4/6/2022

Strategic Investment Blackjack

Basic strategy is not enough! We get emails from people all the time talking about how they downloaded our blackjack charts, took them to a casino, and won some money. That’s great news for them, but it could have easily gone the other way. Basic strategy cannot overcome the house edge even if you get lucky with it from time to time.

  • Aug 01, 2019 Blackjack basic strategy is a set of rules and guidelines which allow you to maximize your winning odds. It is very hard, if not impossible, to make a profit playing Blackjack, especially in the long term, if you’re not employing the basic strategy. The basic strategy can be displayed either as a table (multiple tables) or as text.
  • Strategy adjustment and deviation In blackjack card counting, when faced with changes in true count, you need to adjust the strategy to play cards at the time, so as to get better results. In fact, according to true count to adjust the strategy can also get an additional 0.2% to 0.3% advantage for players.
  • Jul 01, 2019 The Blackjack Framework & Public Market Investing. While the investment world is quite a bit different from the blackjack table, the approach to capital allocation across asset classes and investment strategies should be thought about in a similar framework.
  • Oct 24, 2020 The reason casino blackjack tables have a maximum bet is exactly to counter the Martingale strategy. For example, a $10 minimum Table typically has a $500 maximum.

Some market participants have referred to the stock market as analogous to that of a casino and suggest the market being akin to legalized gambling. While we don’t think those parallels are necessarily warranted, we do think there are substantial overlaps between a public market and games of risk within a casino, particularly as it relates to gaining an edge. In this post, we will take a walk down the path of risk vs. reward as it relates to gaining a small edge using one of the most popular casino games in history – blackjack.

As a backdrop for this post, I can recall one of my first trips to Vegas and reading through the gauntlet of some of the most popular books that claimed to teach the “secrets to winning money in Vegas”. One of the all-time classics in this genre is Beat the Dealer: A Winning Strategy for the Game of Twenty One written in 1962 by Edward Thorp. The book provides granular detail into how one can utilize card counting techniques in order to gain an edge when playing blackjack in a standard casino. Thorp, who actually went on to be a revered investor, was one of the first to use the strategy of counting cards to effectively gain a small mathematical edge over the house. And, when this small edge was present, a player could increase the size of his or her bets to best exploit their edge against the dealer.

While counting cards is not necessarily an easy task (especially given the rules and number of decks used in today’s blackjack games), having the ability to achieve a very small edge against the house can have enormous benefits, particularly if applied consistently over many hands and over long periods of time. In what follows, we will take a look at a small edge as it relates to blackjack, its fragility, and ways to extract as much profit from the edge as possible. We will also explore how the framework of exploiting a small edge can and should be applied in the world of investing.

Basic Blackjack Strategy & Player Expectancy

When playing what is referred to as “basic strategy” in blackjack, one plays each hand in accordance with the highest probable outcome for the player – maximizing chances against the house. Playing with the basic strategy alone, however, still provides a player with negative 0.5-1.0% expectancy (i.e - for every $100 played, the house is expected to collect $0.50-$1.00 on average). This is unfortunate for the player and is why it’s a pretty safe bet to always try to be the house when playing such games. However, by utilizing card counting or “reading” techniques, one is actually able to tilt the odds in their favor, and player expectancy can turn positive by 1.0-2.5%. While this seems like a very small edge, we will explore how the exploitation of this edge can add up to a meaningful sum over time.

Taking a Look at a Small Edge by Simulating Blackjack Hands

Next, we will pretend to sit down at the blackjack table, simulate multiple hands given a small implied edge of 2% in our favor, and analyze the overall results from a capital return and risk perspective. Assuming we have a starting base capital account of $1,000 and bet on average $50 per hand, let’s take a look at our potential gains and losses after 100, 500, 1,000, and 5,000 hands of blackjack. Figures 1-a through 1-d show the results of these simulated blackjack hands and their effect on our overall account.

Figure 1: Profit & Loss Curves from Blackjack Simulation

Figure 1-a: 100 Hands

As we can see in the simulation, the small edge achieved playing blackjack was really not apparent in the first 100, 500 or even 1,000 simulated hands (Figures 1-a, 1-b & 1-c), but as we approached the 5,000th hand (Figure 1-d), the edge becomes very apparent, as our profits start to become substantial – growing from $1,000 to over $15,000 in this particular simulation run. To further analyze this blackjack simulation, we can take a look at the overall return and risk characteristics of our capital account over the full course of the 5,000 hands.

Figure 2: Return & Risk Metrics from Blackjack Simulation (5,000 hands)

As detailed in Figure 2, we can point to the substantial return achieved across the 5,000 simulated blackjack hands with just a 2% edge. On the risk side of the spectrum, it should be noted that swings of 20% of our account balance on average were experienced for every 100 hands played, and our maximum drawdown (i.e. max % loss of capital from any interim account peak) was 74% over the course of the full period. Given these risk metrics, it would likely have been a challenge for us to maintain full faith in our card counting abilities, as at one point our capital account would have declined by nearly three quarters!

Why do these unfavorable risk parameters exist? Well, it’s largely related to the very small edge we have. When deploying a small edge, simple chance always remains as a large part of each individual outcome – meaning streaks of both good and bad luck are likely to occur.

Maximizing the Edge by Betting on Multiple Players, Across Multiple Games

So what can be done to combat the fragility of a small edge and remove much of the potential for bad luck and losing streaks from the equation? What if we financially back multiple players in order to take advantage of multiple games at once. Effectively, we will become the “bank”, providing capital to five separate players, so that they can each extract his or her 2% edge. As the bank, our attention will then be focused on the overall gains and losses across all the players – i.e. the “Team Account” – as opposed to any player individually.

To analyze this concept further, we will re-run the 5,000 simulations for each of five individual players, and then compare their performance to our overall performance (which is the investment of $200 we make in each of the five players, totaling $1,000). By taking this approach, we can explore the outcomes associated with deploying multiple players across multiple games.

Figure 3: Blackjack Simulation (5,000 Hands) for Five Players & Team Account

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Good news, our investment into each of our players exhibited strong positive returns, albeit some performed better than others. Figure 3 above details the account value paths and outcomes for our team of five blackjack players, each playing individual games for 5,000 hands, along with our Team Account, which invested equally across the five players. We can quickly point out that the individual players’ accounts took somewhat random and volatile paths and ended with very different dollar amounts. In analyzing the green line, however, which is our Team Account, we can note the smoothness and stability compared to the individual players. Figure 4 displays the return and risk metrics for each of the players along with the Team Account.

Figure 4: Return & Risk Metrics from Blackjack Simulation (Five Players & Team Account)

As detailed in Figure 4, we can note the return and risk metrics for the individual players is fairly inconsistent, with each having a wide range of outcomes. When compared to our Team Account or “portfolio of the five players” the return and risk metrics outperform significantly, particularly from a risk-adjusted return perspective. More specifically, the return per unit of risk per 100 hands for the Team Account is 1.63, a 70% improvement compared to the best player’s 0.96 and over double the team average of 0.68. Furthermore, our maximum drawdown or total loss from interim account peak was just 15% within our Team Account, whereas the individual players experienced maximum drawdowns ranging from 37%-85%.

As evidenced above, the Team Account provides tremendous benefits in terms of risk reduction compared to the average risk profile of the individual players. We can also note that by substantially reducing our risk through the Team Account, we could then consider borrowing half of our bankroll from the casino (i.e. leverage our account by 50%), and therefore, double our returns and still have a lower risk profile compared to that of the average of our five players. Diversification at work!

The Power of Diversifying Across Edges

So how did the Team Account outperform each of the individuals on a risk-adjusted basis? When we take the profit and loss paths (i.e. equity curves) from the individual players and combine them into a portfolio of multiple players playing multiple games, we are able to allocate our capital across multiple, uncorrelated bets - and as a result, reap substantial diversification benefits.

As each of our bets (individual players) are playing independent games, they win and lose at different times. Therefore, a losing streak for one player is likely to be partially offset by winning hands from the other players. This dynamic makes a well-balanced allocation across all the players a more optimal approach, as the volatility and drawdowns of a team portfolio are likely to be minimized, whereas the expected returns remain fully intact. In more mathematical terms, the profits and losses within each player’s account are uncorrelated to one another. As a result, our overall Team Account is able to average across the total return profile of the individuals, while sharply reducing the overall risk (i.e. volatility and drawdowns).

Essentially, we are maximizing our chances to succeed by diversifying across edges, and therefore, maximizing the overall edge we have by counting cards. This team approach is very much the same as what was deployed by the famous card counting students from MIT and Harvard.

The Blackjack Framework & Public Market Investing

While the investment world is quite a bit different from the blackjack table, the approach to capital allocation across asset classes and investment strategies should be thought about in a similar framework. The end goal for any investor or asset allocator is to maximize returns per unit of risk, while also avoiding large account drawdowns and the risk of ruin. Using Thorp’s blackjack mindset and applying the same framework to an investment portfolio, one has a substantial advantage in achieving a smoother, less stressful investment experience.

If we think of the blackjack example as simply maximizing our number of diversified bets across different games where we have a statistical edge, we can then apply the same concept to traditional investment approaches. The common portfolio of 60% stocks / 40% bonds (i.e. 60/40 portfolio - see analysis here and here) is a good example of passively playing two games to maximize your overall chances of success - however, we feel that this is only a decent first step, and material improvements can still be obtained.

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Whether your favorite investing strategy is growth, value, momentum, quality, etc., it’s always important to remember it never hurts to continue diversifying across managers (multiple players) as well as strategies (multiple games). At RQA, we specialize in seeking to maximize edges as it relates to global assets and strategies, and we spend a significant amount of time carving out as many favorable blackjack games as possible.

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Disclaimer: These materials have been prepared solely for informational purposes and do not constitute a recommendation to make or dispose of any investment or engage in any particular investment strategy. These materials include general information and have not been tailored for any specific recipient or recipients. Information or data shown or used in these materials were obtained from sources believed to be reliable, but accuracy is not guaranteed. Furthermore, past results are not necessarily indicative of future results. The analyses presented are based on simulated or hypothetical performance that has certain inherent limitations. Simulated or hypothetical trading programs in general are also subject to the fact that they are designed with the benefit of hindsight.

The MIT Blackjack Team was a group of students and ex-students from the Massachusetts Institute of Technology, Harvard University, and other leading colleges who used card counting techniques and more sophisticated strategies to beat casinos at blackjack worldwide. The team and its successors operated successfully from 1979 through the beginning of the 21st century. Many other blackjack teams have been formed around the world with the goal of beating the casinos.

Blackjack and card counting[edit]

Blackjack can be legally beaten by a skilled player. Beyond the basic strategy of when to hit and when to stand, individual players can use card counting, shuffle tracking, or hole carding to improve their odds. Since the early 1960s, a large number of card counting schemes have been published, and casinos have adjusted the rules of play in an attempt to counter the most popular methods. The idea behind all card counting is that, because a low card is usually bad and a high card usually good, and as cards already seen since the last shuffle cannot be at the top of the deck and thus drawn, the counter can determine the high and low cards that have already been played. They thus know the probability of getting a high card (10,J,Q,K,A) as compared to a low card (2,3,4,5,6).

In 1979, six MIT students and residents of the Burton-Conner House at MIT taught themselves card-counting. They traveled to Atlantic City during the spring break to win their fortune. The group went their separate ways when most of them graduated in May of that year. Most never gambled again, but some of them maintained an avid interest in card counting and remained in Cambridge, Massachusetts. Two of them, J.P. Massar and Jonathan, offered a course on blackjack for MIT's January, 1980 Independent Activities Period (IAP), during which classes may be offered on almost any subject.

First MIT blackjack 'bank'[edit]

In late November 1979, Dave, a professional blackjack player contacted one of the card-counting students, J.P. Massar, after seeing a notice for the blackjack course. He proposed forming a new group to go to Atlantic City to take advantage of the New Jersey Casino Control Commission's recent ruling that made it illegal for the Atlantic City casinos to ban card counters. Casinos instead have to take other countermeasures like shuffling the cards earlier than normal, using more decks of cards, or offering games with worse rules to destroy the advantage gained by counting—even though these all negatively impact the non-counter as well.[1]

The group of four players, a professional gambler, and an investor who put up most of their capital ($5,000), went to Atlantic City in late December. They recruited more MIT students as players at the January blackjack class. They played intermittently through May 1980 and increased their capital four-fold, but were nonetheless more like a loose group sharing capital than a team with consistent strategies and quality control.

'Mr. M' meets Bill Kaplan[edit]

In May 1980, J. P. Massar, known as 'Mr. M' in the History Channel documentary, overheard a conversation about professional blackjack at a Chinese restaurant in Cambridge. He introduced himself to the speaker, Bill Kaplan, a 1980 Harvard MBA graduate who had run a successful blackjack team in Las Vegas three years earlier. Kaplan had earned his BA at Harvard in 1977 and delayed his admission to Harvard Business School for a year, when he moved to Las Vegas and formed a team of blackjack players using his own research and statistical analysis of the game. Using funds he received on graduation as Harvard's outstanding scholar-athlete, Kaplan generated more than a 35 fold rate of return in fewer than nine months of play.[2]

Kaplan continued to run his Las Vegas blackjack team as a sideline while attending Harvard Business School but, by the time of his graduation in May 1980, the players were so 'burnt out' in Nevada they were forced to hit the international circuit. Not feeling he could continue to manage the team successfully while they traveled throughout Europe and elsewhere, encountering different rules, playing conditions, and casino practices, Kaplan parted ways with his teammates, who then splintered into multiple small playing teams in pursuit of more favorable conditions throughout the world.

Kaplan observes Massar and friends in action[edit]

After meeting Kaplan and hearing about his blackjack successes, Massar asked Kaplan if he was interested in going with a few of Massar's blackjack-playing friends to Atlantic City to observe their play. Given the fortuitous timing (Kaplan's parting with his Las Vegas team), he agreed to go in the hopes of putting together a new local team that he could train and manage.

Kaplan observed Massar and his teammates playing for a weekend in Atlantic City. He noted that each of the players used a different, and overcomplicated, card counting strategy. This resulted in error rates that undermined the benefits of the more complicated strategies. Upon returning to Cambridge, Kaplan detailed the problems he observed to Massar.

Kaplan capitalizes a new team[edit]

Kaplan said he would back a team but it had to be run as a business with formal management procedures, a required counting and betting system, strict training and player approval processes, and careful tracking of all casino play. A couple of the players were initially averse to the idea. They had no interest in having to learn a new playing system, being put through 'trial by fire' checkout procedures before being approved to play, being supervised in the casinos, or having to fill out detailed player sheets (such as casino, cash in and cash out totals, time period, betting strategy and limits, and the rest) for every playing session. However, their keen interest in the game coupled with Kaplan's successful track record won out.

The newly capitalised 'bank' of the MIT Blackjack Team started on 1 August 1980. The investment stake was $89,000, with both outside investors and players putting up the capital. Ten players, including Kaplan, Massar, Jonathan, Goose, and 'Big Dave' (aka 'coach', to distinguish from the Dave in the first round) played on this bank. Ten weeks later they more than doubled the original stake. Profits per hour played at the tables were $162.50, statistically equivalent to the projected rate of $170/hour detailed in the investor offering prospectus. Per the terms of the investment offering, players and investors split the profits with players paid in proportion to their playing hours and computer simulated win rates. Over the ten-week period of this first bank, players, mostly undergraduates, earned an average of over $80/hour while investors achieved an annualized return in excess of 250%.

Strategy and techniques[edit]

The team often recruited students through flyers and the players' friends from college campuses across the country. The team tested potential members to find out if they were suitable candidates and, if they were, the team thoroughly trained the new members for free. Fully trained players had to pass an intense 'trial by fire,' consisting of playing through 8 six-deck shoes with almost perfect play, and then undergo further training, supervision, and similar check-outs in actual casino play until they could become full stakes players.

The group combined individual play with a team approach of counters and big players to maximize opportunities and disguise the betting patterns that card counting produces. In a 2002 interview in Blackjack Forum magazine,[3] John Chang, an MIT undergrad who joined the team in late 1980 (and became MIT team co-manager in the mid-1980s and 1990s), reported that, in addition to classic card counting and blackjack team techniques, at various times the group used advanced shuffle and ace tracking techniques. While the MIT team's card counting techniques can give players an overall edge of about 2 percent, some of the MIT team's methods have been established as gaining players an overall edge of about 4 percent.[citation needed] In his interview, Chang reported that the MIT team had difficulty attaining such edges in actual play, and their overall results had been best with straight card counting.

The MIT Team's approach was originally developed by Al Francesco, elected by professional gamblers as one of the original seven inductees into the Blackjack Hall of Fame. Blackjack team play was first written about by Ken Uston, an early member of Al Francesco's teams. Uston's book on blackjack team play, Million Dollar Blackjack, was published shortly before the founding of the first MIT team. Kaplan enhanced Francesco's team methods and used them for the MIT team. The team concept enabled players and investors to leverage both their time and money, reducing their 'risk of ruin' while also making it more difficult for casinos to detect card counting at their tables.

Team history 1980–1990[edit]

The MIT Blackjack Team continued to play throughout the 1980s, growing to as many as 35 players in 1984 with a capitalization of as much as $350,000. Having played and run successful teams since 1977, Kaplan reached a point in late 1984 where he could not show his face in any casino without being followed by the casino personnel in search of his team members. As a consequence he decided to fall back on his growing real estate investment and development company, his 'day job' since 1980, and stopped managing the team. He continued for another year or so as an occasional player and investor in the team, now being run by Massar, Chang and Bill Rubin, a player who joined the team in 1984.

The MIT Blackjack Team ran at least 22 partnerships in the time period from late 1979 through 1989. At least 70 people played on the team in some capacity (either as counters, Big Players, or in various supporting roles) over that time span. Every partnership was profitable during this time period, after paying all expenses as well as the players' and managers' share of the winnings, with returns to investors ranging from 4%/year to over 300%/year.

Strategic Investments 1992–1993[edit]

In 1992, Bill Kaplan, J.P. Massar, and John Chang decided to capitalize on the opening of Foxwoods Casino in nearby Connecticut, where they planned to train new players. Acting as the General Partner, they formed a Massachusetts Limited Partnership in June 1992 called Strategic Investments to bankroll the new team. Structured similar to the numerous real estate development limited partnerships that Kaplan had formed, the limited partnership raised a million dollars, significantly more money than any of their previous teams, with a method based on Edward Thorp's high low system. It involved three players: a big player, a controller, and a spotter. The spotter checked when the deck went positive with card counting, the controller would bet small constantly, wasting money, and verifying the spotter's count. Once the controller found a positive, he would signal to the big player. He would make a massive bet, and win big. Confident with this new funding, the three general partners ramped up their recruitment and training efforts to capitalize on the opportunity.

Over the next two years, the MIT Team grew to nearly 80 players, including groups and players in Cambridge, New York, New Jersey, Pennsylvania, California, Illinois, and Washington. Sarah McCord, who joined the team in 1983 as an MIT student and later moved to California, was added as a partner soon after SI was formed and became responsible for training and recruitment of West Coast players.

At various times, there were nearly 30 players playing simultaneously at different casinos around the world, including Native American casinos throughout the country, Las Vegas, Atlantic City, Canada, and island locations. Never before had casinos throughout the world seen such an organized and scientific onslaught directed at the game. While the profits rolled in, so did the 'heat' from the casinos, and many MIT Team members were identified and barred. These members were replaced by fresh players from MIT, Harvard, and other colleges and companies, and play continued. Eventually, investigators hired by casinos realized that many of those they had banned had addresses in or near Cambridge, and the connection to MIT and a formalized team became clear. The detectives obtained copies of recent MIT yearbooks and added photographs from it to their image database.

With its leading players banned from most casinos and other more lucrative investment opportunities opening up at the end of the recession, Strategic Investments paid out its substantial earnings to players and investors and dissolved its partnership on December 31, 1993.

1994 and forward[edit]

Strategic Investment Blackjack For Dummies

After the dissolution of Strategic Investments, a few of the players took their winnings and split off into two independent groups. The Amphibians were primarily led by Semyon Dukach, with Dukach as the big player, Katie Lilienkamp (a controller), and Andy Bloch (a spotter). The other team was the Reptiles, led by Mike Aponte, Manlio Lopez and Wes Atamian. These teams had various legal structures, and at times million dollar banks and 50+ players. By 2000 the 15+ year reign of the MIT Blackjack Teams came to an end as players drifted into other pursuits.

In 1999, a member of the Amphibians won at Max Rubin's 3rd Annual Blackjack Ball competition. The event was featured in an October 1999 Cigar Aficionado article, which said the winner earned the unofficial title 'Most Feared Man in the Casino Business'.[4]

In the media[edit]

Books[edit]

  • A variety of stories about a few of the players from the MIT Blackjack Team formed the basis of The New York Times best-sellingBringing Down the House, written by Ben Mezrich. While originally marketed as nonfiction, Mezrich later admitted characters and stories in the book were mostly fictive and composites of players and stories he had heard about through hearsay. The private investigation firm referred to as Plymouth in Bringing Down the House was Griffin Investigations.[5]
  • Mezrich wrote a follow-up book, Busting Vegas, which took even greater liberty with the actual happenings of the team. Many events in this book were at least partly based on incidents that occurred during the team's Strategic Investments era.[6]
  • Jeffrey Ma wrote a book titled The House Advantage: Playing the Odds to Win Big in Business about his time on the 1994 MIT blackjack team.
  • Nathaniel Tilton, a student of former MIT team captains Mike Aponte and Semyon Dukach, authored The Blackjack Life detailing his experiences playing and being trained by the MIT Blackjack Team players.[7]

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Films[edit]

  • The 2004 film The Last Casino is loosely based on this premise and features three students and a professor counting cards in Ontario and Quebec.[8]
  • The 2008 film 21, inspired by Bringing Down the House and produced by and starring Kevin Spacey and Jim Sturgess, was released on March 28, 2008 by Columbia Pictures. Jeff Ma and Henry Houh, former players on the team, appear in the movie as casino dealers, and Bill Kaplan appears in a cameo in the background of the underground Chinese gambling parlor scene. The script took significant artistic license with events, with most of its plot being invented for the movie, hence it refers to being 'inspired by true events' rather than 'based on true events.' One of the most significant departures from reality was the portrayal of the team being run by a professor (the Kevin Spacey character), when in reality the team was always run by students and alumni. The characters in the movie were also fictionalized amalgams of various players throughout the years of the team's existence - for example, the character Choi is very loosely (and inaccurately) based on Johnny Chang, and the character Ben Campbell, is an amalgam of numerous players, with the opening scene based on Big Dave's interview, and subsequent admission to Harvard Medical School, where much of the interview revolved around his participation on the team.
  • The 2010 film Teen Patti is an uncredited remake of 21.

Strategic Investment Blackjack Stocks

Television[edit]

  • The Mysteries at the Museum series on the Travel Channel featured the story of the MIT Blackjack Team in the episode titled 'Siamese Twins, Assassin Umbrella, Capone's Cell'.
  • The story of the MIT Blackjack Team, in its incarnation as Strategic Investments, was told in The History Channel documentary, Breaking Vegas, directed by Bruce David Klein.
  • The Bringing Down The House period was featured on episodes of the Game Show Network documentary series, Anything to Win, and HBO's Real Sports with Bryant Gumbel (episode 116).
  • The BBC documentary, Making Millions the Easy Way, addressed the Bringing Down the House period as part of the renowned 'Horizon' strand (directed by Johanna Gibbon), told the story of a Strategic Investments breakaway group, and revealed the science behind the winning formula.
  • 'Double Down', an episode of Numb3rs concerned a counting group, led by a High School teacher, which launders money through casino winnings.

Other[edit]

Several members of the two teams have used their expertise to start public speaking careers as well as businesses teaching others how to count cards. For example:

  • Mike Aponte of the Reptiles co-founded a company with former MIT Blackjack Team member David Irvine called the Blackjack Institute.
  • Semyon Dukach of the Amphibians founded Blackjack Science.

References[edit]

  1. ^Griffin, Peter A. (1979). The Theory of Blackjack. Huntington Press. ISBN0-915141-02-7.
  2. ^'How a team of students beat the casinos'. BBC.com. Retrieved 26 May 2014.
  3. ^Blackjack Forum interview with Johnny Chang
  4. ^The Twenty One Club: The annual blackjack ball hosts Gambling's Most Furtive (and Quirky) FraternityArchived 2009-04-20 at the Wayback Machine cigaraficionado.com, Sept/Oct 1999
  5. ^Ian Kaplan (March 2004). 'review of Bringing Down the House'.
  6. ^ThePOGG (10 November 2012). 'ThePOGG Interviews – Semyon Dukach – MIT Card Counting team captain'.
  7. ^'ThePOGG Interviews – Nathaniel Tilton author of 'The Blackjack Life''. Retrieved 6 March 2013.
  8. ^The Last Casino on IMDb.Retrieved 2009-11-03.

External links[edit]

Strategic Investment Blackjack Definition

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