Schabacker 1

Casinos and Card Sharps: A Game of Cat and Mouse

Analyzing the incentives, strategies and innovations of casinos and gamblers

DeAnna Schabacker

University of Puget Sound

Professor Matt Warning

Spring 2006

Table of Contents

  1. Introduction

1.1 The Story and the Players

1.2A History of Casino Gambling

1.3Casino Games

  1. Blackjack
    2.1 Blackjack Basic Strategy
    2.2 Advantage Blackjack
    2.2.1 Card Counting
    2.2.2 Other Advantage Strategies
    22.3 Legal Issues of Advantage Play
  2. The Casino’s Side
    3.1 Selection and Screening Process
    3.1.1 Technology
    3.2 Changes to the Game
  3. Conclusion
  4. Glossary
  5. Appendix A-Basic Strategy Chart
  6. References

*N.B. Many footnotes are definitions of gambling terms. They can also be found in the glossary.

1. Introduction

Robin Hood meets the Rat Pack when the best and the brightest of M.I.T’s math students and engineers take up blackjack under the guidance of an eccentric mastermind. Their small blackjack club develops from an experiment in counting cards on M.I.T.’s campus into a ring of card savants with a system for playing large and winning big. In less than two years they take some of the world’s most sophisticated casinos for more than three million dollars. But their success also brings with it the formidable ire of casino owners and launches them into the seedy underworld of corporate Vegas with its private investigators and other violent heavies. (Mezrich 2002)

The preceding comes from the back cover of “Bringing Down the House”, the popular book of six M.I.T. students who won millions of dollars playing blackjack. This dramatic account delves into the big money, fast-paced, and dangerous world of the M.I.T. card counters and their trials, tribulations, and close-calls. Of course, this isn’t the first instance of individuals making millions from casinos, although perhaps it is the most flamboyant. Thirty years earlier, Ken Uston made over a million dollars using teams of card counters in top casinos around the world. He was consequently barred from many casinos. Many people who have made money from casinos have not been so public with their successes; there are many more instances and methods of players exploiting an advantage in order to make money at casinos. It is a story of cheaters and bribers, genius and ingenuity, and the casinos that have to counter them.

The examples of cat and mouse moves between the casino and the player lead to many questions. Is it really possible to make money long term at a casino? Is it possible to make enough money to justify the risk that players with an advantage at casinos face? How do casinos catch these people and why do they put so much effort into doing it? How does each party attempt to gain an edge? What sort of screening mechanisms do casinos institute to attract or detract different types of clientele? How successful are these and what impact does this have on their profits and the profits of the gamblers?

1.1 The Story and the Players

Casino gambling involves many inherent information asymmetries. Both parties, the casino and the individual gambler, have incentives to gain an information advantage over the other, and thereby increase profits. The casino engages in a selection process in order to attract players that will be lucrative for the casino, and discourage or catch the players with an advantage over the house. The gambler may engage in various tactics to increase his or her odds against the house (become an “advantage player”[1]). In any casino, the odds of the games favor the casino; this makes sense since casinos exist to make profits. However, there are beatable games[2] in which various strategies can tilt the odds to be in the players favor. By doing this and becoming an advantage player, one can potentially achieve long term profits. This paper focuses on the complicated relationship between casinos and players, particularly in Nevada, and the ongoing battle to gain an edge. Blackjack, sometimes also called “21”, is the primary game used in this analysis.

The incentives involved in casino gambling lead to steps and counter moves taken by both parties in the transaction to gain an information advantage and increase profits. In general, there are profound information asymmetries between the house and the player. The obvious one for the player is that he does not know when he will win. He does not know with what frequency the slot machines will pay, and he does not know what cards will be dealt at blackjack. He does not know when the dealer will shuffle (the relevance of this will be explained later). He does not know or understand, in general, the inner workings of the casino: the security, the surveillance, the policy on winning players, etc. Similarly, the house does not know the players very well. The casino, initially at least, does not know who its patrons are. It does not know if they have good skills, poor skills, an information advantage, or if they are cheaters. The casino doesn’t know if a given individual has hidden information or will engage in hidden action.

The primary goal of a casino is to achieve profits. The profits that come from gambling are results of inherent house advantages built into the games. If the casino cannot protect this statistical advantage, profits will decrease. Casinos, therefore, want to increase their information regarding their patrons, in order to know which players are not good for their business. Additionally, there will inevitably be players who would like to also gain information about the casino, in order to achieve long term profits through casino games. So what can we expect these players and the casino to do to achieve these ends?

We expect the casino will invest in screening devices and selection processes in order to monitor their patrons. While the monitoring costs will reduce profits, we expect that it will not reduce profits so much as would a lost house advantage. In addition, these monitoring costs will have positive externalities, such as increased security. We further expect the casino to take as many precautions to shield themselves from advantage players as possible, without reducing their marketing potential to other customers. We would also expect that this would be a continuing cycle as the house is required to respond to innovations by the player.

On the side of the player, opportunistic behavior should lead to innovation and willingness to take risks. The large profit potential will make some players risk-preferring. We expect the players to invent strategies, both legal and illegal, as defined by the Nevada Revised Statutes, and to take risks in order to gain an advantage over the house. We expect advantage players to disguise their advantage and sometimes their identities, making it more difficult for the house to detect them, which creates an adverse selection problem.

The Nevada Gaming Commission and the State Gaming Control Board are the primary institutions regulating gambling in Nevada. The Nevada Gaming Commission is a part-time agency that writes the state's gambling rules and grants or denies gaming licenses. The Gaming Control Board is a full-time agency that administers the state's Gaming Control Act and its corresponding regulations. It further protects the stability of the gaming industry through licensing and enforcement of laws and regulations, collects gaming taxes and fees, and conducts investigations (Simpson 2002). The taxes and fees are an essential source of state revenue. The commission also crafts and enacts new regulations and approves control board nominations to Nevada's List of Excluded Persons, the 42-year-old list of people barred from entering the state's casinos, popularly called the Black Book. Regulators also deal with technology and social issues involved with casino gaming.

Information asymmetries and opportunistic behavior of casino gaming lead to imperfect market behavior: adverse selection, high monitoring costs, and hidden action. The casino and the player in the transaction have an incentive to do whatever it takes in order to gain an information advantage and attain profits. The Nevada Gaming Commission and the Gaming Control Board regulate the Nevada gaming industry by writing and enforcing the Nevada Revised Statutes, collecting taxes and fees, and in general, promoting industry stability. The advantage-seeking player, the casino, and the regulatory institutions are the primary actors in this analysis.

1.2 A History of Casino Gaming

In the last two decades, casino gambling has increased dramatically in popularity to become a major industry within the United States. Today, casino gambling is legal in 29 states and generated annual revenue of $40 billion dollars in 2001. Nevada was the first state to legalize gambling in 1931, followed by New Jersey in 1976. There are two types of casino: tribally owned and publicly traded private corporations (Garrett 2003, 4). Corporate casinos are taxed and regulated by the state; however, tribal casinos are sovereign entities from the state. This is relevant because the multi-billion dollar casinos in Las Vegas and Atlantic City are corporate casinos. They pay money to the state and are subject to the laws of the state. The 1990s saw an increase in the number of states with legalized gambling, the primary reason being that states saw the casinos as potential for economic growth (Garrett 2003, 5).

In 2004, 26% of Americans 21 and older gambled at a casino; this is 53.6 million Americans that made at least one trip to a casino to gamble (Harrah’s survey 2004). The greatest proportion of casino gaming revenue comes from slot machines and other gaming devices (such as video poker); in 1998, 65.3% of Nevada’s gaming revenues came from slot machines and 30.6% came from table games (Eadington 1999, 177). Seventy-five percent of casino gamblers play the slot machines and 13% play table games. Table games include blackjack, craps, and roulette. Blackjack is the most common table game played, accounting for nearly ¾ of all table gaming (Harrah’s survey 2004, 21). These numbers show that casino gaming is huge business and big money, especially slot machines and blackjack. A lot of money can be made or lost at these games.
1.2 Casino Games

For casino games, the house advantage can be measured with a probability analysis of the game. Some games are fixed odds game (e.g. normal slot machines) and some games have elements of strategy (e.g. blackjack). In slot machines (at least those without progressive jackpots[3], like some video poker machines), the odds are fixed and the player is betting against an electronically or mechanically determined outcome. With progressive jackpots, the house advantage changes as the size of the prize changes (Eadington 1999, 178). In a typical slot machine, the house advantage is 5% (i.e. most slot machines pay out about 95% of the money that is put into them) and for blackjack the house advantage is between 1-2%, usually closest to 1.4% (Eadington 1999, 179). That is to say that when a gambler makes 1000 bets on a slot machine, she can expect to be down[4] 50 bets on average. So if Gambler A is playing a one dollar slop machine and she plays 1000 times, she should lose $50 on average. Of course, she could win or lose any amount, but in the long run, she should expect to lose $50 for every 1000 spins of the slot machine. Similarly, a blackjack player who utilizes the perfect “basic strategy”[5], which will be discussed later, can expect to be down 14 bets after 1000 hands played. Under normal conditions, both of these games are negative expectation games; that is, one can expect to see negative profits from playing them in the long run. However, when perfect basic strategy is used, blackjack has a much smaller house advantage than slot machines.

2. Blackjack

In casino blackjack, a player is dealt two cards, with the goal being that the total value of the cards comes as close as possible to 21 without going over. If the player’s cards are closer to 21 than the dealer, he wins. If the cards go over 21, the player has “busted”[6] and automatically loses; the dealer can also bust. All cards (2-10) have a value equivalent to their face value. All kings, queens, and jacks have a value of ten. Ace has a value of one or eleven. The player acts before the dealer. On his turn, the player may “hit” (take another card) or “stand” (not take another card and stay on the amount he has now). If a player is dealt two of the same cards, he may “split” them and have a bet on each hand. Also, a player may elect to “double down” after he is dealt his first two cards; this involves doubling his bet and he may only receive one more card. If the player’s first two cards contain an ace and a ten (any king, queen, jack, or ten), it is known as “blackjack” and the player wins one and a half times of his bet (commonly denoted as 3-to 2 payout). If the dealer is showing[7] an ace (that is, the up-card that is visible to everyone is an ace), the player has an option of accepting “insurance”. Insurance is a side bet of half the amount already bet, betting that the dealer has a ten-value card facing down, thus giving him blackjack. If he has blackjack, the player loses his initial bet, but wins the side bet, so is then even. If the dealer does not have blackjack, the player loses the side bet. One further option available at only some games of blackjack is the option to surrender. Surrendering means that the player does not think he can win given his cards and the visible dealer’s card, and is therefore willing to lose half of the bet and not risk losing it all. This is a good option when the dealer is showing a ten and the total of the player’s cards is 15 or 16; the player most often loses in this scenario. The dealer must play according to predetermined rules, which vary from casino to casino, but usually involve drawing[8] to 17 (i.e. she must hit on 16 or less). If there is a tie (the dealer and player have the same amount) it is considered a “push”, and all bets are returned to the player. (Julian 2005, 165)

The player has several advantages over the house in blackjack. First, he doesn’t have to play according to pre-set rules, as the dealer does. This flexibility is an advantage. In addition, the pay-off for getting a Blackjack (21 with the first two cards) is 3-to-2 (he wins back 150% of his bet). However, the house advantage is more significant: the house always wins if the player busts, even if the dealer busts also. If the player played the exact same way as the dealer (i.e. following the same predetermined rules), both the dealer and the player would bust about 9% of the time, thus giving the house a 9% advantage. However, given the Blackjack 3-to-2 pay-off and the fact that players do not have to (and hopefully they don’t) play just like the house, this disadvantage can be much smaller. Using perfect basic strategy, the disadvantage can be closer to 1 to 2 percent (Sklansky & Malmuth 1998, 10). Of course, this is not good enough to achieve long term profits; to become an advantage player, other strategies must be adopted.
2.1 Blackjack Basic Strategy

In 1962, Edward O. Thorp, a young MIT physics professor, developed the first basic strategy for blackjack. Using computer analysis he determined the mathematically correct play based upon the dealer’s up-card (the card that is showing) and the cards held by the player. Since this early break-through in blackjack strategy, many other have used computers to analyze the basic strategy. In short, basic strategy involves when to hit, stand, double down, and split, based on the dealer’s up-card and the cards in the player’s hand. Appendix A illustrates the basic strategy. This strategy also recommends to never buy insurance. Insurance is basically a bet that the dealer’s down-card is a ten and the casino is giving the player 2-to-1 odds on that bet. The true odds that the dealer has a ten are 2.5-to-1, so it is always a bad bet unless the player has some extra information.

An in-depth discussion of basic strategy is not warranted here. However, it is relevant to know that the basic strategy of blackjack does have some variations, depending on the number of decks in use and the specific rules of the game. These strategies were developed using millions of computer simulations, until it was clear what the “correct” play was. It is not the case that every hand stands to win by using this strategy, however, that it is the play that should lose the least in the long run (some hands, like 14 versus the dealer’s shown 4 will always lose money whether the player hits or stands; but if the player stands, he will win about 40% of the time, whereas by hitting, he will win less). Clearly, a lot of work has been done to try to gain a statistical advantage over the casino.
2.2 Advantage Blackjack