# Ultra Rare Holo Foils

I recently bought a full set of Neopets cards on eBay for $85. It’s a collectable card game, like Magic: The Gathering, only the monsters in Neopets are cute and colorful fantasy animals.

A full set of Neopets cards consists of 234 cards, of which 30 are ultra rare holo foil cards, 66 rares, 60 uncommons, and 78 commons. The difference between the rarities comes from the fact that you get a different number of each type in a package of cards, so that you get around 1 rare card for every 2 uncommon cards, and 2 uncommon cards for every 4-5 common cards. Cards come in booster packs, each of which contains 8 cards, and the boosters have a suggested retail price of $3.49.

(updated)

You get an ultra rare holo foil card (I’ll just call them foils from here on out) in about 1 out of every 3 booster packs. That means if you buy 30 booster packs, you are likely to wind up with 10 foils. Given that there are 30 foils in a complete set, you would expect to have to buy about 90 booster packs in order to get a set of 30 foils. At the suggested retail price, that would be $314.10.

But what would you really get, if you went out and bought 90 boosters? You might get 30 foils, but you wouldn’t get 30 unique foils, you’d get some duplicates, maybe 3 of one card, and 0 of some others.

In fact, you’d get a Poisson distribution of cards. It just so happens that the chance of getting 0 copies of a certain card is approximately 37%, and the chance of getting exactly 1 copy of a certain card is also 37%. For a set of 30 cards, you would get, typically, 11 singles, 8 duplicates of 2 or more, and 11 missing cards. (Here’s a calculator)

A collection of 60 foils would get you 4 missing cards, 8 singles, and 18 duplicates.

A collection of 90 foils would still give you 1-2 missing cards. After that, the chances are good that you’d have a full set of all 30 foils.

90 foils would take 270 boosters, or $942.30. Even with a steep discount, that’s quite a lot of cash. But that is the amount I would expect to pay if I wanted to be sure to get all the ultra rare holo foils.

Now, from the seller’s perspective this story is a little different. While I have to worry about the distribution of cards, a seller has access to a large supply of cards. If a seller has opened up 900 boosters, they will likely have several complete sets of foils. The law of large numbers works in their favor; a large number of samples results in a distribution very close to the actual probabilities. So a seller with 300 foils likely has 8 or 9 full sets of foils.

For the seller, the cost of a full set of foils is the same as what it would cost me to get a set of 30 unevenly distributed foils. At the retail price, that was $314.10.

But the seller isn’t giving away all the cards they have, only a full set of 234 cards (out of the 720 they have). The rest of the cards they keep. That set of 720 cards contains (on average) one full set of holos, one and one third sets of rares, three sets of uncommons, and five sets of commons. All of these cards can be sold.

So, if I were a seller and I had all these cards, I can figure that the retail value of a set of holo foils is about 1/4 the cost of the boosters, since the rares are worth another 1/4 of the total, uncommons 1/4, and commons the last 1/4. The expected market value of a full set of foils (or 3 sets of rares, or 6 sets of uncommons, or 12 sets of commons) is: $79.

A set of rares is worth $26.

A set of uncommons is worth $13.

A set of commons is worth $6.50.

I paid $85 for a full set. I should expect to pay $124. But the seller certainly didn’t pay the full retail price, he probably paid wholesale at about 50%, so $62. He made $23. I saved $39.

Not including labor.

**Correction:**

The calculations for foil/rare/uncommon/common sets, at $79/$26/$13/$6.50, are based on the calculation that 30 foils = 90 rares = 180 uncommon = 360 commons. But since there are 66 rares in a full set (more than twice the number of foils), the value of a set of rares would be:

The value per rare card: $79/90 = $0.88

A set of 66 rare cards: $0.88 * 66 = $58

A set of 60 uncommons: $0.44 * 60 = $26

A set of 78 commons: $0.22 * 78 = $17

The expected retail value for a full set: $180

is there a way to know which packs has the holo cards.

because i am buying packs and there is no holo card in most of them.

Is there a way to know if the pack has holo or not. thats all

thanks

There are foils in 1 of every 4 boosters. There is no way to tell which packs have the foils. You might open 10 packs in a row and not find any, and then get 3 in a row.