Magic: The Gathering booster packs are sealed product that players open to obtain collectible trading cards. Booster packs contain a large spread of potential value when opened. Players often open sealed booster packs to find expensive chase cards. In a previous article on probabilities of Magic: The Gathering booster packs, I calculated the likelihood of opening a chase card. In addition, some players will open booster packs for a chance to receive a total value of cards that exceed the purchase price. This practice is often referred to as opening value.
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In a similar regard, individuals purchase lottery scratch-offs for a chance to receive a monetary amount greater than the purchase price. There are given odds to scratch a winning lottery card; however, those odds do not apply to all prizes available. A winning scratch-off could contain the value of the purchase price or a higher amount.

This article compares the probabilities of opening value between a MTG booster pack and a winning scratch-off card. The overall objective is to determine which option has a higher probability of earning a return greater than the purchase price. The base assumption is that a MTG booster pack and scratch-off cost $3.00 USD to buy. The reason I am using $3.00 is because many hobby shops value booster packs at $3.00 in store credit when giving out prizes. Also, some hobby shops offer players promotional pricing of 3 Standard set booster packs for $10.00. Additional data on the calculated probabilities are available here. Estimated value calculations for the Bingo Extra scratch-off and Throne of Eldraine booster pack can be found in the data file.

Scratch-Off Probabilities
​The North Carolina Lottery has a $3.00 scratch-off game called Bingo Extra. This game has listed odds to scratch a winner at approximately 1 in 4. The top prize of $75,000 has approximate odds of 1 in 930,000. I am using this specific scratch-off game as an example because of the price per purchase and simplistic odds of winning. On December 11th, 2019, I recorded the remaining prizes available that were winners. In addition, I recorded the number of prizes remaining at or over $100. The specific information is available in the provided data document found above. The breakdown to win various amounts cash is as follows:

I would like to note that the percentages for $3.00 and over $3.00 equal 25.0% when added together. It appears that there is a higher percent chance to receive a value greater than $3.00 versus breaking even at $3.00. This is because the quantity of remaining prizes above $3.00 is greater than the availability of prizes at $3.00.

​Comparing Potential Value of Magic: The Gathering Booster Packs and Scratch-Offs
To compare MTG booster packs and scratch-offs, I need to make a few additional assumptions. The opportunity cost is saving $3.00 by not buying either item. Second, the value pulled from a MTG booster pack assumes you can sell the cards at an average market price. Potential selling fees and shipping are excluded in this comparison. Third, the cost of a booster pack and scratch-off are the same.

The variance in card value between MTG sets makes it challenging to provide an overall comparison. To simplify matters, I will compare scratch-offs to the Throne of Eldraine set as a representation of Standard booster packs. Using TCGPlayer MID pricing, Eldraine contains 9 mythic and 7 rare valued at $3.00 or higher (December 11th, 2019). The probability to pull a rare or mythic over $3.00 in a booster pack was 1 in 5.26 or 19.01%. When referencing TCGPlayer LOW pricing, the probability drops to 1 in 7.56 or 13.22%. These calculations do not include the chance to open a foil rare or mythic in a pack. The probabilities to open specific foil rare and mythic cards are very low and were excluded for simplicity. 
    
Recall that the Bingo Extra scratch-off game has given odds of 1 in 4 or 25%. The probability to break even on a scratch-off is higher than an Eldraine booster pack. In addition, the calculated probability to win over $3.00 on a scratch-off is 14.89%. This percentage is lower than the TCGPlayer MID pricing for Eldraine, but higher than the TCGPlayer LOW pricing. The preferred pricing method of a player may alter opinions of which option provides better value. 

My takeaway from this comparison is that scratch-offs may provide a higher probability than booster packs to at least break even. Scratch-offs also offer a larger potential payout with top prizes valued higher than any Standard set MTG card. On the other hand, booster packs may provide a higher probability to earn value above their purchase price. It also appears that the estimated values are similar between the Bingo Extra scratch-off and Throne of Eldraine booster pack. Whether you buy a scratch-off or booster pack, the probability to receive more in value than what was spent is relatively low. If you are uncomfortable buying scratch-offs, then you may want to avoid buying booster packs altogether. 

*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.* ​

Over the holiday season, I went on a comedy bus tour for a friend's birthday celebration. We went on a Friday evening, rated R tour offered by Funny Bus. The comedy tour is a one and a half hour bus ride through various parts of Charlotte, North Carolina. The price for the tour was $30.00 per person. The bus stop is located across 7th Street Public Market and next to First Ward Park. A tour guide and driver hosted 28 passengers. Our bus was fully booked for the 6 p.m. time slot. We were allowed to bring alcoholic and non-alcoholic beverages on the bus. Seats on the bus are a first come, first serve basis. On the particular tour I experienced, the bus traveled through NoDa, South End, and other Charlotte neighborhoods. We stopped halfway through the tour for restrooms and beverage purchases at Heist Brewery.

The tour offered a comedic take on the history of Charlotte. While traveling through the city, our guide pointed out historic landmarks and shared interesting information. He also threw out various jokes to engage the audience. The majority of the historical information was new to me. Each member of our group learned something new about Charlotte during the tour. Our guide did a great job entertaining and interacting with everyone. It was clear that our guide was well versed in this specific tour.     

I thought the comedy tour was a great experience for out of town guests and current residents of Charlotte. The tour also accommodates large groups of people. I would recommend taking friends and family on the tour who want a unique experience while visiting Charlotte. The Funny Bus Comedy City Tour is a good option for celebrating your next special occasion or outing in Uptown. 

​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.

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 formula used to calculate pulling a specific mythic in a booster box (assuming 15 mythic and 53 rare cards) is. The calculated result 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 formula for finding 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).

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).

​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.* ​