I recently went to Gambler's General Store in Las Vegas and looked through their cards for sale. I segregated the cards by the pattern on the back-side and purchased one deck for each unique distinct design I observed. Altogether, I purchased 14 decks. About half of these cards had edge sorting issues, the other half were safe, as far as I could tell at first look. After examining these cards more closely, there was one card, in particular, that I considered the safest. That card is the one used by the Cosmopolitan Casino in Las Vegas.

Here is the backside of the card used by the Cosmopolitan Casino, in the largest image size that this blog will allow:

the backside of the card used by the Cosmopolitan Casino, in the largest image size that this blog will allow -  back of a card image

I cut out and blew up the two bottom corners to inspect for subtle differences in the pattern towards the fade.

Here is the lower left corner of the card:

the lower left corner of the card - an image of a back side of a card

Here is the lower right corner of the card:

the lower right corner of the card

If you  look carefully, you will notice that the tiny circles on the left hand edge of the left corner are slightly more visible than the tiny circles on the right hand edge of the right corner. At this magnification the difference is noticeable. In practice, this is a meaningless flaw.

The following are my observations that lead me to the conclusion I reached about the safety of this card:

  • The bleached edge makes identification of an irregularity around the edges very difficult to identify.
  • Even with the bleached edge, the card is cut with extraordinary precision with respect to the fade of the design towards the bleached edge.
  • There are three distinct patterns that are repeatedly tiled: a star, a swirl and a circle. The multiple-design and tilted pattern on the back makes incidental marks and other defects hard to pick out.
  • The pattern around the logo is also cut with precision. Compare the cut of the pattern around the edges of the top and bottom logos: the symmetry is perfect.
  • The corners have symmetric designs.
  • There are the same number of each pattern (star, swirl, circle) between the logo and the edge of the card, and each is cut at the same point.

Staring at this card for the better part of an hour, I could find no meaningful asymmetry whatsoever. None.

No doubt there are other security features in this card, but I am no expert in cheating or illegal methods. For example, I can conjecture that the coloring may make certain cheating methods, like daubing or card marking, more difficult.  Likewise, the pattern and color may make identifying bends more challenging. The grade of paper makes warps and bending due to changes in temperature and humidity less likely. The finish is stain resistant and easy to keep clean. And no doubt, dealers are trained to quickly remove broken cards. These sorts of considerations are above my pay grade.

I do have an improvement: decrease the white area associated with logo or give it a fill color. Many decks put their casino logo in a color blend that matches the card back, rather than a text box. On the other hand, a complex logo gives multiple locations where an irregularity can occur. There is no fade around the logo. Any white area presents a potential danger as incidental marks are clearly visible in this area.

This card should be used as a model. Cards based on the game protection principles Cosmopolitan uses will go a long way towards mitigating card-pattern-based advantage play.

Received his Ph.D. in Mathematics from the University of Arizona in 1983. Eliot has been a Professor of both Mathematics and Computer Science. Eliot retired from academia in 2009. Eliot Jacobson