Frank Floor Talk: The Math That Gaming Made — Again

Frank Floor Talk: The Math That Gaming Made — Again

  • Buddy Frank, CDC Gaming Reports
June 22, 2022 2:00 PM
  • Buddy Frank, CDC Gaming Reports
  • Other

Andrew Cardno and Ralph Thomas, Ph.D

140 pp., 2021, Casino Services Publishing LLC

Not every book can be a page turner that you can’t set down like the mystery thrillers from Connelly or Baldacci. You won’t learn much from them, but they are wildly entertaining.

 width=There are a few books that are both entertaining, yet educational. Some titles that come to mind are Who Moved My Cheese?, Freakonomics and Moneyball.

Then there are the books that have almost zero entertainment value, but you have to read them. For a slot director, that can include non-thrillers like “Section 542.13 of the Federal Minimum Control Standards (MICS)” or “U.S. Code Title 31”. Hard to believe that the Feds make us re-read that dull tome annually!

Another category are those non-entertaining books that are not required, but you should read anyway. Unfortunately, many of those contain the “M” word and are, therefore, avoided like the plague by some. But if you’re in the casino gaming business, you’ll never reach your full potential unless you learn as much as you can about “Math”.

While they may never have taken a course, there are few serious gamblers that don’t have a good understanding of basic probability theory. And many of them know it better than some casino executives. Don’t be one of them.

For the next three book reviews, I’ll discuss those books that should be on your shelf, and hopefully you’ll make a good effort to read them as needed. In reverse order they are Casino Math by Hannum and Cabot; Probability Guide to Gambling by Catalin Barboianu, and this month’s subject, The Math That Gaming Made – Again.

The Introduction of this latest book from Andrew Cardno and Dr. Ralph Thomas is a good summary of what follows and gives a pretty clear reason why you should set aside some time to read it:

Ralph and Andrew love math, difficult problems and exploring new angles to solve analytical challenges of the gaming industry. This refers not only to Mathematics itself, but to applying math dynamics to the operational decisions required to make these ideas practical and to essentially: find the money.”

The “Again” in the title indicates that this is a new version of an earlier work first published in 2008 and 2011, with some co-contributions by author Dr. A.K. Singh at UNLV. Singh is missing from this new version released in November of 2021, but there are several new topics covered here that make this worth reading even if you have worn-out your earlier version like I have.

Surprisingly, you can’t find any discounts on the older book. It is still selling for $99.95 on used book sites (if you can find a copy). That makes buying the latest edition a no-brainer, even without all the updates. Carefully check before ordering. You’ll want to make sure you’re getting the one with the blue cover and the word “Again” in the title.

I once asked another author writing on slot analytics why his book was so expensive. I think his reply works here: “There is a very limited audience for this material and most folks will buy it using the casino’s credit card.” Feel free to tell your boss that I (and probably the authors) say the lessons in this book will almost certainly increase your casino revenues!

At times, the subtitle “Proven Methods For Seeing Into Your Data” seems more like a series of articles (some related; some on diverse topics) rather than a standard volume. That’s because the genesis of this work was a series of magazine articles first penned by Thomas and Cardno for the now-defunct “Casino Management Enterprise” (CEM) monthly edited by the late Peter Mead. Both authors have continued their writing on casino topics with submissions to various books and periodicals through the present day. This book contains the best of them.

Over-simplifying their credentials, Thomas is a mathematician who worked on his masters at Princeton and the University of Chicago before earning his doctorate at UNLV. He left the campus world behind to spend a few years as Director of Database Marketing at Stations Casinos and then nearly six years at Seminole Gaming as VP of Strategic Analytics and DB Marketing. In 2013 he began as a data scientist at Viz Explorer, where he met Andrew Cardno.

Cardno came to the U.S. from New Zealand, where he studied Engineering and Computer Science at the University of Otago and Victoria University. One of his first jobs was as a surveyor where he fell in love with computerized cartography (mapping). Early in 1999, he founded Compudigm, a breakthrough product in casino visualization and data analytics. That company was later acquired by Bally. In 2008 he founded and served as CTO for Viz Explorer, taking analytics and visualization several steps further.

After both left Viz (and a few years away from gaming), they returned in February 2020 to form Quick Custom Intelligence (QCI), a new solution that again advanced casino analytics. Their new product includes a stronger focus on marketing, hosting, faster slot/table visualizations and easy-to-customize reporting. Many of the ideas in this new book are incorporated as part of their QCI product, but the lessons here can be applied using any technology.

Most math books lose the reader within the first few pages by sprinkling in a few derivative symbols (  f  ) or some combination of terms littered with Greek or Latin symbols        . While the authors largely avoid that, they do insert some terms in the Introduction that sound scary, like “Non-Linear Least Squares Regression.” I think they do that to just make sure you realize that they are smart guys (they are!).

But in addition to being certified math nerds, they are also good writers and use an easy-to-follow approach to new analytic methods that are relevant (and understandable) for nearly all operators in slots/tables and marketing (no advanced degree is required).

What would require that degree is a proof of Pierre de Fermat’s 1683 “Last Theorem”. He stated that no numbers greater than 2 exist for “n” in the formula an+bn=cn . The authors use that difficult math concept to explain in Chapter 7 that solutions to complicated math problems have a practical relationship within casino operations. How do you fairly issue comps to reward players on a “multi-game” slot machine where hold percentages vary by customer depending on the game they select? Using the author’s method of analyzing “heuristic” data rather than “applied” data provides a real-world solution when combined with customer data and slot data (trust me, the authors explain it much better than I do).

If you’ve followed the on-line disagreements I’ve had with Dr. Anthony Lucas at UNLV who claims increasing hold percentage on slot machines has minimal impact on play, you might really enjoy Chapter 13 on the “Gaming Floors of the Future”. The authors don’t specifically take a side on the issue, but they correctly point out that calculating hold is far more complex that running computer simulations on machines alone. A proper analysis also requires a deep dive on customer characteristics such as time-on-device, skill, game choice, budget, etc.

Of course, I love their summary statement that says, “We have often heard statements like ‘If we raised the hold percentage by 0.1 percent, we’d make an extra Coin In x 0.1%!’ But as we have illustrated; these kinds of statements are misleading at best and may cost revenue at worst.”

Likewise, if you follow the advice they provide in the chapters on “Control Groups,” “Analytical War Rooms,” and “Incremental Revenue,” you’ll almost instantly recoup the $100 bucks spent on this book many times over.

Finally, I’ve always been a fan of a good “Gaming Glossary.” IGT used to include one online, but it’s no longer available. Cardno and Thomas, with help from Geethra Kanaparan, have included a great one at the end of this book that’s an invaluable resource when you’re not quite sure how to explain “volatility” or the aforementioned “Non-Linear Least Squares Regression”. They even provide definitions that range from “Astragalus” to “Staycation”.

Buy this book. It may not be a page turner, but it is a very valuable read by two of the best and brightest authors in our industry.

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In the rare event that you like reading math-related titles, here are some other suggestions beyond the three that I’ll review:

  • The Mathematics of Games and Gambling by Edward Packel
  • The Theory of Gambling and Statistical Logic by Richard Epstein
  • The Theory of Blackjack & Gambling Ramblings by Peter Griffin
  • Mensa Guide to Casino Gambling – Winning Ways by Mensa