Comparing Potential Value Between Magic: The Gathering Booster Packs and Lottery Scratch-Offs

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.

Throne of Eldraine booster pack sealed

Cards inside pictured Throne of Eldraine booster pack

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:

Bingo Extra scratch-off

Prize	Probability	% Probability
$100 and above	1 in 676	0.148%
Over $3.00	​1 in 6.71	14.894%
$3.00	1 in 9.89	10.106%

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.* ​

This scratch-off was not a winner