Jess Marcum, a physicist for the Rand Corporation, was the first player to devise and deploy a fully-developed blackjack card counting system. Read this Blackjack Forum article to understand more about the early history of card counting.
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Jess Marcum and the History of Card Counting

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Jess Marcum, Mathematical Genius, and the History of Card Counting

By Allan Schaffer, Ph.D.
(From Blackjack Forum Volume XXIV #3, Summer 2005)
© 2005 Blackjack Forum

[Editor’s Note: The thing that keeps striking me about Jess Marcum is the depth and intensity of respect and loyalty to him of the people who actually knew him and his achievements.

Marcum didn’t go for publicity or fame—he avoided it. He never published anything about his pioneering blackjack system. Yet 13 years after his death and over 50 years after his major accomplishments in card counting, he’s still vividly remembered by the professional gamblers who were active in Las Vegas then as the smart guy who figured it out, as well as to his later friends.

We are going to be documenting the history of those early days of card counting by publishing more articles on and by these early players in future issues of Blackjack Forum. Arnold Snyder]

Introduction to Jess Marcum and the History of Card Counting

Jess Marcum, card counting pioneerJess Marcum developed a basic strategy for blackjack and was counting cards a decade before anyone else. Why is it then that not many of the members of today’s gambling community have heard of him? The reason is basically because he was a very private person. In addition, throughout his active gambling career he endeavored to keep his accomplishments secret to protect the opportunities he had discovered.

I am one of the few people who know much of the story. We were close friends for the last 15 years of his life and were also coworkers and partners for extended periods during that time. I had a number of opportunities to ask him questions about his adventures in casino gambling and his answers are the basis for much of this article.

My reasons for writing the article are both to augment the history of blackjack and to correct or verify, as the case may be, some of the things that have been written about Jess.

Jess Marcum at Rand Corporation

Jess Ira Marcum (originally Marcovitch) was born in Knoxville, Tennessee on December 30, 1919. His father had emigrated from Russia in 1904 at the age of 14 and was an entomologist and professor at the University of Tennessee. His mother, a librarian, had come from Austria in 1902. Both were fluent in Yiddish.

There is little evidence in what is known about his early life to suggest that he was destined to become a genius in mathematical analysis. He graduated from college as an electrical engineer about 1940 and went to work for the Westinghouse Corporation in Pittsburgh. His duties later took him to England. After the war he studied for a Ph.D., I believe, at Princeton University, but quit because he lost patience with formal education (perhaps a sign of genius).

In 1947 he joined the highly respected Rand Corporation think-tank located at Santa Monica, California. He was not a founder of Rand, as reported in some articles, but by solving extremely difficult problems that no one else could, he became Rand’s preeminent mathematician with an international reputation. This was an astonishing accomplishment in view of the fact he had only a BS degree and Rand was loaded with brainpower and Ph.D. mathematicians. His genius had emerged.

His principal interest at Rand was statistical physics with emphasis on nuclear radiation propagation, nuclear effects and the processing of electromagnetic wave data. His premiere accomplishment was formulating the original equations for calculating the radar backscatter from a steady target in a noisy background, the so-called signal-to-noise ratio on which all radar design is based. Since the government classified this work as secret, it was many years before the scientific literature could acknowledge it as the Marcum equation.

Thus, his two premiere mathematical accomplishments in life—supplying the formulation for radar design and beating blackjack with card counting—were not widely known. However, this lack of (deserved) fame did not bother Jess at all. He was content with solving problems that others could not and beating the odds.

Marcum Leaves Rand for Gambling

Jess became enchanted with the mathematical analysis of casino gambling around 1949. A few years later he left California for the casino world and lived in that environment for the next 15 to 20 years. Although he still consulted on scientific matters, gambling activities consumed most of his time. Later in this article I will relate what he told me about his blackjack adventures during this period.

Sometime in the late 1960’s or early 1970’s Jess moved back to California and again made scientific work his principal activity. However, he continued to be in high demand as a consultant to both the gambling industry and to gaming commissions. For his scientific habitat in California he joined a company named RDA, formed mostly by ex-Rand luminaries. It was there that I met Jess. We worked together at RDA for a number of years and starting in 1977 were partners in a gambling-related sideline adventure that lasted for almost a decade.

In the late 1980’s Jess became addicted to the sleeping pill Halcion and it almost killed him. Some of the side effects were deep depression, difficulty in concentrating, and physical deterioration. Relatives and friends, myself included, tried unsuccessfully to convince him to seek medical help. Finally one friend literally forced him to go to a hospital and, once there, he made a remarkably fast and almost complete recovery.

He then moved to Reno, his favorite place, where he spent the last few years of his life living in a hotel. In 1990 he briefly returned to casino consulting in an episode so spectacular that it made the front page of the Wall Street Journal. His efforts rescued the Trump Plaza Casino from a mysterious “whale” who had, in a previous visit, won six million dollars at baccarat. I will give some more information about this episode near the end of the present article.

Jess died from natural causes in Reno at the age of 72. He had been dead for several days when his body was discovered in his room by a hotel employee. His death certificate is dated January 16, 1992.

Jess Marcum Invents Card Counting

What I know about Jess and blackjack comes directly from his answers to my questions. It was not his manner to volunteer information about his exploits, but I was curious and he answered each of my queries straightforwardly. In retrospect I wish that I had asked more questions.

You may be wondering why he gave me this information when, to my knowledge, he never provided it to anyone else. The reason is probably that our close relationship came late in his career when his casino playing days were long over.

One day in 1949 a coworker at Rand, who often visited Las Vegas on weekends to gamble, talked Jess into accompanying him on one of these trips. At that time Jess knew little about casino gambling. He spent this first visit to Las Vegas observing the various games, particularly blackjack, which at that time was played with a single deck dealt down to the last card.

On the drive back to California he shared with his friend the (then startling) observation that, if one were to keep track of the cards previously dealt from the blackjack deck, one would have a significant advantage at the end. In fact, one could know exactly what the last card was going to be. He said that he was going to analyze this situation and felt obliged to offer his friend the opportunity to join him. His friend declined. I believe that this was the only time that Jess ever considered partnering with anyone in blackjack.

Jess carried out his analysis of blackjack with only pencil, paper and his mathematical genius. Jess never used a computer to solve a problem; in fact he was, by choice, computer illiterate. He solved everything analytically; that is, he derived equations to obtain his answers. In some cases, once he had derived the relevant equations, he might have an associate carry out any ensuing routine calculations on a computational machine of some type, but in the case of blackjack, I do not believe that even this secondary association with such machines occurred.

The equations that he developed for blackjack produced both a strategy for betting and algorithms for recording the running card count and translating the results into an actionable assessment. To my knowledge his notes have not survived, but it is safe to say that his feat has never been duplicated, since subsequent blackjack analyses have largely been based on computer simulations whereby many thousands of hands are played to analyze each situation statistically.

Jess determined that his overall advantage against the casinos was about 3%, a number within the range of later results quoted for computer simulations with similar systems.

When Jess moved full force on the Las Vegas casinos in the early 1950’s, they literally never knew what hit them. He was aware that counting cards was tedious and that realizing the fruits of a 3% advantage required many long and patient hours, but he also knew that the outcome was a certainty.

He won steadily. He tried to be as inconspicuous as he could, but before too long he began to attract the attention of casino management. The pit bosses hovered over him continuously, but, although it was evident to them that he had a never-before-seen winning method, they had no idea as to how he was accomplishing this feat.

Nine months passed and they were still baffled. Finally in desperation the Las Vegas casinos joined together and banned him from further play. He might be the first person ever banned anywhere for simply being too good at gambling. No one knows how much money he won during this, or any of his subsequent, blackjack ventures.

After Las Vegas the next target area was Reno. The story was the same. He won steadily and the casinos were completely befuddled. After six months, desperate, they engaged a detective, who shortly after uncovered Jess’s Las Vegas exploits. Of course the Reno casinos immediately banned him.

He then moved on to various other casino locations. One place that he mentioned was Hot Springs, Arkansas, at that time a gambling hotbed. Another was Havana. Although I never personally discussed with him any details of his Havana venture, Sam Cohen (whose biography of Jess I will deal with later) reports seeing a clipping from the front page of the Miami Herald that described Jess’s triumph in Havana.

Jess Marcum and Ed Thorp

I was surprised one day when Jess made a less than complimentary remark about the blackjack analyses of Dr. Edward Thorp, who wrote the classic book Beat the Dealer published in 1962. The problem, as Jess expressed it to me, was that Thorp had to use computer simulations to solve a problem that Jess had solved analytically a decade earlier.[i]

This criticism has always seemed unfair to me in view of the fact that Jess had chosen to keep his own work secret. In any event Jess said that he had no quarrel with the correctness of Thorp’s results and that they were consistent with his own.

Jess also told me that he had tried unsuccessfully via an emissary to dissuade Thorp from publishing the book[ii]. When I asked Jess why he cared, since I was under the impression that he had exploited all of the available opportunities, he growled back “there was still the Caribbean”. He meant that he had not as yet visited the Caribbean casinos, and in fact he never did. Apparently, however, he had covered all of the casinos in the U.S. as well as Havana and perhaps elsewhere.

Upon the publication of Thorp’s book, Jess chose to end his own active blackjack career. Beating the casinos had been his private province for about a decade, and he was no longer interested when the winning techniques became available to the public.

Although Dr. Thorp did not personally know Jess (out of courtesy he referred to him only as “the little dark-haired guy from Southern California”), he does include in his book a few of the stories about Jess that have circulated around the gambling world. Only one of these stories is, I believe, factual; namely that Jess was the sole player to have been barred from blackjack in Las Vegas up until that time.

Marcum and Ruchman

Peter Ruchman, in his year 2000 column entitled “How BJ Card Counting Really Started” and his follow-up 2001 column entitled “Thorp Steps Up to the Plate,” purports, among other things, to recount Jess’s blackjack adventures. Although Ruchman does properly deduce that Jess was the first person to calculate a Basic Strategy, his deduction is based on the idea that Jess was able to use a high powered computer for this purpose.

Ruchman says that Jess fed thousands of punch cards through an IBM 704 computer to develop his blackjack strategy, which he subsequently shared with a small group of Las Vegas gambling friends to form a winning consortium. What Ruchman wrote is very different from the account that Jess gave me. In particular, Jess took pride in the fact that he had developed his system mathematically.

Jess Marcum and Sam Cohen

Sam Cohen, who was a coworker and sometime friend of Jess’s, wrote Jess’s only biography, which he titled The Automat—Jess Marcum, Gambling Genius of the Century. One reason for my writing the present article is to comment on Cohen’s book.

It is unfortunate that his biography was written by a man who felt extremely hostile to Jess. The book contains many interesting facts and anecdotes about Jess. However, Cohen’s statements that Jess became sadistic, psychotic, and ultimately committed suicide are completely at odds with my experience and with the testimony of all of his friends and associates with whom I conferred. Jess did have some quirks, such as being exceedingly tight with money, but nothing that any of us considered highly abnormal.

I can think of two reasons why Cohen came to hate him. One is that Jess needled Cohen incessantly. The incentive for this needling probably stemmed from Jess’s intense interest in psychiatry, which rivaled his interest in mathematics. His psychiatric self training led him to analyze each of his acquaintances and then to treat them as he concluded that they deserved to be treated. He evidently concluded that Cohen deserved to be needled, but I know of no other person, regardless of status, that Jess treated uncongenially.

The other reason for Cohen’s animosity probably resulted from the strong motherly affection that Cohen’s wife displayed for Jess. She continually looked after Jess despite Cohen’s objections. When Jess went through his disastrous times with Halcion, Cohen’s wife and I, unknown to each other, were both with him a lot and concluded independently that his problems, which were severe, were almost entirely due to the pills. By Jess’s own statement to me later, 90% of his problems disappeared when he finally ended his addiction to the pills.

From the gambling viewpoint there are several apparent fallacies in Cohen’s book. He states that it “is meant to be a tale mainly about the life and exploits of Jess in the world of gambling”. However, Cohen’s account differs greatly from what Jess told me.

Moreover, as I will explain, some of what Cohen thought he knew appears to be based on disinformation. Cohen states that Jess’s original gambling accomplishment was the development of a system that won at horse racing, and that he moved to Las Vegas to exploit this system, was successful and “became the first horse better in Las Vegas history to be barred from betting”.

In actuality, Jess was not an expert in horse racing, nor was it ever really a major focus of his interest. However he did, while at Rand, develop two short-lived schemes that made him some money at horse racing.

One scheme involved using the suggested odds from a newspaper handicapper, which Jess determined could show a profit. This endeavor was terminated after a year or two by the death of the newspaper handicapper.

The other scheme involved win/show anomalies. By peering into the totelizator control room, Jess would surreptitiously observe the win and show pools at certain tracks where, at that time, this information was not displayed publicly on the tote boards. Whenever he detected a gross disparity in the wagering pools, he would make sizeable show bets.

Jess apparently used these two modest ventures in horse racing to mislead Cohen and others at Rand into believing that he was off to Vegas to play the races. Of course, he was going there to play his never-before-seen system for beating blackjack.

Cohen devotes just one page of his book to Jess’s blackjack adventures. He briefly summarizes what he had gleaned, or surmised, about Jess’s various exploits and states that Jess’s major forays were bankrolled by some big time gambling friends. This statement rings untrue to me. Jess was never in need of money and definitely not the type to share his gambling knowledge or winnings with anyone. I think that Cohen was again the victim of disinformation—this time to shield information about the magnitude of Jess’s winnings from others.

Cohen also says that while in Las Vegas Jess became a magnificent poker player. This statement too does not agree with what Jess told me. He said that, although he did play some in the big games in Las Vegas, he soon concluded that he was inherently not good enough to compete with the very top players and therefore lost interest in the game. [Editor’s note: This was a period when cheating was widespread in the poker rooms.]

Poker did not fall within Jess’s characterization of a potentially playable gamble because he could not definitively calculate the outcome. He gambled seriously only when he could calculate a positive return.

Jess Marcum’s Final Triumph

Although the vast majority of Jess Marcum’s gambling income came from playing blackjack, his gambling studies were certainly not limited to blackjack; in fact, he analyzed almost all of the common gambling games and devices from sports books to slot machines. In the various sports books he capitalized on occasional miscalculations by the oddsmakers. With regard to slot machines, his expertise in their statistics and fluctuations led the Nevada Gaming Commission to call on him often as a consultant.

It was principally in this role as consultant to the industry that Jess continued his association with gambling long after his active blackjack days were over. Very late in his life he gained national notoriety from a consulting assignment that he undertook for Donald Trump and his associates in Atlantic City, as I will discuss briefly next.

On June 28, 1990 Jess called me from his hotel in Reno and mentioned that there was an article concerning him on that day’s front page of The Wall Street Journal. It was entitled “Tale of a Whale: Mysterious Gambler Wins, Loses Millions” and it describes how Jess saved the Trump Plaza Casino from a mysterious gambler who, in his previous visit there, had won $6 million at baccarat.

This exciting story (it even includes a murder) was later masterfully researched and recounted by David Johnston in his book Temples of Chance, chapters 1 and 24. Johnston provides a realistic insight into the working of Jess’s mind as Jess combines his mathematical prowess with his (self-taught) psychiatric skill to harpoon the Whale.

In view of these extensive previous accounts of this episode, I am only going to summarize briefly Jess’s part in it. He described the whole thing rather succinctly to me. He said that in winning the first $6 million, the Whale had simply not played enough hands (700) to have a high probability of losing. Therefore, Jess advised the Trump people to just “let him play.” Although they were very nervous about following this advice, they did and ultimately the Whale lost $9.4 million.

I learned from the written accounts cited above that there were two key components to Jess’s analysis of this problem. First, he calculated that if the Whale could be enticed into playing 5000 hands or so, he would have only about a 15% chance of winning. However, since the Whale made a practice of quitting suddenly if he was winning significantly, a scheme was needed to ensure that he would not quit early.

Based on observing the Whale’s mannerisms at the gaming table, Jess concluded that the Whale would readily agree to a double-or-nothing rule; that is, play would end only when the gambler had either doubled his bankroll or lost it all. Jess calculated that the Whale was five times as likely to lose his bankroll as he was to double it.

As Jess (via his “psychoanalysis”) had predicted, the Whale agreed to the double-or-nothing rule. Play proceeded and, of course, turned out precisely as Jess had predicted. After 5,056 hands, the Whale had lost $9.4 million (84% of his bankroll). At that point, he quit in a huff.


After his Atlantic City triumph Jess returned to Reno and contented himself with exploiting sportsbook betting anomalies that sometimes arose due to calculational inaccuracies by the oddsmakers. He died suddenly less than two years after his return to Reno.

His epitaph should read mathematical genius and gambling legend. The scientific literature abundantly attests to the former. My hope is that this article will cement the latter. ♠

i Jess may possibly have been unaware of the early analytical work performed by Dr. Thorp prior to his resorting to the computer.

ii Dr. Thorp has informed me that he has no recollection of being contacted by an emissary from Jess Marcum.

For more information on Jess Marcum and the history of card counting, see The Big Book of Blackjack, by Arnold Snyder.

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  Jess Marcum and the History of Card Counting
Jess Marcum worked out the first fully-developed blackjack card counting system in the 1950s, many years before Beat the Dealer was published. But because Jess Marcum was profiting from his blackjack card counting system himself—and card counting was especially lucrative because the casinos had not seen it before—he did not publish his card counting system. Learn more about the early history of card counting in this article about Jess Marcum.