I did the math

And it was hard.

I am not good at math. I have never been good at math. In school, by the time I actually grokked whatever math concept we were learning, the class was already three chapters ahead of me. However, I am smart enough to know I don't know math, and am stubborn enough to think that I can force my way through it if I use enough formulas and such if I really, really have to know the answer to a math-related question.

This is one of those times when my curiosity, stubbornness and ineptitude join forces and combine to brute force a simple task.

I have to know the exact odds of pulling a non-short-printed 2010 Allen & Ginter base mini card OR I WILL GO COMPLETELY INSANE.

After a hobby box and several blasters I have noticed that base minis are few and far between. This is not quite enough to get me obsessed with finding out the ratio. What has pushed me over the edge is that damn Strasburg mini. You know, the one that drops at the same ratio as normal garden variety minis? Yeah, that one.

BUT WHAT WAS ODDS?

That's actually a good question, what the hell are the odds of pulling a base mini from a pack of A&G? There are plenty of odds listed for all the other flavors of mini cards, but none for the base minis. You shouldn't have to post odds for the base minis, should you? Those are the most common ones, right? Base minis are the water that the parallel sugar and the insert Kool-Aid packet goes into right? Well they don't seem so common this year to me, so I gotta find the odds. Here are the odds for all the other minis as listed on a retail pack:

Parallels:
Base SP - 1:13
A&G back - 1:5
A&G back SP - 1:65
Black border - 1:10
Black border SP - 1:130
No Number - 1:188
Bazooka - 1:376

Inserts:
National Animals - 1:8
Lords of Olympus - 1:12
Monsters of the Mesozoic - 1:12
World's Biggest - 1:12
Wordsmiths - 1:24
Sailors of the Seven Seas - 1:24
Creatures of Legend, Myth and Joy - 1:128

Did I miss any? Those are just the ones we have odds for, I don't even know about the Salty Sailors and Zodiac stealth inserts. Seems like an awful lot of inserts to me, in your average 24 pack box you're looking at pulling 10 of the common inserts. This is not counting the tough inserts or ANY parallels. So have base minis been squeezed out of the set altogether? 

I slept though the lecture on probability (and didn't understand a damn thing in the book anyway) so I'm going to break this down the best I can. I know that if I have 10 marbles, and the odds of a red marble is 1:5, then I can determine the number of marbles that aren't red, but figuring out the number of red marbles and subtracting form 10. 

10/5=2 

10-2=8 

So there are 8 marbles that are not red. Easy peasy. Now I'm going to do this with these damned A&G inserts. 

So I can do this without having to deal with messy fractions, I need to find the least common multiple of all these odds. That seems like a lot of odds, but there are only four numbers I really have to deal with to make this all even.
24 - is divisible by 8, 12 and 24
130 - is divisible by 5, 10, 13 and 65
376 - is divisible by 188
128 - is divisible by none of these other numbers
Finding the least common multiple of those three numbers will allow me to divide that number by all those odds without getting a fraction. Then I can add all those numbers up, subtract that total from the least common multiple, and then divide the least common multiple by that number to get the odds of pulling a base card from a pack of A&G. I know, you're confused. So am I. The only thing I do worse than math is explain how to do math. It should work out fine assuming I don't make a simple calculating error. Odds of that are about 1:3, but we don't need those odds.

I can't manage to do the simplest math, but I'm going to find the least common multiple of four large numbers? No! I'm not! The internet to the rescue! I just need to go to this site and plug in all the numbers. The least common multiple is:

1173120

Ok, that's a lot of cards. That's almost forty-nine thousand boxes. I don't think that many A&G minis were printed. It will work with the math at any rate, so let's go for it.

Base SP - 1:13 - 1173120/13 =  90240 cards
A&G back - 1:5 - 1173120/5 = 234624 cards
A&G back SP - 1:65 - 1173120/65 = 18048 cards
Black border - 1:10 - 1173120/10 = 117312 cards
Black border SP - 1:130 - 1173120/130 = 9024 cards
No Number - 1:188 - 1173120/188 = 6240 cards
Bazooka - 1:376 - 1173120/376 = 3120 cards

National Animals - 1:8 - 1173120/8 = 146640 cards
Lords of Olympus - 1:12 - 1173120/12 = 97760 cards
Monsters of the Mesozoic - 1:12 - 1173120/12 = 97760 cards
World's Biggest - 1:12 - 1173120/12 = 97760 cards
Wordsmiths - 1:24 - 1173120/24 = 48880 cards
Sailors of the Seven Seas - 1:24 - 1173120/24 = 48880 cards
Creatures of Legend, Myth and Joy - 1:128 - 1173120/128 = 9165 cards

These are not the total number of cards out there (although you could calculate that using the Bazooka minis - but that's another post) but it will give us an idea of how many minis are not parallels or inserts. First, we add the totals together:

90240 cards
+ 234624 cards
+ 18048 cards
+ 117312 cards
+ 9024 cards
+ 6240 cards
+ 3120 cards
+ 146640 cards
+ 97760 cards
+ 97760 cards
+ 97760 cards
+ 48880 cards
+ 48880 cards
+ 9165 cards
Equals
1025453 non-base mini cards

To find the total number of base minis, subtract:

1173120
-1025453
Equals
147667 base mini cards

Ok! We've got the total number of cards and the total number of base minis. Divide these two numbers and we have the odds for a base mini.

1173120/147667=
7.94

Let's just round this off to account for any stalth Zodiac Sailor inserts that may be floating around out there and the odds for a base mini in 2010 Allen & Ginter is....

1:8 packs

Now about that Strasburg...
If a base mini falls at one per eight packs... and there are 301 base minis available... the odds of pulling the Strasburg out of a retail pack of 2010 Allen & Ginter is.............

1:301 blasters

or

just over 1:100 24 pack retail boxes.

To put this in perspective, assuming my math is correct, it is easier to pull a Rip card out of a hobby pack than to pull a Strasburg out of a blaster. Of course the odds are the same for pulling an Eric Byrnes base mini out of a blaster so there's some small consolation if you actually do so. These numbers are for retail only, Hobby odds are slightly different and I don't have time to calculate them right now. If anyone feels ambitious, knock yourself out and let me know what you find.

Well, Topps didn't completely squeeze base minis out of the set, but just add one more insert set and they can still pull it off in 2011. So when you're out there in that shop or on eBay looking for Allen & Ginter minis, remember that A&G minis are the 'commons' in 2010 and that if you really want a Strasburg, you're probably better off just buying it at whatever inflated price it's going for instead of trying to rip packs until you find one.