I'm pretty sure many of us have thought about buying a few Divine Order packs to try our luck although we know we'd likely be better off simply just buying individual cards from the secondary market. It's commonly known that a pack is worth less than the sum of the value of the cards inside the packs on average, but by how much? Let's take a look.
I may make errors in calculations, so please correct me if there are any.
TL;DR Infographic
For everyone who just wants a look at the results, here's a quick infographic that sums it all up. The rest of the post goes into quite a bit of math.
Card Pack Prices
With the discount pool being emptied out, the costs of Divine Order packs are as follows:
- $2.49 for a rare pack
- $6.99 for an epic pack
- $24.99 for a legendary pack
- $149.99 for a shiny pack
For buying packs to be a better way to spend your money rather than buying individual cards, we should be getting more than $2.49 worth of cards in a rare pack, $6.99 worth of cards in an epic, and so on.
Understanding Card Slots
To understand how card packs work, I will be using the official Divine Order: Buyer's Guide as a reference.
Card packs of each variant all contain the same number and type of card slots, which determine the rarity of the cards that appear.
| Card Slot | Rare Pack | Epic Pack | Legendary Pack | Shiny Legendary Pack |
|---|---|---|---|---|
| 1 | Rare | Epic | Legendary | Shiny Legendary |
| 2 | Common | Rare | Rare | Rare |
| 3 | Common | Common | Common | Common |
| 4 | Common | Common | Common | Common |
| 5 | Common | Common | Common | Shiny Common |
| Card Type | Common Slot | Rare Slot | Epic Slot | Legendary Slot |
|---|---|---|---|---|
| Common Card | 92.4890% | 0% | 0% | 0% |
| Rare Card | 6.1875% | 85.294% | 0% | 0% |
| Epic Card | 1.1580% | 12.8675% | 98.1615% | 0% |
| Legendary Card | 0.1655% | 1.8385% | 1.8385% | 100% |
For a rare pack, there will always be 4 common slots and 1 rare slot. In each of the common slots, there's a ~92% chance that it'll be a common card, but there's a chance that it turns out to be a rare, epic, or even a legendary card. For the rare slot, although it will turn out to be a rare card most times, there's a chance that a rarer card shows up instead.
For each of these cards, they go through another round of RNG to determine their card quality.
| Quality | Most Cards | Shiny Common or Shiny Legendary |
|---|---|---|
| Meteorite | 93.8% | 0% |
| Shadow | 5% | 74.8% |
| Gold | 1% | 25% |
| Diamond | 0.2% | 0.2% |
For illustration, the chances of obtaining a Shadow Rare in a Common slot would be 6.1875% * 5% = 0.309%, or about 1 in every 324 occurrences.
Promo Cards
Since the Mythic card in the Divine Order set has already been unpacked, it is no longer possible to obtain it through packs. In place of the Mythic card, promo cards are dropped on a per-pack basis with the following probabilities:
| Probability | Rare Pack | Epic Pack | Legendary Pack | Shiny Legendary Pack |
|---|---|---|---|---|
| Promo | 0.01% | 0.03% | 0.01% | 0.01% |
From my understanding, promo cards will show up as an additional card alongside the 5 other cards in the pack, so they will not replace any slots when unpacked. Although there's not much demand for them, they are priced at 0.3ETH and above on TokenTrove. When factoring in these promo cards, I will simply take their value to be $1000 for simplicity.
Card Value
I scraped TokenTrove prices for Divine Order cards and obtained the following data. Do note that these values are constantly changing and what I have is merely a snapshot of the prices.
| Min | Max | Mean | Median | |
|---|---|---|---|---|
| Common Meteorite | $0.04 | $1.39 | $0.10 | $0.05 |
| Rare Meteorite | $0.10 | $3.33 | $0.37 | $0.13 |
| Epic Meteorite | $0.56 | $15.83 | $2.85 | $1.08 |
| Legendary Meteorite | $5.19 | $68.12 | $16.35 | $12.52 |
As the market for cards with card qualities above Meteorite tend to be much more illiquid, I will estimate prices for Shadow, Gold, and Diamond qualities of the same card to be 2x, 5x, and 15x the Meteorite prices respectively. All calculations will also use the mean/average value of each rarity.
Calculating the Expected Value of a Pack
The Expected Value (EV) of a pack is what you can expect a pack's contents to be worth on average after opening. This does not assume anything about a particular card pack's value, but the more packs you open, theoretically the closer the average pack values will be to the EV.
Before we calculate the EVs of the packs, we need to first calculate the EV of each type of slot. And before we can calculate that, we need to calculate the expected value of a random Common, Rare, Epic, and Legendary card.
EV(Common) = P(Meteorite)EV(MeteoCommon) + P(Shadow)EV(ShadowCommon) + P(Gold)EV(GoldCommon) + P(Diamond)EV(DiamondCommon)
= (0.938 * 0.10) + (0.05 * 0.10 * 2) + (0.01 * 0.10 * 5) + (0.002 * 0.10 * 15)
= 0.0938 + 0.01 + 0.005 * 0.003
= 0.1118
The expected value of a random common card is derived by taking the probabilities of getting the various qualities and multiplying them by the value of a common in that quality before summing them all up. From this, we find out that the expected value of a random common card should be ~11.18 cents.
Doing the same steps for the other rarities, we have the following results.
| EV | Value |
|---|---|
| Random Common Card | $0.1118 |
| Random Rare Card | $0.4137 |
| Random Epic Card | $3.1863 |
| Random Legendary Card | $19.0151 |
Now that we've got the EVs for each type of card down, we can now calculate the EVs of each type of slot. For illustration, I will be showing the working of calculating the EV of a common slot.
EV(Common Slot) = P(Common)EV(Common) + P(Rare)EV(Rare) + P(Epic)EV(Epic) + P(Legendary)EV(Legendary)
= (0.92489 * 0.1118) + (0.061875 * 0.4137) + (0.01158 * 3.1863) + (0.001655 * 19.0151)
= 0.1974
We can do the same for the other types of slots to obtain the following results.
| EV | Value |
|---|---|
| Common Slot | $0.1974 |
| Rare Slot | $1.1125 |
| Epic Slot | $3.4773 |
| Legendary Slot | $19.0151 |
Whew, that's a lot of math! Finally, we can calculate the expected values of each pack by summing up the expected values of each slot without considering the possible promo card inclusion for simplicity. As usual, I'll show you how this is done with the Rare Pack:
EV(Rare Pack) = 4 EV(Common Slot) + EV(Rare Slot)
= 1.9025
And the results for each type of pack, excluding the Shiny Legendary since it requires more calculations:
| EV | Value |
|---|---|
| Rare Pack w/o promo chance | $1.9025 |
| Epic Pack w/o promo chance | $5.1823 |
| Legendary Pack w/o promo chance | $20.7201 |
To make things complete, we'll factor in the expected value of getting a promo card (which I value at $1000 for simplicity's sake). A 0.01% chance at a $1000 card has an EV of $0.10, and a 0.03% chance has an EV of $0.30. I'll also pull in the official pack prices for easier comparison.
| EV | Value | Price on official site |
|---|---|---|
| Rare Pack | $2.0025 | $2.49 |
| Epic Pack | $5.4823 | $6.99 |
| Legendary Pack | $20.8201 | $24.99 |
With this, we can now calculate how much we are overpaying per pack on average.
| Pack | Overpaid on average by |
|---|---|
| Rare Pack | 24%, or $0.49 |
| Epic Pack | 27%, or $1.42 |
| Legendary Pack | 20%, or $4.17 |
Conclusion
I have always wanted to do this analysis on how much value a card pack actually holds, and I hope that this post has quenched some of your curiosities as well. Even though we may know that a card pack doesn't hold that much value on average, the feeling of unpacking random cards that may be worth much more than what we paid is always tempting.
What do you guys think? Would you still buy packs after knowing this?
Pack images from the Gods Unchained blog.