Probabilities of Opening Valuable Cards in Magic: The Gathering Booster Packs

​I recently participated in a Pioneer format event for the Magic: The Gathering card game. The prize payout for the event was one booster pack or $3.00 store credit per win. Multiple players asked for packs of Eldritch Moon as their prize for winning at least one match. I asked a few of them why they chose booster packs from Eldritch Moon. The players said they were trying to pull three valuable rare and mythic cards. The specific cards were Collective Brutality, Lilliana, and Emrakul. I watched as each player opened their packs and were disappointed with the cards found inside. While I knew the probability of opening either of the valuable cards were low, I was unsure of the exact percentage. If the players knew the probability for pulling one of the three cards in a booster pack, would they have chosen the $3.00 in store credit?

In MTG, trading cards come in sealed booster packs. Each booster pack typically contains one rare or mythic card along with multiple uncommon and common rarity cards. Most new sets for MTG contain 15 mythic cards and 53 rare cards with differentiating abilities. The given probability of opening a mythic card in one booster pack is 1 in 8 or 12.50%. This means that the percentage of opening one rare in a booster pack is 7 in 8 or 87.50%. While these percentages refer to opening a mythic or rare card, they do not determine the probability of a specific mythic or rare. Additionally, the mythic and rare cards in each set vary in demand, playability, and monetary value on the secondary market. The calculations and data used in this article can be downloaded here.

Magic: The Gathering booster packs

Determining Probabilities for Opening Specific Rare and Mythic Cards
Calculating probabilities for opening specific rare and mythic cards is determined by how MTG cards are printed. According to Gamepedia’s MTG Wiki, current MTG cards are printed on 11 x 11 sheets. These sheets contain 121 cards. The rare and mythic cards for a set are printed together on one sheet. Print sheets contain one copy of each mythic and two copies of each rare in a set. Calculating the percentage of opening a specific mythic in a booster pack is simply 1 divided by 121 or 0.83%. Pulling a specific rare of out a booster pack is 2/121 or 1.65%.

​Each booster box of MTG cards typically contains 36 packs. Calculating the probability of opening a specific rare or mythic in a booster box combines 36 tries with the odds previously stated. The calculated result for pulling a specific mythic in a booster box (assuming 15 mythic and 53 rare cards) is 1 in 3.87 booster boxes or 25.83%. I believe it is important to understand how often you are likely to pull a specific high value mythic when buying a sealed booster box. The probability of pulling a specific rare in a booster box is 1 in 2.21 booster boxes or 45.12%. Pulling a specific rare in one booster box is not guaranteed.   

​​Probabilities for Opening Value in Throne of Eldraine
Throne of Eldraine, as well as other new Standard sets, typically contain 15 mythic and 53 rare cards. Not every mythic or rare in a set is valuable. There are usually chase cards that players want for a multitude of reasons. Using TCGPlayer MID pricing data from MTG Dawnglare on December 11th, 2019, I counted 9 mythic and 7 rare cards valued over $3.00. The probability of pulling a valuable mythic is 1 in 13.44 or a 7.44% chance. The probability for a valuable rare is 1 in 8.64 or 11.57%.  The odds for pulling any valuable rare or mythic over $3.00 are 1 in 5.26 or 19.01% (23/121). To summarize, you have a 19.01% chance of pulling at least the value of a booster pack in the slot for a mythic or rare card in Throne of Eldraine.
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If you would rather use TCGPlayer LOW pricing to calculate the probabilities for pulling value in booster boxes, the number of mythic cards over $3.00 drop to 8 and the rare cards drop to 4. This means that the probability of pulling any valuable mythic or rare card in a Throne of Eldraine booster pack is 1 in 7.56 or 13.22% (16/121).

Throne of Eldraine booster pack

Back of Throne of Eldraine booster pack

Probabilities for Opening Value in Eldritch Moon
The initial story in this article referred to a scenario of players opening Eldritch Moon booster packs. Eldritch Moon is a small set containing 14 mythic and 47 rare cards. Assuming these sheets were printed in the same method as Throne of Eldraine, the mythic and rare slot sheet would have a total of 121 cards. This means that 108 cards on the sheet are mythic or rare, with the remaining 13 slots containing filler cards. Because Gamepedia does not confirm the sheet’s rarity breakdown further, this logic will be used for probability calculations.

Since Eldritch Moon is a small set, the probability of pulling a specific mythic or rare card in a booster pack is slightly better than Throne of Eldraine. The probability for pulling a specific mythic is 1 in 108 or 0.93% and a specific rare is 1 in 54 or 1.85%. Using TCG Player MID pricing, there are 7 mythic and 8 rare cards in the set worth over $3.00. I included Mind’s Dilation and Game Trail in this count. The probability for opening a valuable mythic is 1 in 15.42 or 6.48%. The probability opening a valuable rare is 1 in 6.75 or 14.81%. The probability for finding a valuable rare or mythic in a booster pack is 4.69 or 21.30% (23/108). Note that these percentages are better than Throne of Eldraine due to more valuable rare cards and the smaller size of the set.
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When using TCGPlayer LOW pricing, the percentages become worse. The probability for opening a value mythic is the same as TCGPlayer MID (including Mind’s Dilation); however, the probability of opening a valuable rare decreases. With only four rare cards valued over $3 using TCGPlayer LOW, the probability becomes 1 in 13.5 or 7.41%. The probability for pulling a valuable mythic or rare card is 13.89% (15/108).

Eldrich Moon booster pack

​The Probability of Opening Collective Brutality, Emrakul, or Lilliana in an Eldritch Moon Booster Pack
We now have the information to calculate the probability of pulling Emrakul, Lilliana, or Collective Brutality. There are four total copies between the three cards on a print sheet. The probability of pulling one of these three cards in an Eldritch Moon booster back is 1 in 27 or 3.70% (4/108). To pull one of the cards in a booster box, the probability becomes 1 in 1.34 or 74.30%. If you had to choose between $3.00 in store credit or a 3.70% chance of pulling a chase card, which option would you pick? I would be curious to know if the players would still take an Eldritch Moon pack over $3.00 store credit after knowing these percentages.
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Many players at a Friday Night Magic event must make a similar decision between store credit and booster packs. I now know the choice per win is either $3.00 in store credit or a 19.03% chance on opening something more valuable from Throne of Eldraine. You may hear other players suggesting to always take store credit. Depending on the price of singles at a local game store, this recommendation is reasonable. I hope being more informed on the probabilities for pulling valuable cards helps you make better prize out decisions.

*The information in this article is of my own knowledge and opinion. It is meant for informational purposes only. I am not a registered financial professional or trying to act as one.* ​