Lorcana Enchanted Rarity

Enchanted is Lorcana’s sixth rarity, and its rarest rarity. Enchanted cards alternate art cards with a special finish and design, but the same mechanics as a lower-rarity card.

Left: Belle, Strange but Special. Right: The exact same card, but 10x more expensive.

In Lorcana, First Chapter boosters, enchanted cards can only show up in the foil slot of the booster. This means you have at most one chance to pull an enchanted card per pack.

So what are the approximate odds? There’s no official source for these odds. Instead we’re going to look at two separate sources of experimental data.

The first is from Digital TQ, who posted their breakdown here. I don’t trust this breakdown very much for several reasons, but I’m still going to use it, and I’ll talk about why in a bit.

This data set has 216 booster packs opened (9 boxes worth) and 5 enchanted cards pulled. This puts them at an experimental probability of 2.3148% odds of a booster pack containing an enchanted card.

The second data set is from a game store in Halifax, Nova Scotia called The Deck Box. They posted their own data from opening 18 booster boxes online, and had an experimental probability of 0.9259%.

Wonderful graph made by The Deck Box, with the experimental probabilities of various cards. Like, seriously. This is a really nice infographic.

So, we have two different sets of numbers. You might have noticed that what I didn’t do is just average these two numbers together, because that would violate principal one of the Fundamental Constraints of Math.

This might be better worded as “The Two Fundamental Constraints of Mathematical Analysis”. Also, in this diagram, the stupid person is me. I’m the stupid.

As such, experimental data indicates that the experimental probability of opening an Enchanted card is likely around 1%.

Math Time

Disclaimer: Any of the below writing and statement of the problem is the result of my requesting that some friends help me out. As a result, any mistakes for dumb shit, misinterptation of math, or misuse of statistics should fall to me, chief idiot of Gametrodon. Any praise for analysis or clever thought should go to them.

However, just because I’m stupid doesn’t mean my friends are. In fact, some of them are quite smart, and actually do statistics based things.

So I reached out to one of these friends, and asked him to help me calculate a range of probabilities for what the true rarity of enchanted cards is likely to be, and here’s what he came up with.

VanillaWald HighWilsonWilson LowWilson High
Estimated Probability of Rare0.0090.0180.01360.00360.0236

So based off these numbers, here’s what we can say.

Based on the assumption that the 432 packs were opened were a representative sample of Lorcana booster packs, we believe that the true probability of opening an Enchanted rarity Lorcana card in any given random pack is between 0.3%, and 2.3%.

So, assuming that’s the case, how many boosters would you need to open to probably get an enchanted card, for each of these probabilities?

Packs OpenedOdds of Getting At least 1 Enchanted Card at 0.3%
51.49%
102.96%
246.96%
9625.06%
Packs OpenedOdds of Getting At least 1 Enchanted Card at 1%
54.90%
109.56%
2421.43%
9661.90%
Packs OpenedOdds of Getting At least 1 Enchanted Card at 2.3%
510.98%
1020.76%
2442.79%
9689.29%

There are a lot of assumptions here, and I’m sure real statisticians are looking at this and wincing, but the point I mostly want to make with these charts is the following:

If something has a 1/100 chance of occurring, and you do it 100 times, there’s no guarantee of getting that 1/100 chance odds. Actual odds are around 60%.

Author’s Note: I don’t care about enchanted cards, because when all is said and done, they’re alt-arts, and that’s it. That said, leaving them out entirely seemed rude to people who might care. So I’ve compromised by giving them their own post.