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. Also, 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 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 an 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 an MTG booster pack and scratch-off cost USD 3.00 to buy. The reason I am using $3.00 is that 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. Also, 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 of 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 an 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. Also, 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 offers 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 knowledge and opinion. It is meant for informational purposes only. I am not a registered financial professional or trying to act as one.*​

2/1/2020 12:33:35 pm