Our Researcher Profile series highlights researchers and who have used resources in Special Collections & Archives (SCA) for a variety of projects ranging from articles and books to exhibits and documentaries and more.
This week's post focuses on the work of Dr. Mark E. Bollman, Chair and Professor of Mathematics in the Department of Mathematics & Computer Science at Albion College in Albion, MI.
Tell us a little bit about the project (book, exhibit, article, documentary, report) you researched in UNLV Special Collections & Archives.
I have conducted research for six books on gambling mathematics, all published or soon to be published by CRC Press/Taylor & Francis:
- Mathematics of Keno and Lotteries (MKL), © 2018
- Mathematics of Casino Carnival Games (MCCG), © 2020.
- Mathematics of the Big Four Casino Table Games (MB4), © 2021.
- Basic Gambling Mathematics: The Numbers Behind the Neon, 2nd edition (NBN), © 2023. (The first edition was published in 2014, before my first visit to the SCA).
- Intermediate Poker Mathematics (IPM), © 2025.
- Blackjack Mathematics for Non-Mathematicians, (BJMNM), under contract and in preparation, to appear in 2026.
My first trip to Special Collections and Archives was a three-week visit in the fall of 2017 while I was on sabbatical from Albion and working on both MKL and MCCG. I have made occasional return visits when I've been visiting Las Vegas (while my wife Laura enjoys the spas at the resort hotels) in some targeted searches for material in support of one of my other projects. I spent another 3-week sabbatical period in SCA in the spring of 2025 working specifcally on BJMNM.
How did you hear about Special Collections & Archives?
In 2006, I met David Schwartz, former director of the Center for Gaming Research* in Special Collections and Archives, at the launch for his book Roll the Bones (because every tourist goes to book launches when they visit Las Vegas, right?). This was probably the first time I was aware that these collections existed. At the time, I was working in other areas of mathematics, but I continued to follow his work and when I had shifted my research emphasis to gambling mathematics, I started planning to visit UNLV SCA.
What resources, collections or materials from Special Collections & Archives were most
impactful for your research?
For my second book, MKL, I made particular use of the John Hamilton Collection of Keno Pay Charts, which is an excellent repository of materials that aren't very durable and aren't readily available online or anywhere in the Midwest. When I was working on MB4, it was extremely helpful to find the John Ponticello Papers. He was the chief administrator of an interesting casino experiment called Stakes and Odds, about which little information exists outside of UNLV SCA. Similarly, the Benjamin F. Smith (System Smitty) Papers were very useful in my most recent visit working on BJMNM.
While writing each book, I found myself working through complete or near-complete runs of gaming periodicals such as Current Blackjack News, Gambling Times, Blackjack Confidential, and WIN Magazine. Again, these are resources that are difficult to locate at any other library. It's a fun little puzzle to sift through multiple issues of gambling magazines in search of the occasional nugget that is useful in my work.
Most recently, I had occasion to look into the Stardust Resort and Casino Collection in search of some documentation for a blackjack variant called Draw 21, which was offered at the Stardust in 1993. There were several copies of the rack card for Draw 21in one of the boxes; these are close to the only surviving rack cards from this game.
How did you become interested in the topic(s) you wrote about?
I have been interested in card games since childhood. I have a 1970 copy of According to Hoyle that I received as a gift in the early 1970s and has followed me throughout my many moves. Reading and rereading that book eventually combined with my professional development as a mathematician.
Beginning in 2002, I started teaching a course called "Chance" in the First-Year Seminar program at Albion College. This course, as I have come to describe it, focuses on "applications of probability and statistics for the educated citizen". Chance can trace its origins to a course originally developed at Dartmouth College; I inherited the outline and some of the readings from a retiring colleague. Over the course of several years teaching Chance, I found it difficult to find a mathematics book that covered the topics I wanted to explore without also covering a lot of extra topics that were not part of the Chance syllabus. In early 2012, after going through several math books over the years, I decided that I would simply have to write my own book. That became the first edition of NBN.
After NBN was published, I continued to read and write about the mathematics of casino games, both new game variations and historical games that I uncovered. Eventually, I realized that I had accumulated enough material to spin some of it off into a second book, which led to MKL. The other books followed as similar spinoffs from a continuing body of work; for me, research is more of a continuous process than a set of discrete projects. As the other books followed, I came to describe my research area as shifting from combinatorial number theory (the area of my Ph.D. thesis) to gambling mathematics or "applied probability," if I want to be taken a little more seriously as a mathematician.
I have since taught other courses on gambling mathematics in Albion's Honors Program, in the Albion Area Lifelong Learners local Elderhostel program, and a course offered to mathematics and computer science majors that travels to Las Vegas over spring break to compare theory and practice.
What surprised you the most about your research in Special Collections & Archives?
The obvious answer is the sheer volume of material that's been preserved in SCA, but that's not necessarily surprising as much as what one might reasonably expect from a well-curated library collection. What's also amazing is the wide range of artifacts, both print and otherwise, that someone saw fit to set aside on the off chance that someone might be interested in seeing them again someday.
What advice would you give to other authors/researchers using Special Collections & Archives? (Otherwise known as what I wish someone had told me before I visited Special Collections & Archives)
Pace yourself. There's a lot of great information in SCA, and the materials aren't going anywhere. On my first day visiting in 2017, I nearly blew out my eyes trying to read as much as possible as fast as possible.
Also: Be aware of Rebel Hours. Fortunately, I checked the library's operating hours before traveling to Nevada in 2025, far enough ahead of time that I was able to request permission to enter Lied Library
How did your research in Special Collections & Archives change your perceptions about Las Vegas?
I'm a history buff of sorts, and over time have become interested in the history of Las Vegas. Laura and I made our first visit to town in 2000, to get married exactly 2000 days after we met. We have returned many times since, and I have discovered in my exploring the area that there's a lot of history that gets lost as the Strip and other tourist areas are redefined and redeveloped. So much of the history of this town has been remarkably well-preserved at SCA, and it's been a privilege to be able to explore these documents and memorabilia so close to their origin.
What are you working on next?
After BJMNM is published, I don't have an obvious next book in mind, which is a little unusual for me. I am looking into some smaller topics such as casino games played with nonstandard card decks, the mathematics of Class I games, and some new casino carnival games that I have worked with Albion students to develop in summer research projects. With the 2018 legalization of sports betting in the USA beyond Nevada, there may be some good mathematics to be uncovered in that area as well. Perhaps something in there will lead to book #8.
Something else I've been looking at is the rise of video keno and state lottery keno games even as live keno has declined on the Las Vegas Strip. A possible second edition of MKL could get into that at much greater length than the first edition did.
If you are from out of town, what other places did you visit (could be other sites for research, restaurants, etc.)
I regularly visit the Gambler's Book Club, Gambler's General Store, and Spinetti's Gaming Supplies when I'm in Las Vegas. There's a lot of gaming history in the form of memorabilia from those places that's found its way into my books. Additionally, I have visited every casino in Las Vegas, North Las Vegas, and Henderson multiple times to assess conditions on the ground.
Laura and I have an increasingly-long list of favored restaurants in town, including Lindo Michoacan on Desert Inn (both before and after the sinkhole in their dining room), Chicago Joe's, Metro Pizza on Decatur, Nora's, and the Bootlegger. Some of these have been recommended to Laura by spa employees. We are also big fans of Valley of Fire State Park; it's nice to enjoy the sense of quiet isolation that prevails there so close to the lights and sounds of the city
In my travels to Las Vegas with students, I have taken them to the Museum of Organized Crime and Law Enforcement, the Neon Museum, and the Atomic Testing Museum. There may not be a lot of math in those museums, but I like the students to come away with an appreciation that Las Vegas is a lot more than just a gambling town.
What is the biggest challenge you faced while working on your project?
There are times when it's challenging to convince people outside mathematics that studying gambling math is a serious scholarly pursuit and not just a way to justify hanging out in casinos. This is where "applied probability" is a useful way to describe what I do. It helps that I can point to my work in Special Collections and Archives as an important part of my research.
*Although the Center for Gaming Research (1988-2024) no longer has a physical presence, the gaming collections exist as part of Special Collections and Archives.
