Art Benjamin: USBGF Board of Directors and TED Talk Mathemagician

By Karen Davis

Art Benjamin, a member of the USBGF Board of Directors since 2011, has made a video called Counting Magic: Handy Mental Shortcuts to Improve your Game. This lecture was originally presented at the 2018 Michigan Summer Championships and then taped at the 2018 Silicon Valley Open. It provides simple math tricks for counting, memorizing, and calculating that will markedly improve your game. Once you see the way that Art calculates with his fingers, you’ll appreciate the “Handy” in the video’s title! Be sure to view the Silicon Valley Open presentation.

Video – Counting Magic: Handy Mental Shortcuts to Improve your Game

Besides being a fine backgammon player and a lucid and entertaining teacher, Art has made many contributions to backgammon over the course of an interesting career.

Professional Career

Art grew up in Cleveland, where he attended public high school, going on to receive a Bachelor of Science degree in applied mathematics and statistics at Carnegie Mellon University in Pittsburgh in 1983. He received his Ph.D. in mathematical sciences in 1989 from Johns Hopkins University in Baltimore, where he met the love of his life, his wife Deena. Back then, Art was a frequent participant in the Beltway Backgammon Club weekly tournaments in nearby Washington, D.C., and began to study backgammon more seriously. He devoured Danny Kleinman’s and Bill Robertie’s books and became a strong intermediate player.

He joined the mathematics faculty at Harvey Mudd College in Claremont, CA, in 1989, where he has taught ever since. Known as a “mathemagician,” he has demonstrated and explained his mental arithmetic techniques to audiences throughout the world. Reader’s Digest calls him “America’s Best Math Whiz.” His book, Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks, is one of the most popular math books for the general public, with over 300,000 copies sold worldwide. It has been translated into a dozen languages. His most recent book, which was a New York Times bestseller, has the fun title The Magic of Math: Solving for x and Figuring Out Why.

He has produced five math courses for the video series The Great Courses. These are: Secrets of Mental Math; Joy of Mathematics; The Mathematics of Games and Puzzles: From Cards to Suduko; Discrete Mathematics; and his newest course, Math and Magic. The Great Courses has produced a successful course called How to Play Chess, and Art is hoping to convince them to do a course on backgammon too.

Art has given three TED Talks (Mental Math, Statistics vs. Calculus, and Fibonacci Numbers) which have been viewed over 20 million times.

He makes presentations to 50-60 groups a year around the country, including colleges, high schools, teacher organizations, managers, home schoolers, TED-like conferences (including one recently in Mexico), and science groups.

He spent 2012 and 2013 on sabbatical at Oxford University, where he participated in the London backgammon scene, meeting community leaders like Raj Jansari and Peter Bennet.

Service to the USBGF and the Backgammon Community

We were thrilled when Art accepted our invitation to serve on the USBGF Board of Directors. He has a passion for stimulating interest in the game and for educating young people. He has served as the chairman of the USBGF Education Committee, and currently chairs the USBGF Governance and Nominating Committee. As reflected in his Platinum Founding Sponsor status, he has been a generous financial donor to the organization as well.

Having been an integral part of the USBGF since its inception, Art takes pride in its progress and permanence. All the issues that have been worked through in the early years will, he believes, be taken for granted ten years from now—moving to a democratic membership-elected Board of Directors; refining bylaws; establish- ing a ratings and statistics system; promulgating tournament rules; and mounting a sophisticated communication outreach including a top-notch quarterly magazine (PrimeTime Backgammon) and the use of social media. A lot is happening, and it is an exciting time to be part of the organization.

Art is currently turning his talent to writing a feature column called “Math Overboard” for PrimeTime Backgammon, featuring bite-size techniques for backgammon counting, memorizing, and calculating.

Collegiate Backgammon

As a member of the USBGF Board of Directors, Art has assisted with efforts to interest college students in backgammon. In 2011 the USBGF reached out to college students across the U.S., stressing that the game would help them acquire valuable skills in math, statistics, and decision analysis. Under the leadership of Joe Russell, current chairman of the USBGF Board of Directors, and Phil Simborg, USBGF Education Adviser, the USBGF provided webinars, loans of backgammon boards, and qualified USBGF coaches. As a result, backgammon groups were formed at a dozen colleges and universities across the U.S., and online collegiate tournaments were held from 2011 through 2013.

Art formed a Harvey Mudd team. It was one of eight teams in the 2011 event, won by the University of California, Los Angeles, whose team was captained by Joe Roth and coached by Joe Russell. In 2012 Harvey Mudd won the tournament, defeating UCLA in the final. Its team consisted of Nathan Hall, Louis Ryan, and Jonathan Schwartz, who split the $690 scholarship first prize. Joe Russell noted, “I was truly impressed by the high quality of play. Harvey Mudd entered a strong team.”

Art coached the Harvey Mudd backgammon team consisting of (left to right) Jonathan Schwartz, Nathan Hall, and Louis Ryan which won the 2012 USBGF Collegiate Backgammon Championship.

The collegiate initiative ended in 2013, but a number of the players, including David Presser (Northwestern University), Ben Friesen (University of Michigan-Flint), and Michael Zakrajsek (University of Texas at Austin), have continued to be active, winning awards and contributing to the growth of the game.

Backgammon at Joint Math Meetings

Art has leveraged his status as a leading member of the professional mathematics community to introduce thousands of math professors and graduate students to backgammon. His efforts began in August 2011, when over 1000 mathematicians gathered in Lexington, Kentucky, for MathFest 2011, the annual meeting of the Mathematical Association of America. At Art’s initiative, the meeting featured “Backgammon Night,” a free social event offering group lessons, a quiz designed especially for top-level mathematicians, and a tournament to test their newly acquired skills. Art prepared the quiz and, along with Jennifer Quinn, math professor at the University of Washington, Tacoma, presented analysis of the problems afterward. Phil Simborg, USBGF Education Adviser; Chuck Bower, winner of the 2011 Chicago Open; and Frank Frigo, former world champion of backgammon, gave quick lessons on basics and answered questions throughout the tournament. Karen Davis, chairman of the USBGF Board of Directors, handled registration and USBGF enrollment. The quiz was won by David Nacin, an assistant professor of mathematics at William Paterson University in New Jersey. Nacin stated that the quiz questions would be appropriate for his combinatorics class. Art has also enlisted fellow players and math professors Bob Koca (Howard Community College) and Jason Lee (USBGF Online Match Series Editor) to provide mini-courses and lectures on backgammon, puzzles, and games at summer mathematics meet- ings in Hartford, CT, and Washington, D.C. One Boston session was covered on National Public Radio.

In the last few years, Art has arranged an evening of social backgammon at the Joint Mathematics Meetings (JMM) of mathematical societies that take place each January in cities around the U.S. For example, at the 2014 JMM in Baltimore, Art, Bob Koca, and Jason Lee teamed up with D.C.-area players including Karen Davis, Ed O’Laughlin, Bill Finneran, and Eva Mitter (now Eva Koca) to work with professors and graduate students of different skill levels. The workshop was designed to highlight the math aspects of backgammon and recruit more college students and professors to the game. Conference attendee Matt Lehman (University of Massachusetts, Boston) had this to say. “It was a lot of fun. I got to play a lot of people at my skill level. Backgammon is a fun, social game. The games are fast and you can talk. Especially enjoyable at the end of a long conference.”

A similar format has been followed for JMM ever since. The 2019 JMM will take place in Baltimore, where Art will host another evening backgammon session on Friday night, January 18, with the help of Bill Finneran, Ken Indart, Lew Webber, Jason Lee, and other local players.

ABT Tournament Record and Backgammon Career

An accomplished player, Art is #10 on the All-time American Backgammon Tour with a total of nearly 201 points. He had a lot of early success playing in southern California. Propelled by winning the 1993 Autumn Grand Prix Tournament in La Jolla, California, he placed second to Marty Storer in the first ABT in 1993. He then went on a fantastic winning streak, placing in seven tournaments from 1993 through 1997, finishing third in the ABT in 1996 and winning in 1997. In 1997 he won the Michigan tournament, his first major tournament win outside of California. He finished second in Pittsburgh in 1998.

Art’s life and priorities changed with the birth of his daughters Laurel in 1998 and Ariel in 2002. He no longer played in any out-of-town tournaments and focused on being a dad as well as a math professor and lecturer. Over the years Art has been a highly sought-after doubles partner—probably, he jokes, because he counts pips quickly. He won doubles with Trish Hegland at a Los Angeles tournament in 1990 and parlayed that into winning the 1990 Caesars Tahoe doubles event in Nevada.His involve- ment with the USBGF has brought him back into backgammon. He was late to computer analysis, in part because he owns a Mac which requires Parallels to run XG. Now that his kids are older, he has more time to devote to the game. He’s been taking lessons over the last two years from David Presser and is beginning to compete again in ABT tournaments. He has resumed his success in Doubles events. With Christian Briggs, he won the Doubles at the Nevada State Championships in November 2017, and in the May 2018 Tournament of Stars, again with Christian, he split first place with the team of Joe Russell and Chris Trencher. He and Chuck Bower were Open Doubles runners-up at the 2018 Michigan Summer Championships. He’s placed in the money in several recent ABT events, including winning the Seniors event at the 2017 California State Championship; 2nd Consolation at the 2014 California State Championship; tied for 3rd Consolation in the 2016 Los Angeles Open; tied for 8th in the 2017 Silicon Valley Open; and tied for 2nd in the 2018 Silicon Valley Open.

On the USBGF Online Tournament Circuit, he has an Elo rating of 1850, which puts him 12th on the USBGF Online Leaderboard. In June 2017, he won the Masters Divisional XLVII, defeating Karen Davis in the 21-point final match. Art finds both online and live play appealing. He knows he must spend more time on study if he wants to improve his game, but considers playing—with humans, not bots—to be more fun. And he loves, loves, loves importing his matches into XG and seeing his mistakes.

Backgammon Masters Awarding Body

Art participates in the Backgammon Masters Awarding Body (BMAB) qualification process. He has a 4.91 PR and is ranked as a BMAB Master, Class 3, with Class 2 award pending. His goal is to get to a 4.0 PR and a Grandmaster ranking. He plans to have his matches at future ABT tournaments recorded and submitted to BMAB for PR analysis.

When playing in a BMAB event, he is not thinking about winning or losing; he’s just trying to achieve a low PR. He aims for simple positions. He doesn’t care about the prize pool. He’s done well in BMAB events, but when he plays in Masters Jackpots or the Open division, he cares more about the win. His teacher and coach, David Presser, urges him just to play his best game, and not to change his play based on his opponent.

Looking Toward the Future

In Art’s opinion, backgammon is the best game for the mathematically inclined. It can also be a great tool for learning mathematics. He hopes to build even more connections between the USBGF and the collegiate mathematics community. In a very short amount of time, he has seen the USBGF put out a fantastic magazine and website, offering useful information for both new and experienced players. In the coming years, he sees the USBGF offering more tools and resources for tournament directors and a rating system that should attract international recognition. He is proud to be a USBGF Founding Sponsor. In the future, he would like to see the USBGF continue to: retain members, produce a high-quality magazine, support tournament directors, and support novices. He looks forward to seeing improvements on the USBGF website and rating system, and hopes a good backgammon server can be developed on which all members can play.

He concludes: “Why do I love backgammon? I can think of no better game where a little bit of math goes such a long way.”

This article originally appeared in the Fall 2018 issue of PrimeTime magazine. USBGF Premium and Founding Sponsor members enjoy access to valuable content designed to help improve your game.  Join or renew today to get insight from backgammon pros, keep up-to-date with tournament news, read player profiles, and more.

Ray’s Instant Replays: Cracking The Re-Whip in San Jose

Instant replays enhance sports viewing immeasurably. They are also now used to determine the right call by game officials at crucial moments of a contest. I think I can expand my horizons a little here and apply that concept to Backgammon Tournaments. Smart phones, live streaming, and recording stations proliferate the scene nowadays. As a result, specific plays can be highlighted and discussed. This will be my purpose here.

With such an endless supply of material available to us the USBGF wants to be on the leading edge of the backgammon information age with this blog. April Kennedy is a talented promoter and has become the Social Media Director for the USBGF, under the direction and influence of Karen Davis. They approached me with this idea as I have written a few articles for Prime Time magazine and have the most experience playing on the American Backgammon Tour over the last 25 years. Writing comes easily to me but I have never done a blog except to post occasionally at Stick Rice’s BG Online which remains a great source of real time backgammon information. I envision a process where I can log on and share pertinent positions, ideas and problems I have recently encountered over the board. Perhaps even between matches at a tournament. Maybe there will be an opportunity for Questions and Answers too.
As one of the most active players on the ABT, I can serve as your guide through the many maze like situations you will face playing matches. I might be able to bring obscure concepts into clearer focus for you or shine a light on those that you were not aware of. The possibilities are intriguing to me and I hope to gain knowledge and understanding myself while sharing it with you. We can all learn together and maybe a certain synergy will develop in the process.

The upcoming fall issue of Prime Time magazine highlights the return to backgammon of the great Art Benjamin. I think the American Backgammon Tour is in its 25th year and not many people know that Art was once the leader of the ABT for the first five years or so before he took a leave of absence to start his family and pursue his career as a math professor. It occurs to me that all of the current and former number one players on the ABT are now working closely with the USBGF in some capacity. Marty Storer, Art, and Neil Kazaross are current board mebers, for instance. I write freelance and will be the Captain for the maiden voyage of this blog.


So, let’s bust a bottle of champagne on the bow, and christen the SS INSTANT REPLAY shall we?

People like stories and I like telling them so here we go. Once upon a time, in the year 2018, I journeyed to San Jose… Intent upon playing in the Silicon Valley Open backgammon tournament run by Ken Bame and his staff. Ken runs a Swiss movement tournament and was ably assisted by Jeb Horton, a sort of travelling expert on Backgammon Tournaments. Ken and Jeb worked hard all weekend to get the job done but they were plagued by some inevitable slow play, as usual for most backgammon tournaments even though the use of play clocks has become widely accepted.

Regardless I was enjoying some good fortune in the event having won my first four matches. At that point there were three players left undefeated: Myself, Art Benjamin and the ever present Jack Edelson from Wisconsin. The draw was posted for round five, and Jack was going to play Art, then something went haywire and I noticed that I was paired against a player whose record was 2-2. Winners play winners in this format, so that would not do. The draw was redone and now I was to face Art and our match was designated to be streamed live.

Not wanting to embarrass Art who would soon be featured in Prime Time magazine, I let him win our match 9-2/9. Few players possess the innate sensitivity to work with a story line as I do (smile). Art sent me to bed with a respectable 4 and 1 record. Jack won his match so Jack and Art would go up the hill to fetch a pail of ABT points the next day. Jack fell down and lost his crown and Art remained undefeated. The leader board was taking form by now.

I had lost to Art and the next two players I played on day two. Having reached round eight, even Art had now lost a match to Chris Knapp, a player from Canada. Evidently Chris had a different idea for the ending of this story! As it happens Chris and Art played two more times in this event… The second of which spawned the subject of this article. I was watching them play and Art was leading 2-1/9. Art owned the cube on 2 and they were in a bear off. Art rolled a fortunate set and the position became this:

Rays Instant Replay Art 4 roll 9-11-18 XG answer


I thought idly that Art should redouble Chris and Chris would take it and this game would weigh heavily in the outcome of this relatively short match. Then Art fooled me! He began thinking and staring at the board. His hands were held at an awkward angle and his head was cocked to the side. It bounced a little as bits of information struggled to take center stage in his conscious thought process.
Art ciphers quicker than most so I didn’t have to wait long for his decision. He rolled the dice without redoubling. Both he and Chris, at his turn, rolled non doublets and then Art redoubled and Chris passed. The score was changed to 4-1/9 in Art’s favor. I took my leave at that point and resolved to revisit the situation with Art later. Meanwhile another great player and one of the fastest ever on the American Backgammon Tour walked by. Frank Talbot, another member of the USBGF Board of Directors. Frank likes to talk backgammon so I showed him the position too. Frank quickly recognized that double ones and double twos did not “work” for Art, and after some careful consideration Frank said: This is a hold, and he mentioned the score being a factor. That means no redouble in BG lingo, for the uninitiated.
In hindsight we can all see that Art and Frank have erred on the side of caution, while I would have carelessly re whipped a 4 cube over. Interestingly enough Art took second to Chris in the tournament, and Frank also cashed, while I did not. Frank’s feat was all the more impressive when you consider that he was 2 wins and 3 losses after five matches, necessitating that he win at least six matches in a row to cash. I was glad he proposed to call off our side bet in the money round after I lost it, lol.

I think we can learn something here given these circumstances. In general it may well be better to err on the side of caution than to have an itchy redoubling finger. Wild West gunfighters may not have been too adept at backgammon because somebody is likely to take you out with one lucky shot if you get into a lot of gunfights.

Fortunately after writing this article I got a call from Art, who was more than happy to have his match play boo boo shared with you. Art is secure in his masculinity and does not fret about showing he is human after all. In fact, the math professor in him explained to me the lesson that can be learned from this exercise. I think we all agree that though XG has a definitive idea about the line of play here, those lines get distorted in the human v human experience.

Let’s pick Art’s brain as I paraphrase what he told me before and after the XG analysis.
At the tournament Art was well prepared for my question which was why didn’t he redouble in the four roll position. He told me that he had memorized all the take points of 4 cubes in 9 point matches (!). Needless to say, I haven’t. He therefore knew that Chris Knapp had a take in a three roll position and so he could not lose his market in the four roll position unless he rolled a working doublet, thank you very much. I was playing for money on the side when he explained this and my opponent put the three roll position into XG mobile which said Chris should pass. I told him I would trust Arts math over XG mobile because Art has published more math and done more seminars than his smart phone. Then I lost thirty points to Stepan Nuniyants son Vadim. Get the picture???

After I had time to enter the position into XG and learn the bottom line, Art called me on the phone.
He explained that his chart (he has a chart?) noted that assuming 80% cube efficiency, the trailer’s take point at the score of 2-1 to 9 goes all the way down to 19%. Loosely translated that means because of potential future cube leverage you can take more freely at this relatively innocuous sore than usual. For example, the leader will need 30% game winning chances take an 8-cube if the game turns around.
In general terms, this would coincide with match play conventional wisdom. Leaders should protect their lead while trailers can become more aggressive.

The problem here, according to Art, was that, in retrospect, Chris does not have nearly enough cube efficiency. Efficiency is what Art called it and it was difficult for him to describe to me because he says it is complicated to ascertain. Enough said, Art! To try and explain the concept in layman’s terms, let’s think of cube efficiency as a function of time. In a holding game or long race the trailer would have sufficient time to find a good spot to effectively use the cube leverage the leader was handing him. Got it?
Here, in this four roll hybrid, the one thing we have little of is time! The dice will weigh heavily in the outcome and Chris must LOSE HIS MARKET by a mile to win. He won’t be able to get in any cute little 8 cubes on the come. Are you following me? If Chris rolls doubles to get an advantage, his winning chances won’t be 70%, they’ll be closer to 85%. His 8-cube would be very inefficient.

Anyway, due to this lack of cube efficiency Art said that Chris’ take point reverts back to the normal area of 25%. This makes holding back on the redouble a definite error, and the three roll position a blunder to take!

Rays Instant Replay Art 4 roll 9-11-18 XG answer

I guess Art will be revising those charts. Frank will become more deadly accurate OTB. I will remain confused. This game is hard, man.

In closing I will say that it is great to have Art back. He has a way of simplifying difficult problems and passing them on to us. He gave a seminar at this tournament and the last and I believe he will revolutionize the game and the way we think about it in the near future. Second place was a fine showing of his talent(s).

Congratulations Chris Knapp on winning your fourth ABT championship in recent years. If you can beat Art two out of three matches, you deserve it!

About Ray Fogerlund

Ray has the distinction of Backgammon Giant from 2007 to present, he was inducted into the USBGF Hall of Fame in 2017, and is the most active American Backgammon Tour player of all time.  The Ray’s Instant Replays blog series will catalog his playing experiences and bring some of his hard-earned wisdom to the masses.


Socrates knew a thing or two – OLM the USBGF Member Benefit you never heard of!

“what is the meaning of life?”

“When do you leave your anchor?”

“On the Final Roll do you double from 2 away 4 away with 2 on the deuce?”

Questions that would do Socrates proud.  The Socratic Method – Question, Answer, Debate, Learn!

[The is MSA (Member Services Announcement) #1, the first in a series of articles covering USBGF membership benefits]

One of the best kept secret USBGF Membership Benefits is the OLM (OnLine Match), as described by OLM Moderator Jason Lee:

I’m the moderator of the USBGF OLM, which has been in action since 2012.  The USBGF Members play a match against Neil Kazaross, at the pace of one move per day.  There is a vote each day on the move to make.  Think of the OLM as a giant consulting match — Neil Kazaross vs. the collective mind of the USBGF Members.

I have an email mailing list where people can get an update when a new position is posted for voting.  I try to put up a new position every day — occasionally days slip by without a vote, but lately I’ve been pretty on top of it.

One does not need to be on the mailing list to vote.  To vote, you could just go to the USBGF site, and look in the middle under “What’s New” — you can see a link that says “USBGF OLM” and then a date.  If you click on that, it brings you to the most recent posting.  Each posting will give the previous day’s position, a rollout, and the voting results.  Then I have expert commentary, currently written by Grant Hoffman and Steve Sax (formerly by Marty Storer and Mary Hickey).  After that, Neil has his position that he has to play, and gives his commentary.  Finally at the bottom, there’s a position to vote on, with a box to type in your move.  One must be a USBGF Member and be logged into the site with their USBGF credentials to vote.  I receive all the votes, tabulate them, and the move with the most votes is what is actually played by the USBGF Members.  I tabulate the results, get the commentary from my expert panel, get Neil’s move and commentary, and start all over again.

When I make the post each day, I send out that email to inform people that there is a new vote in the offing.

On each day’s posting, there is a place at the bottom where people can comment on the play, offering their opinions and generally discussing the move at hand.

On average, about 30 people vote each day.  The mailing list currently numbers around 80… not everybody participates every single day.

I think the OLM has value to players of all skill level.  There are a number of of Open level players who participate regularly, along with plenty of Intermediate and Beginners.  I think the skill level of the participating players varies widely.  In spite of that diversity of skill level, the USBGF Members, as a collective mind, play at a World Class level.



The OLM alone makes USBGF membership worthwhile to me.”  S.T. 2/27/18

Simborg Video Lesson: The Rule of Four

USBGF Teaching Pro Phil Simborg explains the Rule of Four and how using the formula will help you make a decision about doubling.
Featured content exclusively for USBGF Premium, Youth, & Basic Members.

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