Doing the Math: Booster Packs

After learning something very interesting in Math class, I've decided to take the material and put it into YGO booster pack form.

Today's question: What are the odds of pulling a holo out of a pack?

In a typical box of an expansion set, you get 5 Super Rares, 2 Ultra Rares, 1 Ultimate Rare, and 1 Secret Rare. You would never expect to pull a Ghost Rare, so we'll leave that part of the equation out. Also to point out that are 24 packs in a single box. That's 9 holo's out of 24 packs! If we do the math, we'll get the result of each rarity as follows:

Super Rare: 5: 24
Ultra Rare: 1: 12
Ultimate and Secret Rares: 1: 24

To answer our question, the odds of pulling a holo: Using the probability of 9/24, converting that into odds in your favor is 9: 15. To simplify that, the actual odds of pulling a holo are 3: 5! In other words, if you buy 8 packs, you will probably pull 3 holo's of an unspecified rarity(s). 

Lets say you wish to buy a box of Order of Chaos, and you want to pull an Inzektor Hornet, Wind-Up Carrier Zenmaity, and Tour Bus from the Underworld. You're going to ask yourself this: What are the odds of pulling an Inzektor Hornet?

In OROC, there are 14 Super Rares in the entire set, and as mentioned above, there are 5 Super Rares in a typical box. By the box, the probability of pulling the Hornet is 5/14, making the odds 5: 9 in favor of pulling the Hornet. Meaning you would probably have to buy about 2-3 boxes, depending on your luck, just to pull the one hornet you need.

For Wind-Up Carrier Zenmaity, there are 10 Ultra Rares in the set, and 2 per box. This means that the odds of pulling a Zenmaity are 1: 4. Meaning that there's one of those in every 5 boxes.

And for Tour Bus, that's an easy one. 1 Secret per box, and 8 Secrets in set. The odds are 1: 7 to pull a Tour Bus, or any other Secret in the set.

Hope you learned something today, and tonight, I might write about something else, or even maybe the weaknesses of the Fenix OTK deck. Who knows? Just keep following!