Unpacked 7 BP
   
4. 1 card (16 Apr 2019) - Unpacked 8 BP
   
5. 2 cards (20 Apr 2019) - Unpacked 10 BP
   
6. 1 card (28 Apr 2019) - Unpacked 7 BP
   
7. 1 card (7 May 2019) - Unpacked 9 BP
   
8. 1 card (11 May 2019) - Unpacked 9 BP
   
9. 1 card (18 May 2019) - Unpacked 8 BP
   
10. 1 card (22 May 2019) - Unpacked 9 BP
    
11. 1 card (23 May 2019) - Unpacked 9 BP
    
12. 1 card (27 May 2019) - Unpacked 13 BP
    
13. 1 card (28 May 2019) - Unpacked 10 BP
    
14. 2 cards (31 May 2019) - Unpacked 9 BP
    
15. 1 card (2 June 2019) - Unpacked 9 BP
    
16. 1 card (5 June 2019) - Unpacked 10 BP
    
17. 1 card (18 June 2019) - Unpacked 9 BP

* I unpack booster pack everyday