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Booster Boxes are boxes of booster packs. They are how the booster packs are transported after being manufactured. They will generally have 24 packs for a normal Booster Pack, 30 for a Duelist Pack and 10 for a Starter Deck, Structure Deck or Special Edition .
Advantages of buying a booster box
One advantage to buying a booster box instead of normal packs is that the cards could not yet have been scaled, and as a result you have a better chance of getting Super Rare and Ultra Rare cards. Another advantage is that if you are buying booster boxes of a pack that contains a Ghost Rare card, you have a 1/36 chance of getting one. To calculate the chance of getting multiple Ghost Rares per box, the formula is 1/36^number of Ghost Rares you are calculating the probability of. The third advantage of buying a booster box is that it is a lot cheaper per pack and per card than buying booster packs. A booster box of 24 booster packs will have 216 cards and will be between $.50 a card and $.25 a card (supposing every booster has only commons, to calculate prices). The same amount of cards buying single boosters will be between $.88 and $.30 a card.
Advantages of buying individual packages
One advantage to buying a Booster Pack is that you might not want a full box of the same pack. Also, if you want less than the amount of boosters in a booster box it is sometimes cheaper to buy the booster packs as opposed to the box. Another advantage is because if there are an abundant amount of Commons in the Booster, you can reduce the chances of accumulating the exact same cards you collected instead of buying an entire Booster Box which will increase your odds.