Upon request of a client we graded two International Edition cards from the game Magic: the Gathering: a Mox Sapphire and a Black Lotus. In addition to our normal grading and authentication service, the client asked if we could verify if the cards have been tampered with by cutting the edges of the cards.

Since International Edition cards have square corners, they are more susceptible to this type of tampering. One reason to cut the edges is to ensure the cards are more centered, resulting in a higher grade. Another reason is to created smoother edges that are free of whitening and damage. This would also result in a higher grade.

Approach

To determine if the cards have been tampered with, we accurately measured the dimensions of height, width and weight of both cards and compared these to a random sample of 50 International Edition cards.

The table below shows the dimensions of the card. These have been measured using a precise kitchen scale (0.01 gram accuracy) for the weight and a digital caliper (0.01 mm accuracy) for the height and width.

To determine if the cards have been modified by cutting the edges, we compared the Black Lotus and Mox Sapphire with a random set of 50 International Edition cards. These were purchased from a single source. We assumed they have not been tampered with individually. Since these are low-value cards of several euros apiece, we consider this assumption justified. Measuring the heights, widths and weights of all the cards using the same techniques as described above yields the following mean values:

Results

Using a simple statistical analysis for the weight and height values of the Mox Sapphire and Black Lotus, we deduce the probabilities that these values are equal to or smaller than those of the cards. The results are presented in the following table:

The width and height values for the Mox Sapphire are well within one standard deviation from the mean values. The same goes for the height of the Black Lotus. The Black Lotus' width, however, is 1,42 standard deviations away from the mean value. This means that about 10% of International Edition cards are less wide than this Black Lotus card.

Conclusion

Have the cards been tampered with? To answer this question we must first consider the analysis above. We've established that there is a significant probability that the Mox Sapphire has not been tampered with. The same goes for the height of the Black Lotus. The width of the Black Lotus falls outside of one standard deviation from the mean. This means that 90% are wider than this Black Lotus card.

But how likely is it that this is due to tampering? Consider the mean value for the width of International Edition cards. This value is 63,0 mm. To cut this down to the width of the Black Lotus would require a blade not wider than 0,2 mm. Scalpel knives are available in widths smaller than this, so there is a possibility that the height of this card has been altered. Still, given the analysis above, the values for the height and width of the Black Lotus seem plausible. Combining these values with the centering values in the grading report we consider the probability of this card being tampered with as unlikely.