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Poker: Public Policy, Law, Mathematics and The Future of an American Tradition Anthony Cabot1 Robert Hannum2 Introduction Gambling in its many different variants has seen a proliferation across the United States of unprecedented proportions. Despite its growing popularity, gambling is still a controversial activity that sparks emotions and debates in elections and legislative battles. While ostensibly, most debate centers on amoral pragmatic issues such as problem and underage gambling, the rhetoric often reduces to hyperboles, such as referring to the any type of gambling then being debated as the “crack cocaine of gambling.”3 In theory, a pragmatic approach to policymaking in the context of gambling Anthony Cabot is a partner in the law firm of Lewis and Roca. His practice emphasis is on gaming law. He is the president and was a founding member of the International Masters of Gaming Law Association, a worldwide organization of prominent gaming attorneys devoted to the on-going education of and communications within the gaming industry. Mr. Cabot is the co-Editor-in-Chief of the Gaming Law Review. He is the founding editor of The Internet Gambling Report Vlll (2005), covering the evolving conflict between technology and the law. Mr. Cabot authored Federal Gambling Law (Trace 1999) and Casino Gaming: Public Policy, Economics and Regulation (International Gaming Institute, University of Nevada, Las Vegas 1996), a 527-page book covering all aspects of casino gaming. He coauthored Practical Casino Math (International Gaming Institute, University of Nevada, Las Vegas 2002), and is co-editor and contributing author of International Casino Law (Institute For the Study of Gambling and Commercial Gaming, University of Nevada, Reno, 1991, 3d ed January 1999). Mr. Cabot is listed in Best Lawyers in America. Robert Hannum is Professor of Statistics at the University of Denver, where he teaches probability and statistics, with particular interests in the mathematics of gambling, the business of commercial gaming, and data mining. His publications include the books Practical Casino Math and Introductory Statistics: A SelfStudy Manual, as well as numerous articles in statistical, gaming, and law journals, including Annals of Probability, Annals of Statistics, John Marshall Law Review, Sociological Methods and Research, International Gambling Studies, Quantity and Quality in Economic Research, Finding the Edge: Mathematical Analysis of Casino Games, and Global Gaming Business.. 3 2 1 Various types of gambling called “the crack cocaine of gambling: Casinos: The Capital Times (Madison, WI); 1/6/2004; Novak, Bill (“Calling casinos the “crack cocaine” of gambling, the head of a national anti-gambling organization implored a packed meeting room of casino opponents to work … “Women say it’s electric morphine,” said the Rev. Tom Grey, executive director of the Washington, D.C.-based National Coalition Against Legalized Gambling, referring to what he called the “trance” players can get in when sitting in front of a slot machine. ) Video Lottery Terminals: StatsCan: VLTs ‘crack cocaine’ of gambling, Canadian Press, Toronto Star, December 12, 2003. (“One in four people who play video lottery terminals is at-risk or a problem gambler, would involve comparing the costs and benefits of a certain activity as the basis for allowing, prohibiting or regulating the activity. Increasingly, both the opponents and proponents attempt to justify their respective positions on gambling on the bases of pragmatic arguments as opposed to religious/moral arguments on the opponent’s side or natural rights4 on the proponents’ side. When this debate occurs, distinctions between different types of activities where persons can risk money on the outcome of an uncertain event should become relevant. For example, do some gambling activities have greater benefits because they teach a desirable skill or greater burdens because they really are the “crack cocaine” of gambling in terms of being more likely to lead to problem gambling. says a first-ever study released today by Statistics Canada. This confirms “the much-reported notion that VLTs are the ‘crack cocaine’ of gambling,” says a landmark report culled from the 2002 Canadian Community Health Survey on Mental Health and Well-being.’) Gambling’s Crack Cocaine (editorial),Sunday, June 13, 2004; Page B06 (“THERE IS NO mystery to why some experts on gambling addiction call “video lottery terminals,” or VLTs, the crack cocaine of gambling. According to one source, VLTs are the most addictive because they provide a “very fast, highly stimulating, rate of play.”) Video Poker Machines: SO YOU THINK GAMBLING IS HARMLESS, HUH?, FAMILY NEWS, by Dr. James Dobson-via The West End Way, January 17, 1999. (Or that more than 30,000 video poker machines, which are called the “crack cocaine of gambling”, are scattered through South Carolina, and that the governor who opposed them (David Beasley) was voted out in November?”) Online Casinos: “Virtual casinos are the hard-core crack cocaine of gambling.” - Dr. Howard Schaeffer, Harvard Center for Addictive Studies. http://www.winneronline.com/articles/june2002/classicquotes.htm Online Gaming: Lawmakers Take Another Look at Net Gambling Thursday, May 29, 2003, Liza Porteus, Foxnews. Rep._Spencer Bachus (search), R-Ala.,_said in an e-mail to Foxnews.com. “Cyber gambling is the crack cocaine of gambling and will create a new generation of addicts unless we stop it.” Scratch-off tickets:State lottery bad economic deal: speaker, 08/27/02, BILL HILES, (Finally, Wright said the preferred form of lottery ticket sales, machines that vend “scratch-off” tickets, are particularly attractive to teen-agers and are a way of “hooking” them on gambling. ,”The scratch-off card sold in vending machines has been called the crack cocaine of gambling,” he said. “A lottery poses a great danger to our children.” ) Philosophical support exists for the position that government should not dictate what consensual behavior is acceptable and that which is not. From the age of enlightenment came John Locke’s notion that all persons have “natural rights,” which included the right to pursue happiness. See generally, Peter McWilliams, Ain’t Nobody’s Business If You Do: The Absurdity of Consensual Crimes in a Free Society, pp. 41-49 (1993).Government should only play a role in protecting a person’s property and to defend the country. If a person engages in an activity that is harmful to himself but not to others, government’s role, if any, is to educate the person. Locke viewed persuasion, not government intervention, as the means of influencing others’ behavior. If smoking leads to cancer, government should warn the public of the risks, not ban cigarettes. He wrote “It is one thing to persuade, another to command, one thing to press with arguments, another with penalties.” Similar to Locke, John Stuart Mill felt that government should only interfere with the lives of its citizens in limited circumstances. He wrote: [A person] cannot rightfully be compelled to do or forbear because it will be better for him to do so because it will make him happier because, in the opinion of others, to do so would be wise, or even right. There are good reasons for remonstrating with him, or reasoning with him, or persuading him, or entreating him, but not for compelling him, or visiting him with any evil in case he does otherwise. John Stuart Mill, On Liberty (Everyman’s Library (1992)). 4 Of the various forms of activities often classified as gambling, the game of poker has reached unprecedented popularity because of a variety of factors including television and Internet exposure. Poker, however, differs in substantial respect from lotteries and most casino-style games because poker has various elements of skill not present in lotteries and in most casino games. Historically, the presence of skill in poker has perplexed courts in determining whether to classify poker as illegal gambling or a permitted activity. This is because most courts in the United States have relied on a “predominance test.” Under this test, an activity is considered illegal gambling if a person risks something of value on an activity predominated determined by chance for the opportunity to win something of greater value than he or she risked. In some states the courts have concluded that poker is a game predominately determined by skill, in others the courts have determined that poker is a game predominately determined by chance and still others have determined that poker is a game of mixed skill and chance. In most cases, these courts have made these decisions without distinguishing between the variants of the game of poker and in the absence of empirical evidence as the nature and degree of skill involved in the game. Equally, relevant is whether the predominance test is still supportable as a basis for the public policy debate. For example, the growing popularity of gambling on the Internet has lead to the introduction of federal legislation designed to prohibit the use of financial transactions to fund gambling transactions. Notable is that recent legislation attempts to abandon the traditional predominance test and adopt a new test that defines gambling as “the staking or risking by any person of something of value upon the outcome of . . . a game subject to chance…”5 This new “any chance” test has ramification not only for poker, but any game that has any element of chance including bridge, casual games like Tetris or Bejeweled, and video games played over platforms such as the Sony Playstation and the Microsoft Xbox. This departure from historic precedent is being dome without any consideration of the merits of abandoning the predominance test. This article explores the origins and purposes of both poker laws and the predominance rule. The article then proposes that the courts need to distinguish between the variants of poker and its method of play and must understand with particularity the skill elements of the game before deciding whether to classify the game as one of skill or chance. Finally, the article suggests that the current debate over gambling should consider the issue of games of skill including variants of poker in a different public policy perspective than games of chance. 5 Prohibition of Funding of Unlawful Internet Gambling Act, Sect. 5361(1) (2005) History and Nature of Poker While card games were invented in Europe, and some elements of the game of poker may have come from various parts of the world6, the game the world now knows as poker is uniquely American. Poker has been called by various experts the most popular card game among Americans,7 America’s national game,8 the national vying game of the United States,9 and the most popular international card game in history.10 Its international prominence is due as much to the influence of American culture as to its own individual merits.11 Poker originated about 1830 in the French-dominated area of New Orleans. Many researchers credit the derivation of old 20-card poker to the Persian game of AsNas, a game whose origin and age are in dispute,12 and its various descendants. One descendant of As-Nas, known as Poque in French, came to the United States with the French colonists of New Orleans. Though numerous authors assert that poker is probably an amalgam of several vying games, with immediate ancestors including 6 Playing cards were first created in China around 900 A.D. and were based on the game of dominos. Suited cards were developed from Tarot cards and had four original suits: swords, clubs, cups and coins. “Playing cards originating in Asia evolved from symbols and paraphernalia associated with ancient divinatory practices.” DAVID M. HAYANO, POKER FACES 8 (1982). “In the same way that dice came into existence with religious ritual, cards appeared alongside the divinatory use of the arrow around the twelfth century.” GERDA REITH, THE AGE OF CHANCE 49 (1999). The cards of Asia and Europe were miniature pieces of artwork with the social and cultural life of their country of origin embodied in the exquisite detail of their design. “They were as individual and faithful a mirror of the taste and temperament and traditions of the people as other braches of their arts.” CATHERINE HARGRAVE, HISTORY OF PLAYING CARDS 170 (1966). During the late thirteenth and early fourteenth centuries cards were introduced, along with paper money, and gunpowder, into Europe through India and the Middle East. Over the next several centuries the design of European playing cards was modified to reflect their social and political milieu, eventually resulting in the present-day four suits and court figures – kings, queens, and knaves. Originally the hand-crafting of cards made their cost prohibitive to the majority of the population; it was not until the invention of the printing press in the fifteenth century that cards came into mass everyday use and became widely disseminated throughout Europe. HAYANO, at 8; REITH, at 50. 7 RICHARD A. EPSTEIN, THE THEORY OF GAMBLING AND STATISTICAL LOGIC 201 (1995). 8 A. ALVAREZ, POKER: BETS, BLUFFS, AND BAD BEATS, 22 (2001); DAVID PARLETT, THE HISTORY OF CARD GAMES 115 (1991). 9 PARLETT, supra note 8, at 86. 10 JOHN SCARNE, SCARNE’S GUIDE TO MODERN POKER, 13 (1980). 11 PARLETT, supra note 8, at 86. 12 Parlett describes the conclusions of Michael Dummett (THE GAME OF TARO, 1980), who conducted painstaking research on the matter. Iran (formerly Persia) is indeed the home of As-Nas playing cards, so called from the game typically played with them. Actual cards surviving from the seventeenth century, consonant with descriptions of the game, reveal twenty or twenty-five to a pack, consisting of four or five each of ranks designated Ace (or Lion and Sun), King, Lady, Soldier, and Dancing-girl. There are no suits, although each rank is sometimes associated with a color. Players receive five cards each and vie on them as in non-draw poker, based on combinations of pairs, triplets, fulls, and quartets. Contrary to some who claim amazing antiquity regarding As-Nas, there is no evidence of the game being mentioned in Persian literature at any date earlier than the oldest surviving cards, nor do we have any rules of the game earlier than the nineteenth century. The kinship of As-Nas to other games can be more plausibly explained as a borrowing from European games than vice versa, especially when it is observed that ‘As’ is not itself a relevant Farsi (Persian) word, but does happen to be the French for ‘Ace.’ PARLETT, supra note 8, at 112113. Poque13, Bouillotte14, Prima15 and As-Nas,16 Poque is the likeliest candidate for the name of the game.17 In Poque, betting is carried out by announcing ‘Je poque de dix’ (or whatever the sum involved) with two syllables to the key word. It has been suggested that ‘poque’ so pronounced was interpreted by English-speaking southerners as ‘pokah.’18 An English version of the game is Brag and another French offshoot is named Ambigu. The full 52-card deck version of poker is generally agreed to have been born in the early part of the 19th century in the gambling saloons of New Orleans, quickly spreading north on the Mississippi riverboats, then west to the gold fields and on to the rest of the world.19 Today more than 70 million Americans play poker and hundreds of millions more play the game worldwide.20 Comedian Joe Cowell, in a book published in 1844,21 described how he first encountered the game, whose origin he attributed to Henry Clay, aboard a steamboat from Louisville to New Orleans in December 1829: The aces are the highest denomination: then the kings, queens, jacks and tens: the smaller cards are not used; those I have named are all dealt out, and carefully concealed from one another; old players pack them in their hands, and peep at them as if they were afraid to trust even themselves Poque was a multiple stage game. In one stage, the players won or lose by virtue of the strength of their hands compared to other players. At this stage, the play was based on five-card hands and the hands were restricted to one pair, two pair, triplets, and four of a kind, at http://www.pagat.com/stops/poch.html #18-19 14 Four-handed Bouillotte was played with a 20-card pack. It had an Ace, King, Queen, 9 and 8 in four suits. The game only had three hand rankings: The Brelan Carré was three cards of the same rank that matched a turned up card. The Brelan was a hand of three cards of the same rank, different from the turned up card. If more than one player has a Brelan, the hand with the highest rank would win. If no one has a Brelan Carré or Brelan, the winning hand was determined by exposing all the players’ hands. The total points showing in each suit are counted, with Aces worth 11 points, Kings worth 10 points, Queens worth 10 points, Nines worth 9 points, and Eights worth 8 points. The suit with most points showing was deemed the winning suit, and the winning hand was the hand with the highest card of that suit. See, e.g., http://www.pagat.com/vying/bouillotte.html#hands. 15 The French game Primero had four card hands but whose ranking included flushes: Chorus: Four of a kind (e.g., four sixes) Fluxus: Four cards of the same suit, equivalent to a poker flush (e.g., 2, 4, A, and 6 of hearts) Supremus: Ace, 6, and 7 of the same suit (e.g., A, 6, 7 of spaces, 3 of diamonds) Primero: One card of each suit (e.g., 3 of hearts, 5 of diamonds, K of spades, 7 of clubs) Numerus: Two or three cards of the same suit. This is by far the most common hand (e.g., Q, 4, 6 of clubs, and 4 of spaces). 16 As-Nas might be credited for the invention of the ‘full’ (though so might logic), Parlett, supra note 7. 17 The word ‘Poker’ can be traced back via French Poque to one or more fifteenth-century German games variously recorded as Boeckels, Bocken, Bogel, Bockspiel, etc., which, when not denoting one of similar title played with balls or stones was the original of the still-played game of Poch, or Pochen. Its basic meaning is ‘bash’ or ‘knock’, and, by extension, ‘knock, provoke, brag, vie’, and suchlike. PARLETT, supra note 7, at 86. 18 PARLETT, supra note 8, at 112-113. 19 For information on the origins and history of poker see, e.g., ALVAREZ, supra note 2, at 32-44; EPSTEIN, supra note 6, at 201; SCARNE, supra note 9, at 23-25. 20 See, e.g., GREG DINKIN AND JEFFREY GITOMER, THE POKER MBA, xi (2002); ALVAREZ, supra note 2, at 23. 21 See, e.g., DAVID SPANIER, TOTAL POKER (2002), at 58; A. ALVAREZ, POKER: BETS, BLUFFS, AND BAD BEATS (2001), at 36-38; HERBERT ASBURY, SUCKER’S PROGRESS (1938), at 23-25. 13 to look. The four aces, with any other card, cannot be beat. Four kings, with an ace cannot be beat because then no one can have four aces; and four queens, or jacks, or tens, with an ace, are all inferior hands to the kings when so attended. But holding the cards I have instanced seldom occurs when they are fairly dealt; and three aces for example, or three kings, with any two of the other cards, or four queens, or jacks or tens, is called a full, and with an ace, though not invincible, are considered very good bragging hands. The dealer makes the game, or value of the beginning bet and called the ante - in this instance it was a dollar - and then everybody stakes the same amount, and says, “I’m up”.22 Thus it appears that a prototype of Poker played with a 20-card pack (A-K-Q-J-T) was played in the United States as early as 1829.23 In this 20-card version, each of four players receives five cards, there is no draw, and bets are made, raised and called on a limited number of combinations – one pair, two pair, three of a kind, ‘full’ (the only combination in which all five cards are active) and four of a kind.24 Poker’s position as America’s national card game in the twentieth century may not have been foreseeable towards the end of the nineteenth. Citing Foster’s Complete Hoyle of 1897, Parlett notes: 25 There is no authoritative code of laws for the game of Poker, simply because the best clubs do not admit the game to their card rooms, and consequently decry the necessity of adopting any … In the absence of any official coded, the daily press is called upon for hundreds of decisions every week. The author has gathered and compared a great number of these newspaper rulings, and has drawn from them and other sources to form a brief code of Poker laws… Parlett continues, noting the widespread opposition to the game prevalent in the United States at this time and suggesting American society at the end of the nineteenth century was notoriously more Victorian than the Victorians.26 Quoting Blackbridge’s The Complete Poker Player of 1880:27 22 23 JOE COWELL, THIRTY YEARS PASSED AMONG THE PLAYERS IN ENGLAND AND AMERICA (New York, 1844). The game was similarly described by JONATHON GREEN in EXPOSURE OF THE ARTS AND MISERIES OF GAMBLING (1843). See also JAMES HILDRETH, DRAGOON CAMPAIGNS TO THE ROCKY MOUNTAINS; BEING A HISTORY OF THE ENLISTMENT, ORGANIZATION, AND FIRST CAMPAIGNS OF THE REGIMENT OF U.S. DRAGOONS (1836) (where he notes that soldiers played the game in their barracks and on occasion “The M- lost some cool hundreds last night at poker…”), at 128-130. More generally, see PARLETT, supra note 8, at 111-115; DAVID SPANIER, TOTAL POKER 58 (2002); A. ALVAREZ, POKER: BETS, BLUFFS, AND BAD BEATS 36-38 (2001); HERBERT ASBURY, SUCKER’S PROGRESS 23-25 (1938). 24 It is noteworthy that the top hand in this old Poker is, unlike modern Poker, an unbeatable hand. 25 PARLETT, supra note 8, at 115. 26 The Honorable Robert Schenck, American ambassador to Great Britain is often credited with the introduction of Poker into English society in 1872 and perhaps the first codification of poker in history. Parlett, supra note 8, at 114-115; JOHN MCDONALD, STRATEGY IN POKER, BUSINESS, AND WAR 37 (1950). 27 Parlett, supra note 8, at 115. This opinion operates in the United States to such an extent as to produce an almost total outlawry of games of chance in social circles… and especially all games in which stakes are an essential element. This is evidenced by the immense number of childish and frivolous games which are everywhere sold at the shops, in which people contrive to mingle a slight favor of the intellectual diversion that real playing cards afford, with a great deal of useless lumber in regard to painters and authors; ancient English and Choctaw kings; famous poets and pickpockets, and the thrilling details of the private life of the Dr Busby family… By the middle of the 19th century, the game saw amazing transformation. First, by 1850, the game evolved from 20 cards to its standard configuration of 52 cards.28 The expansion of the deck probably took part in steps and is thought to have occurred to accommodate more players and the second innovation, the draw. This innovation was first mentioned in 1850 American edition of Bohn’s New Handbook of Games.29 The draw was the most substantial innovation that turned poker from a gamble into a game of skill.30 Other innovations that were developed around this period were the “flush” and the “straight.” The Basic Rules of the Game Poker is a five-card vying game played with standard playing cards. A vying game is one where, instead of playing their cards out, the players bet as to who holds the best card combination by progressively raising the stakes until either (a) there is a showdown, when the best hand wins all the stakes, or (b) all but one player has given up betting and dropped out of play, when the last person to raise wins the pot without a showdown.31 Most variants of poker are based on a standard five-card poker hand ranking system according to strength from the strongest hand to the weakest. The ranking of the cards in a standard 52 card deck is as follows: A Royal Flush, the top hand, consists of an Ace, King, Queen, Jack and 10, all of the same suit. A Straight Flush is any five-card sequence in the same suit. A Four of a Kind is all four cards of the same value. An early working description of the 52-card game appears in a supplement to the 1850 reprint of a Philadelphian Hoyle under the title ‘Poker, or Bluff,’ and a Boston Hoyle of 1857. Parlett, supra note 8, at 111. The contemporary 52-Card Deck used in the U.S. today was developed in Rouen, France in the 1500s. The English and the Americans adopted what was generally referred to as the “French Pack”. 29 Bohn’s New Handbook of Games 384 30 David Parlett, A History of Poker, http://www.pagat.com/vying/pokerhistory.html. In his authoritative book, A History of Card Games, Parlett also refers to the introduction of the draw as a change that turned Poker from a gamble to a “science.” Parlett, supra note 8, at 112. 31 Parlett, supra note 8; David Parlett, A History of Poker, at www.pagat.com/vying/pokerhistory.html. 28 A Full House is a Three of a kind combined with a pair A Flush is any five cards of the same suit, that are not in sequence A Straight is any five cards in sequence, but not in the same suit A Three of a Kind is any three cards of the same value Two Pair are any two separate pairs A Pair is any two cards of the same value If a hand contains none of the above combinations, it’s valued by the highest card in it. In standard poker has no ranking of suits. If two hands are identical apart from the suits of the cards then they count as equal. In standard poker, if there are two highest equal hands in a showdown, the pot is split between them. Poker is a game with many variants. These typically fail into one of four categories: draw games32, stud games33, shared or community card games34 and miscellaneous games. The most popular game played in 2005 is Texas Hold’em. The game accommodates 2-10 players. In the initial deal, each player is dealt two cards face down. These cards are unique to the player to whom they were dealt. A round of betting is held after the deal. During each round of betting, players can either start the betting, meet or raise the betting, or fold his cards. The later removes that player from the game. If the number of players is reduced to a single player, then that player wins regardless of his or her hand. After the betting, three shared cards are placed face up in the middle of the table. Another round of betting follows. One more table card is flipped, followed by another round of betting. The last shared table card is then flipped and a final round of betting may occur. If at that point, two or more players are still active, the person with the highest hand wins. Played in a casino, poker differs from other games in that cardroom poker (such as Texas Hold’em, as opposed to poker-based house-banked games such as Caribbean Stud) does not pit the player against the casino. Instead, players compete against each other and money won or lost merely is transferred from one player to another. The casino provides a dealer, who does not play, and makes its money by taking a percentage of each pot, charging an hourly fee, or collecting a flat amount for every hand. The first of these is most common; a rake (percentage extracted) of 5% to 10% is typical. Casino poker games are played table stakes, which means a player may bet only with the chips (or money) he has on the table during a hand. If a player runs out of chips Wikipedia lists 13 variants such as five card draw, Gardena jackpots, California lowball, Kansas City, California high/low split, High/low with declare, Four-before, Double-draw, Triple-draw, Johnson, and Q-Ball. http://en.wikipedia.org/wiki/Draw_poker 33 Wikipedia lists 17 variants such as five card stud, six card stud, seven card stud, Razz, London lowball, Eight-or-better high-low stud, Mississippi stud, and Mexican stud. 34 Wikipedia lists 15 variants such as Texas Hold’em, Pineapple, Tahoe, Double-board hold’em, Omaha hold’em, Manila and Pinatubo. http://en.wikipedia.org/wiki/Community_card_poker 32 when calling or betting, he cannot add more until the hand is over, and must go all-in to stay in the hand. When a player goes all-in, all subsequent wagers by other players go into a separate side pot in which the all-in player has no interest – he may win the main pot, to which he contributed, but may not win the side pot even if his hand is the best. The limits, or absence of limits, on how much a player may bet and raise will dramatically affect the game dynamics, including players’ decisions and strategies, and the relative balance of luck versus skill in the game. A variety of betting structures are possible. In a fixed-limit game, no bet or raise may exceed a specified amount. This amount usually varies with the betting round, with later rounds allowing higher bets and raises than early rounds. In a $5−$10 fixed-limit game, for example, players may bet or raise exactly $5 in early rounds and exactly $10 in later rounds. Spread limit games are similar to fixed-limit, but allow any bet between the two amounts at any time. Thus in a $10−$20 spread limit game, bettors may make wagers of any amount between $10 and $20 at any time, with the provision that any raise must be at least equal to the preceding bet. In pot-limit games, bets or raises are limited only by the amount of money in the pot at the time the wager is made. In no-limit games, a player may bet or raise any amount he has in front of him (table stakes limit betting in a hand to the chips and money on the table). Pot limit and no limit formats are generally used only for more serious games (nolimit is used in the World Series of Poker, the premier high-stakes tournament). In most limit games, a bet and a maximum of either three or four raises per betting round (such maximum to minimize the effects of possible collusion among players) are permitted. While the distribution of cards is random, the methods and steps in betting, the analysis of playing habits of other players, and the management of your chips from hand to hand are all skill. In Draw poker, players are each dealt five cards and have the opportunity to assess the initial hand, discard cards, and retrieve new cards. While the initial distribution of cards, and replacement cards are random, the decision on which cards to discard, the methods and steps in betting, the analysis of playing habits of other players, and the management of your chips from hand to hand are all skill. Tournament play minimizes the impact of any single hand by placing a greater emphasis on chip management and strategies over time. Most poker tournaments feature one of two types of poker games, Texas Hold’em and Draw Poker. Legal Definition of Gambling Generally Historically,] [a]t common law . . . gambling . . . where practiced innocently and as a recreation, was not unlawful. Such games were unlawful, however, where they became an incitement to a breach of the peace, so as to constitute a nuisance, tended to immorality . . . or for any peculiar reason were against public policy, or were conducted by means of cheating or by fraud. . . . Thus, gambling essentially is a crime only when and to the extent that the legislature has so declared it.35 35 38 Am. Jur. 2d Gambling § 31 (1999) (citations omitted). “Gambling” itself does not have a single definition; it is made up of three separate categories. In the first category of gambling games are “lotteries” or chance games involving schemes where a person pays valuable consideration for the opportunity to win a prize based on a game of chance. 36 The second category of gambling games is “bookmaking.” Bookmaking occurs when a person risks something of value on the outcome of an uncertain event, in which the bettor does not exercise any control, but has the opportunity to win something of greater value than that which was risked.37 Whether sports wagering is an activity predominately determined by chance or skill can be the subject of much debate. Most states avoid this debate by enacting separate laws defining bookmaking as a criminal offense. The key difference between bookmaking and lottery laws is that a predominant element of chance, a prerequisite in many states to illegal gambling, is not a specific prerequisite to a bookmaking violation.38 In this context, gambling is, as one court noted, where two persons “ stipulate for a price that the determination as to who shall gain or lose (i. e., get or not get the prize) shall depend upon the happening of an uncertain event in which such parties have no interest except that arising from the possibility of such gain or loss.”39 In this case, the uncertain event can be a game of skill.40 Despite this, not all bookmaking is illegal. For instance, “trading commodity options” is a legal form of bookmaking.41 Prior to federal legislation that specifically authorized such trading, the great majority of courts held that a contract to speculate in the rise and fall of commodities is illegal gambling if there was no intent that the underlying commodities would be delivered.42 The final category of “gambling” involves activities that are predominantly skillbased “contests,” but because state legislatures want to eradicate these types of 36 See Darlington Theatres, 190 to the term “lottery” as a “species of gaming”). 37 See note 35, generally id. §§ 44-47. 38 See note 35, generally id. §§ 44-47, 61-76. S.C. at 291, 2 S.E.2d at 786 (referring 39 Westerhaus Co. v. City of Cincinnati, 165 Ohio St. 327, 135 N.E.2d 318, Ohio 1956. 40 Id. 41 Commodities trading is regulated by the Securities Act of 1933. See 15 U.S.C. § 77a et seq. (2000). See also Richard A. Brealey, Fundamentals of Corporate Finance 257 (1995) (”Commodity futures allow firms to fix the future price that they pay for a wide range of agricultural commodities, metals, and oil. Financial futures help firms to protect themselves against unforeseen movements in interest rates, exchange rates, and stock prices.”). 42 See, e.g., Pearce v. Rice, 142 U.S. 28 (1891); see also Farless v. Morehead, 201 F. 310 (6th Cir. 1912) (holding that transactions were really “bets” or “wagers” on the fluctuations of the market, because all parties understood that no stock was to be in fact purchased and received); Wade v. United States, 33 App. D.C. 29 (1909) (holding that contracts tied to the probable rise and fall of market prices, without actual equity ownership, constitutes gambling and is prohibited); Joslyn v. Downing, Hopkins & Co., 150 F. 317 (9th Cir. 1906) (holding that the pretend buying and selling of stocks or commodities were merely gambling transactions); Morris v. Norton, 75 F. 912 (6th Cir. 1896) (holding similarly and stating that such gambling contracts are void). activities, they have grouped them with illegal gambling. The best example of this type of activity is poker. Of the three forms of gambling, the courts and the governments historically have shown the most hostility towards lotteries. As one court noted : “Of all the forms of gambling, lotteries have been the most condemned by the courts.”43 Historical references to the social evils of lotteries date over 150 years. In 1850, the United States Supreme Court noted: “Experience has shown that the common forms of gambling are comparatively innocuous when placed in contrast with the widespread pestilence of lotteries. The former are confined to a few persons and places, but the latter infests the whole community: it enters every dwelling; it reaches every class; it preys upon the hard earnings of the poor; it plunders the ignorant and simple.”44 A reference from the librarian of Congress in 1893 shared these sentiments: “’a general public conviction that lotteries are to be regarded, in direct proportion to their extension, as among the most dangerous and prolific sources of human misery.”45 As a result of the problems encountered with lotteries and general public opinion against them, most states adopted specific constitutional prohibitions against lotteries in the nineteenth century.46 Whether the states at the time intended to include all games of chance in the definition is doubtful. For example, one court during this time noted: “there may be an adventure or hazard without a lottery; every throw of the die, even for an ordinary wager, is an adventure or hazard, and I am sure it never entered the mind of any man that it constituted a lottery.”47 Despite that the prohibitions against lotteries have a common origin and most states adopted the predominance test, application of that test has been anything but even. Most agree that a lottery is “a scheme for the distribution of prizes by lot or chance.”48 In games of mixed chance and skill, the lottery prohibition typically only applies to those activities where chance is the predominate factor.49 The presence of skill becomes significant only where it plays a greater role in the outcome than chance.50 Hence, the name “predominance test’ is commonly used. 43 Mobil Oil Corp. v. Danforth, 455 S.W.2d 505, 509 (Mo. banc 1970). 44 Phalen v. Commonwealth of Virginia, [49 U.S.] 8 How. 163, 168, 12 L.Ed. 1030, 1033 (1850). 45 34 B.C.L.Rev. at 12-13, citing A.R. Spoffard, Lotteries in American History, S. Misc. Doc. No. 57, 52d Cong., 2d Sess. 194-95 (1893) (Annual Report of the American Historical Society). 46 34 B.C.L.Rev. at 37. 47 Pinchback, 4 S.C.L. (2 Mill) at 34. 48 Troy Amusement Co. v. Attenweiler (1940), 64 Ohio App. 105, 116, 17 O.O. 443, 448, 28 N.E.2d 207, 213; see Stevens v. Cincinnati Times-Star Co. (1905), 72 Ohio St. 112, 73 N.E. 1058. 49 See, e.g., Johnson v. Collins Entm’t Co., 508 S.E.2d 575, 583 (S.C. 1998). Stevens v. Cincinnati TimesStar Co., 72 Ohio St. 112, 73 N.E. 1058, 106 Am.St.Rep. 586. 50 See id. In some states, the courts have retained the more conservative definition that was prevalent in the nineteenth century. For example, in Mississippi, the only form of prohibited lotteries is those that use tickets. The popular game of bingo therefore is not a lottery. Here the Mississippi Supreme Court noted: “pursuant to the “popular” meaning of the terms, bingo is not a lottery. This Court’s conclusion is reinforced by the structure and wording of [the prohibition]. The provision twice prohibits selling lottery “tickets”- i.e., (1) “… or its tickets be sold in this state,” and (2) “or its tickets sold.” This rather clearly connotes a particular kind of lottery: one with tickets.”51 In contrast, other states have interpreted the definition to effectively include all types of gambling. For example, the Kansas Supreme Court held that pari-mutuel betting on dog races constituted a lottery and the sale of lottery tickets.52 In these states, a lottery is basically any activity where a person wagers on the outcome of any activity that is determined in part by chance. These conclusion has been justified despite the conclusion that the predominance test is the proper standard by one court as follows “”If the result of the distribution is to be determined solely by skill or judgment, the scheme is not a lottery, even though the result is uncertain or may be affected by things unforeseen and accidental. Where elements both of skill and of chance enter into a contest, the determination of its character as a lottery or not is generally held to depend on which is the dominating element.”53 Most states, however, have a common definition of the predominance test. Under the predominance test, one must envision a continuum with pure skill on one end and pure chance on the other. The element of chance is met if chance predominates over skill in determining the outcome of the contest, even if the activity requires some skill. In theory, an activity crosses from skill to chance exactly in the middle of the continuum. On the continuum, games such as chess would be almost at the pure skill end, while traditional slot machines would be at the pure chance end of the continuum. Between these ends, there are many games that contain both skill and chance. In this area, a legal risk exists because it is a subjective assessment as to where on the continuum a game that is part skill and part chance lies. What is skill? The following definition by the Alabama Supreme Court is a worthy starting point: “Skill”-in the context of activities … is merely the exercise, upon known rules and fixed probabilities, of “sagacity,” which is defined as “quickness or acuteness of sense perceptions; keenness of discernment or penetration with soundness of judgment; shrewdness; [the] ability to see what is relevant and significant.” Webster’s New International 51 KNIGHT v. STATE of Mississippi, ex rel., Mike MOORE, Attorney General and Mississippi, 574 So.2d 662, (Miss. 1990) 52 State ex rel. Moore v. Bissing, 178 Kan. 111, 283 P.2d 418 (1955) 53 795 So.2d at 641 (quoting 54 C.J.S. Lotteries

4 (1987)). Dictionary 2198 (2d ed. (Unabridged) 1953). Thus, an activity that results in an award based upon the exercise of these qualities in conjunction with definite rules and probabilities that can be learned and calculated by the bettor is not prohibited [a prohibited lottery]54 “Generally, chance is defined as a lack or an uncertainty as to the occurrence of those events.”55 of control over events Legal Survey Of How Courts Have Classified Poker In The Past Courts in some states have analyzed the skill and chance elements of Poker. In some states, poker is identified as a skill game. In other states, poker is identified as a prohibited game with a significant skill component. In still other states, poker is identified as a game of chance. Many states have no modern analysis of whether poker is a skill game or a game of chance. When analyzed in light of constitutional and statutory lottery prohibitions that prohibit games of chance, court opinions and attorney general opinions have frequently found poker to be of sufficient skill as not to be a lottery game.56 When viewed in light of gambling prohibitions regardless of skill and chance or when chance is presumed without analysis, most courts find poker to be a gambling game.57 Poker Classified As A Game Of Skill Some states, particularly in the western United States provide commercial venues where its residents can play poker. This resulted because courts in those states did not classify poker as a game of chance. As a result, a commercial industry grew around poker in California, Washington and Montana. In California, courts have held that traditional poker tournaments are games of skill.58 In Bell Gardens Bicycle Club v. Dept. 54 OPINION OF THE JUSTICES 692 So.2d 107 April 8, 1997 55 See “chance”). Black’s Law Dictionary 231 (6th ed. 1990) (definition of 56 See, e.g., Harris v. Missouri Gaming Com’n, 869 S.W.2d 58 (Mo. Sup. Ct. 1994). See also, e.g., Bell Gardens Bicycle Club v. Dept. of Justice, 36 Cal.App.4th 717, 741 (2nd Dist. 1995). See also, e.g., Col. Op. Att’y Gen., No. 93-5, 1993 WL 380757 (April 21, 1993). See also, e.g., Ginsberg v. Centennial Turf Club, 251 P.2d 926, 929 (Colo.1952). See also, e.g., State v. Coats, 74 P.2d 1102, 1106 (Or.1938). 57 See, e.g., State v. Mathis, 105 S.W. 604, 605-06 (Mo.1907). See also, e.g., Indoor Recreation Enterprises, Inc. v. Douglas, 235 N.W.2d 398, 400-01 (Neb.1975). 58 See e.g. Bell Gardens Bicycle Club v. Dept. of Justice, 36 Cal.App.4th 717, 741 (2nd Dist. 1995).In the Bell Garden’s opinion, the court was tasked with determining whether a game called “jackpot poker” was variation on poker that maintained the skill elements of poker or whether it was a prohibited lottery style game. The court concluded that the underlying poker game remained a skill game; however, the jackpot feature was a prohibited lottery tacked on to the poker game. Nevertheless, the Bell Gardens court also held that “jackpot poker” is not a game of skill. Part of its reasoning was that the rules of jackpot poker are different than regular poker. Specifically, unlike the pot distributed in each “regular” poker game, in jackpot poker, the distribution of the prize by the lottery operator depends solely upon fortuity or random event (i.e., one person having the second best hand and another person having the game’s best hand at the same time). See Bell Gardens Bicycle Club, 36 Cal.App.4th at 747. In California, video poker was also found to be a game of chance. See Score Family Fun Ctr. Inc. v. County of San Diego, 225 Cal. App. 3d 1217, 1222 (1990) (explaining that such games involve “at most, only an illusion of skill . . . .”); see also Ca. Op. Att’y of Justice, skill has specifically been held to predominate over chance in traditional poker. In Montana, the court defined poker as “…a game played by individuals with one player pitting his skills and talents against those of the other players.”59 The court, in distinguishing poker from video poker, stated that poker is a game “played by individuals with one player pitting his skills and talents against those of the other players.”60 The issue before the court in D&R Music was whether the state constitutional prohibition on lotteries was applicable to video poker, in light of a lower court opinion that equated video poker with licensed traditional poker.61 The court in Washington has stated that the lottery statutes do not prohibit poker because poker is a game of substantial skill.62 Specifically, the Barnett case listed a series of games, including poker, that were “predominantly games of skill and that one who is skilled will win consistently.”63 The court went on to hold that while not a lottery, poker was still a prohibited gambling game in Washington.64 An earlier attorney general opinion from Washington states that poker contains a substantial element of skill, though playing for money is prohibited because it is a card game.65 In other states, the courts have addressed the classification of poker for other reasons. In Missouri, a court analyzed the skill elements of Poker to determine that it was a game of skill that was not prohibited by the state constitution’s prohibition on lotteries, which the court defined as games of chance.66 In an older case, without any meaningful analysis of that issue, poker was held to be a game of chance.67. In an older case, the court in Oregon identified poker as a gambling game; however, it was not a game of chance under the lottery statutes in Oregon, because the game was one of Gen. 83-610, 1983 WL 144844 (Sept. 15, 1983) (opining similarly about draw poker and low ball poker, played as electronic poker games). . See id at 743; cf. In re Henshaw’s Estate, 157 P.2d 390, 396 (Ca. Ct. App. 1945) (stating that poker is a game of chance); see also Lavick v. Nitzberg, 188 P.2d 758 (Ca. Ct. App. 1948)(holding similarly). 59 See Gallatin County v. D & R Music & Vending, Inc. 208 Mont. 138 (1984). 60 See Gallatin County v. D & R Music & Vending, Inc. 208 Mont. 138 (1984). 61 See Id. 62 See State v. Barnett, 488 P.2d 255 (1971). In an older case, the court in Montana states that poker is a game of skill; however, wagering on poker is still gambling. See Daussalt v. Kilburn, 109 P.2d 1113 (1941). see also State v. Brotherhood of Friends, 247 P.2d 787 (1952). 63 See id. 64 See id. 65 See Op. Att’y Gen. 1969-9 (WA 1969). 66 See Harris v. Missouri Gaming Com’n, 869 S.W.2d 58 (Mo. Sup. Ct. 1994). Cf. Thole v. Westfall, 682 S.W.2d 33 (Mo. 1984)(holding that, in video poker, while skill plays a part, the outcome depends in a material degree upon chance). See Harris v. Missouri Gaming Com’n, 869 S.W.2d 58 (Mo. Sup. Ct. 1994). 67 See State v. Cannon, 134 S.W. 513 (Mo. Sup. Ct. 1911). substantial skill and judgment.68 A recent Colorado attorney general opinion concluded that poker is a game of skill.69 Additionally, the FCC has addressed the issue of whether advertising Poker violates anti-lottery the FCC’s enforcement statutes and regulations. 70 In that letter, the FCC states that “where a poker tournament involves a closed-ended arrangement in which all players start with an equal amount of money and play in a “winner-take-all” elimination contest, without limit as to time, the contest is a game of skill.”71 Poker Classified As A Game Of Chance While many court opinions support the position that poker is best classified as a game of skill, contrary modern court decisions exist in Illinois, Nebraska, New York, and North Carolina.72 Most of the court opinions from these states do not analyze the elements of poker when determining poker is a game of chance, the opinions usually state poker is a game of chance without analysis, discussion or debate. In People v. Mitchell,73 the court held that, even though Illinois statute then provided an exception for “bona fide contests . . . of skill or strength” in which prizes are awarded, this exception probably does not apply to poker.74 The court in Nebraska has identified poker, along with blackjack, bridge, checkers and chess, as a game of chance.75 The Indoor Recreation opinion has recently been favorably cited by the attorney general of Nebraska when looking at the state constitutionality of a state bill to authorize electronic gaming devices.76 The courts in New York have identified poker as a game of chance, even though there may be some significant skill involved in the game.77 In an older case, the court in North Carolina has identified poker as a game of chance 68 See State v. Coats, 74 P.2d 1102 (1938). 69 Furthermore, the Attorney General opined that “[t]here is a considerable difference in the chance-skill equation when applied to ‘video poker’ machines.” Id. at *5. In Charnes v. Central City Opera House Assn., 773 P.2d 546, 551 (Colo. Sup. Ct. 1989), the Colorado Supreme Court held that, in Colorado, poker is an illegal gambling game of chance. 70 See Calnevar Broadcasting, 8 FCC Rcd. 32 (1992). 71 See id. 72 See e.g. Indoor Recreation Enterprises, Inc. v. Douglas, 194 Neb. 715, 235 N.W.2d 398 (1975).In the Indoor Recreation court opinion, the court concluded that a list of games that included chess and poker, were games where the outcome was predominantly determined by chance, though the court provides no analysis of such games to reach such a conclusion. 73 444 N.E.2d 1153, 1155 (Ill. Ct. App. 1983), 74 See id. Citing to California legal authorities, the Illinois Attorney General opined that draw poker, when played electronically, was a “game of chance.” Ill. Op. Att’y Gen. 82-019, 1982 WL 42777 (June 28, 1982). Additionally, today, Illinois statutorily groups “poker” with gambling games. See Ill. St. ch. 230 § 10/4 (2002). 75 See Indoor Recreation Enterprises, Inc. v. Douglas, 194 Neb. 715, 235 N.W.2d 398 (1975). 76 See Op. Atty. Gen Opinion 95085 (Neb. 1995). 77 See People v. Turner, 629 N.Y.S.2d 661 (City Crim. Ct. 1995). See also People v. Dubinski, 31 N.Y.S.2d 234 (City Crim. Ct. 1941). when analyzing whether a poker table was a gambling device.78 While other court opinions in North Carolina have found poker to be a game of chance, the context of each of these cases is whether someone can offer poker games for money without violating state gambling prohibitions.79 Older decisions, most of which were decided around the turn of the 20th century have found poker to be a game of chance in Massachusetts, Minnesota, South Dakota, Utah80, West Virginia81 and Wisconsin. In an old Massachusetts case, the jurors were instructed that, to find the defendant guilty, they must find that poker was a game of chance. When the jurors voted to convict, their verdict was upheld by the Massachusetts Supreme Court.82 In an older Minnesota case, without any analysis of the skill issue, the court held that the plaintiff’s complaint properly alleged that defendants were “running and playing games of chance, called ‘poker.’”83 In a South Dakota case from 1933 the court identified poker as a game of chance to find that the owner of the building hosting the game was keeping a building for the purpose of gambling, which was prohibited under statute.84 in Utah has identified poker as a game of chance. In an 1888 case that predates modern securities law, a Wisconsin court opined that commodity futures trading was a game of chance like poker or faro.85 78 See State v. McHone, 90 S.E.2d 539 (1955). 79 See e.g. State v. McHone, 90 S.E.2d 539 (N.C. 1955). 80 See Collet v. Beutler, 76 P. 707 (1904). 81 See State v. Dean, 126 E. 411 (1925). 82 See Edward F. Chapin v. John Haley, 133 Mass. 127 (Mass. Sup. Ct. 1882). A federal court, applying Massachusetts law, held that chance predominated over skill in the playing of a video poker game. See United States v. Marder, 48 F.3d 564 (1st Cir. 1995). Previously, however, the Massachusetts Court of Appeals has held that “video poker” does involve en element of skill and judgment. See Commonwealth v. Club Caravan, 571 N.E.2d 405 (1991). 83 Parsons v. Wilson, 103 N.W. 163 (Minn. Sup. Ct. 1905). 84 See City of Wessington Springs v. Melborn, 49 N.W. 747 (1933). 85 See Everingham v. Meigh, 13 N.W. 269 (1882). In addition, there is an attorney general’s opinion that cites the Indian Gaming Regulatory Act nearly in its entirety, which includes a list of games of chance that contains poker, though poker is never analyzed in the attorney general’s opinion. See Op. Atty. Gen. Wis. 390 (1990). Several states have attorney general opinions or statutes identifying poker as a game of chance, but have no reported court opinions regarding the issue.86 Additionally, Maine, New Mexico and Ohio specifically identify poker as a game of chance in their statutes. In Maine, a “game of chance” by statutory definition appears to include games where the result is determined through utilizing “decks of cards.”87 Poker is listed as a game of chance by statute in New Mexico, and has been listed as a game of chance since territorial times in New Mexico.88 The statute has been cited favorably by the court in New Mexico in several court opinions.89 Poker also is listed as a game of chance by statute in Ohio.90 The statute has been cited favorably by the courts in Ohio on a number of occasions.91 Poker Classified As A Game Of Mixed Chance And Skill Two states have had such difficulty in classifying poker as a game of chance or a game of skill that they have concluded it is a mixed game of chance and skill. A court in Texas has identified poker as being a game of equal chance and skill, even though poker, as a card game, is prohibited under the statutory prohibition on wagering on a 86 Without any meaningful detail or analysis, the Arizona Attorney General opined that games played with cards are “games of chance.” See Ariz. Op. Att’y Gen. No. I98-002 (R97-009), 1998 WL 48550 *3 (Jan. 21, 1998). Additionally, the Arizona Supreme Court held that taking bets on casino poker games, regardless of whether they are skill-based or chance-based, is illegal. See State v. Ducci, 727 P.2d 316 (Ariz. Sup. Ct. 1986). Without much analysis, the Connecticut Attorney General grouped poker with “other . . . games of chance.” Conn. Op. Att’y Gen. No. 2002-003, 2002 WL 727600 *3 (January 31, 2002). Additionally, Connecticut statutory definitions and structure appear to support an argument that “poker” is a “gambling game” and not a “contest of skill.” See Conn. St. § 53-278a(2) (2003). A Kentucky Attorney General opinion found poker to be a game of chance, with no reasoning given. See Ky. Op. Att’y Gen., 80-409 (June 17, 1980). Additionally, while reversing a ruling on other grounds, the Kentucky Court of Appeals presumed that poker was a “game of chance.” See Dills v. Commonwealth, 154 S.W.2d 543 (Ky. Ct. App. 1941). Lastly, the Kentucky statutory provisions on charitable gaming appear to group poker with “other game[s] of chance.” K.R.S. § 238.505 (2000). In construing a statute permitting certain charitable gaming, the Louisiana Attorney General had assumed that “poker” was a game of chance. See La. Att’y Gen. Op. No. 01-0263, 2001 WL 1044459 *1-2 (Aug. 28, 2001). The Tennessee Attorney General has identified poker, while having some element of skill, as prohibited by the state’s lottery statute, thus implying that poker is a game of chance since the lottery statute prohibits events consisting of prize, chance and consideration. See Op. Atty. Gen. TN 94-139 (1994). See also Op. Atty. Gen. TN 92-35 (1992). 87 17 M.R.S.A. § 330 (2001). In an unpublished opinion, the Maine Attorney General opined that an electronic poker device was a “game of chance.” Me. Op. Att’y Gen (Jan. 2, 1981). 88 See N.M. Stat. 15.4.9.9(2004). See also N.M. Ter. Laws Section 1, c. 64, p. 25, (1907). 89 See State v. La Rue, 353 P.2d 367(1960). See also State v. Orr, 138 P.2d 267 (1943). 90 See Ohio Rev. Code. 2915.01(D)(2003). 91 See Flamingo Lounge Of Ashtabula, Inc., v. Ohio Liquor Control Commission, 2003 WL 21386273 (Ohio App. 10 Dist.). See also ETB Corp. v. Ohio Liquor Control Commission, 2003 WL 257517 (Ohio App. 10 Dist.). See also Volger v. City of Sydney, 1987 WL 17254 (Ohio App. 3 Dist.). card game.92 In an older Kansas case, without any meaningful analysis, poker was found to be a game of mixed skill and chance.93 While citing to conflicting authorities from other jurisdictions, the Arkansas Attorney General explained that the issue of determining whether poker is a game of chance or skill is “by no means clear.” 94 Likewise, while no reported court opinions from South Carolina analyze poker with regard to traditional poker being a game of skill, an opinion from the South Carolina Attorney General favorably cites the Club Caravan opinion from Massachusetts in stating that the “outcome of a live poker game can be significantly affected by a player’s betting decisions.”95 The Mathematics of Poker Gambling games can be categorized as those of pure chance and those involving an element of skill.96 Games of pure chance include Roulette, Craps, Keno, Bingo, (traditional) Slots, and Lotteries. In these games, the outcome is determined by chance alone, and no strategy or skill can affect the long run percentage of money won or lost.97 Casino games involving skill include Blackjack, Video Poker, many of the newer poker-based casino games such as Caribbean Stud Poker, Let It Ride Poker, and Three Card Poker.98 In games involving skill, decisions and strategies can affect the outcome and in a gambling environment, a player’s level of skill will affect the long-term percentage of money won or lost. Poker, generally, is a game of skill. That is not to say that chance does not play a role,99 but, as most authors emphasize, in the long run, a skilled player will beat an 92 See Gaudio v. State, 1994 WL 67733 (Tex.App.-Dallas). 93 State v. Terry, 44 P.2d 258 (1935). In Games Management, Inc. v. Owens, 233 Kan. 444, 445-6 (1983), the Kansas Supreme Court held that electronic video card games, such as “Double-Up,” were gambling devices. (In Double-Up, the player is essentially playing poker, where the game is programmed “with a minimum standard for a winning hand such as ’jacks or better.’’) The court found the fact that the card sequences are electronically programmed in each machine to be significant. Thus, the court concluded that the small amount of skill used to play such game is overshadowed by pure chance. Id. at 449. 94 Ark. Op. Att’y Gen No. 98-141, 1998 WL 549232 *1 (June 26, 1998). More recently, however, the Supreme Court of Arkansas held that video poker was a game of chance. See Sharp v. State, 88 S.W.3d 848, 852 (Ark. Sup. Ct. 2002). 95 See Op. Atty. Gen. (May 23, 1997). See, for example, ROBERT C. HANNUM AND ANTHONY N. CABOT, PRACTICAL CASINO MATH, 2nd ed. (2005). For some games of chance, such as craps, the house advantages for different wagers vary so the overall long-run percentage of money won (lost) will depend on which bets are made. This is not an issue of skill. 98 A game of pure skill is one devoid of all probabilistic elements, and would include Tic-Tac-Toe, Checkers, Chess and Go, among others. See, e.g., RICHARD EPSTEIN, THE THEORY OF GAMBLING AND STATISTICAL LOGIC, 201 (1995), at 337. Such games of pure skill are not usually offered in a casino environment. 99 “Poker is a game of skill and chance.” DAVID MAMET, Things I Have Learned Playing Poker on the Hill, in WRITING IN RESTAURANTS, 93 (1986); “Luck has an influence, but skill has a more pronounced effect.” BASIL NESTOR, THE SMARTER BET GUIDE TO POKER 13 (2003). One author explains further: “It should be pointed out here that the analytical distinction between games of chance and games of skill is somewhat artificial. As noted earlier, all games, even those most amenable to the skillful prediction of the player, contain an element of chance. The distinction outline above is therefore not an absolute separation, for even in games like poker, a winner depends on not being dealt appalling cards while opponents are dealt favorable ones, and all the skill involved in handicapping is rendered obsolete if at the last minute it rains or a horse 97 96 unskilled player. The general argument is that the cards will “even out” over the long term (which they will, assuming random deals) and the winners will be the better players. Although chance, or luck, can play an important role over the short term, poker is in the long run predominately a game of skill.100 Numerous authors have drawn analogies between poker and other endeavors involving strategic decision making.101 It is not surprising that John von Neumann and Oskar Morgenstern devoted an entire chapter to poker in their seminal book on game theory.102 “A seemingly trivial and playful pursuit like poker, von Neumann argued, might hold the key to more serious affairs for two reasons. Both poker and economic competition require a certain type of reasoning, namely the rational calculation of advantage and disadvantage based on some internally consistent system of values (‘more is better than less’). And in both, the outcome for any individual actor depends not only on his own actions, but on the independent actions of others.”103 In comparing poker to other games involving an element of skill, one famed gambling author and expert writes: There are few professionals who earn a living playing blackjack, and even fewer who sustain themselves playing video poker, but it’s tough. Perfect play will produce a one to two percent player edge. Skill has a part in those contests, but luck and the percentages still hold the greatest sway. It’s the other way around in poker. Bad luck can hurt, but skill always beats luck over time.104 Often cited in support of the argument that skill is a major factor in poker is that the same group of players, or roughly many of the same players, tend to win in poker and rise to the top of tournaments. If skill were not a significant factor, the collection of winners would be more representative of a random selection from the field of all players. becomes ill. No amount of skill can ever eliminate uncertainty and confer absolute control, for chance is an ontological feature of the world; its influence is pervasive and the outcome of a gamble is always a contingent event.” GERDA REITH, THE AGE OF CHANCE 94 (1999). Referring to the proliferation of card games in nineteenth-century America, another author observes: “Cards and dice games flourished throughout the century. Some of them were purely games of chance. Others, poker above all, clearly required skill, judgment, and psychological strength.” RICHARD SASULY, Bookies AND BETTORS: TWO HUNDRED YEARS OF GAMBLING 67 (1982). 100 Noted expert Oswald Jacoby, champion bridge player and at one time the leading contemporary authority on the subject, called poker the most skillful of all card games. He distinguishes poker on the principle that it concerns the management of money, whereas other card games concern the management of cards. JOHN MCDONALD, supra note 25, at 24-25. 101 For general references, see, for example, JOHN VON NEUMANN AND OSKAR MORGENSTERN, THE THEORY OF GAMES AND ECONOMIC BEHAVIOR (1994); JOHN MCDONALD, supra note 25; DINKIN AND GITOMER, supra note 19. One author’s comments about poker absent the sometimes wild and crazy rules sometimes found in home games indeed applies to many forms of competitive poker today: “Poker – and I mean real five-card draw or stud poker with nothing wild – is a game of control and strategy. It is akin to competitive business, to highlevel diplomacy, and, for that matter, to war.” CLYDE BRION DAVIS, SOMETHING FOR NOTHING 127 (1955) 102 JOHN VON NEUMANN AND OSKAR MORGENSTERN, supra note 101; see also KEN BINMORE, FUN AND GAMES: A TEXT ON GAME THEORY, 571-602 (1992). 103 SYLVIA NASAR, A BEAUTIFUL MIND, quoted in DINKIN AND GITOMER, supra note 19, at 47. 104 BASIL NESTOR, THE UNOFFICIAL GUIDE TO GAMBLING, 173-174 (1999). Ask the question, “Who are the top five poker players in the world?” and you can receive a meaningful response. One can debate the precise set of five, but the question itself is meaningful because skill is a determining factor. The question, “Who are the top five roulette (or craps) players in the world?”, however, is utterly meaningless. There is no such thing as a “good” roulette player. Much anecdotal evidence exists among authors and other experts regarding the role of skill in poker. The collective opinion of these experts is unequivocal: Poker is a game in which skill plays a large part and in the long run a skilled player will beat an unskilled player. The following passages are typical: Over the long run everybody gets the same proportion of good and bad cards, of winning and losing hands. Beginning poker players rely on big hands and lucky draws. Expert poker players use their skills to minimize their losses on their bad hands and maximize their profits on their big hands, they are also able to judge better than others when a big hand is not the best hand and when a small hand is the best hand. … For above all, … poker is not primarily a game of luck. It is a game of skill.105 One of the finest illustrations of the laws of chance is furnished by the game of poker. It is not a game of pure chance, like dice and roulette, but one involving a large element of skill or judgment.106 There’s no doubt that luck plays a major role in short-term poker success, but over the long run poker is certainly a game of skill.107 In any Poker game, be it Stud or Draw Poker or any of their countless variations that combine skill and chance, the more skillful player will win the money in the long run. … Poker contains a greater skill element than any other card game, including Contract Bridge, Pinochle, and Gin Rummy. Poker is the one and only game where a skilled player may hold bad cards for hours and still win the money.108 Poker is a game of skill; luck and psychology also play a part, but unlike other casino games that rely entirely on luck, winning poker requires skill. A skillful poker player can change the odds by using position, psychology, bluffing, and other methods to increase his chances to win the pot and increase the size of the pots he wins.109 DAVID SKLANSKY, THE THEORY OF POKER 2-4 (1999). HORACE C. LEVINSON, CHANCE, LUCK AND STATISTICS, 111 (1963). 107 ANDREW BRISMAN, AMERICAN MENSA GUIDE TO CASINO GAMING, 192 (1999). 108 SCARNE, supra note 9, at 32. Scarne devotes an entire chapter in this book to the subject of skill versus chance in poker, 29-37. 109 GARY CARSON, THE COMPLETE BOOK OF HOLD’EM POKER, 4-5 (2001). 106 105 The excerpts above are not anomalous; it is difficult to find an expert who does not claim that success in poker depends in large part on skill.110 As one author put it, “Of course, luck plays a major role in short-term poker success, but over the long run poker is certainly a game of skill.”111 The result from an individual poker session has a lot to do with luck; the structure of the game, however, is such that a player with an understanding of the game can be a long-term winner, whereas those who don’t really understand the game will be losers.112 Experts agree there are several components to the skill necessary to play poker well. These include mathematics, psychology, assessing competition, reading hands, recognizing tells, exploiting position, and money management.113 These factors are, of course, interrelated and good poker strategy and tactics require the use of a combination of these skill components. Deceptiveness and savvy (bluffing) are essential to the game.114 In his classic book on the theory of gambling, Epstein notes that poker games have a large number of strategic alternatives115 and certain types, such as five-card Stud Poker and Seven-Card Stud, are almost purely strategical.116 Artificial Intelligence and Poker Poker has been heralded as a game worthy of research into artificial intelligence because it “is a game of imperfect information, where multiple competing agents must deal with probabilistic knowledge, risk assessment, and possible deception, not unlike decisions made in the real world.”117 When scientists began studies to undertake to build computer programs to play poker, they began to recognize the limitations of artificial intelligence in defeating skilled human players. In one case, scientists at the University of Alberta built and tested a computer program to defeat human players. Their first attempts failed. “Our initial experience with a poker-playing program was positive (Billings et al. 1997). However, we quickly discovered how adaptive human players were. In games played over the Internet, our program, Loki, would perform quite well initially. Some opponents would detect patterns and weaknesses in the program’s play, Success relates to winning the most money, not winning the most pots, a mistake often made by novice and unskilled players. “A quick way to go broke is to play every hand. Yes, you’ll win more pots along your personal road to ruin, but your objective is to win the most money, not the most pots.” LOU KRIEGER, HOLD’EM EXCELLENCE: FROM BEGINNER TO WINNER, 30 (2000); See also SKLANSKY, supra note 105, at 5-7. 111 BRISMAN, supra note 107, at 192. 112 CARSON, supra note 109, at 5. 113 See, e.g., DOYLE BRUNSON, SUPER/SYSTEM: A COURSE IN POWER POKER (1978); CARSON, supra note 109; SCARNE, supra note 9; SKLANSKY, supra note 105. 114 See, e.g., JOHN VON NEUMANN AND OSKAR MORGENSTERN, supra note 101; KEN BINMORE, FUN AND GAMES: A TEXT ON GAME THEORY, supra note 102. 115 EPSTEIN, supra note 6, at 201. 116 Id. at 211. 117 DARSE BILLINGS, AARON DAVIDSON, JONATHAN SCHAEFFER, AND DUANE SZAFRON, The Challenge of Poker, 134(1-2) ARTIFICIAL INTELLIGENCE JOURNAL 201-240 (2002). 110 and they would alter their strategy to exploit them. One cannot be a strong poker player without modeling your opponent’s play and adjusting to it.”118 In many ways, modeling a computer program capable of beating the best players proved more difficult than programs created to beat the best chess players. As one study noted: “The artificial intelligence community has recently benefited from the tremendous publicity generated by the development of chess, checkers and Othello programs that are capable of defeating the best human players. However, there is an important difference between these board games and popular card games like bridge and poker. In the board games, players always have complete knowledge of the entire game state since it is visible to both participants. This property allows high performance to be achieved by a brute-force search of the game tree. In contrast, bridge and poker involve imperfect information since the other players’ cards are not known, and search alone is insufficient to play these games well. Dealing with imperfect information is the main reason why progress on developing strong bridge and poker programs has lagged behind the advances in other games. However, it is also the reason why these games promise higher potential research benefits.”119 Games are an abstraction of worlds in which hostile agents act to diminish each other’s well-being. Thus, they can be used to design and analyze situations with multiple interacting agents having competing goals. Since real life contains many situations of this kind, a method to solve a game may be applied to problems in other areas. For example, in Theory of Games and Economic Behavior, Von Neumann and Morgenstern state that a study of ‘games of strategy’ is required in order to develop a theory for the foundations of economics and for the main mechanisms of social organization, because games are analogous to a variety of behaviors and situations that occur in these two areas. In fact, games are already used to model certain economic problems.120 In modeling various elements of skill in Texas Hold’em, the most popular form of poker played today, the authors of a leading artificial intelligence software package considered the following aspects of poker:121 Aaron Davidson, Opponent Modeling in Poker: Learning and Acting in a Hostile and Uncertain Environment (2002) (M.Sc. thesis, University of Alberta, available at http://www.cs.ualberta.ca/~games/poker/). 119 Jonathan Schaeffer, Darse Billings, Lourdes Peña, and Duane Szafron, Learning to Play Strong Poker, ICML-99, PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON MACHINE LEARNING (1999). 120 Lourdes Peña, Probabilities and Simulations in Poker (1999) (M.Sc. thesis, University of Alberta, available at http://www.cs.ualberta.ca/~games/poker/), quoting John Von Neumann and Oskar Morgenstern, THEORY OF GAMES AND ECONOMIC BEHAVIOR (1st ed. 1944). 121 Darse Billings, Denis Papp, Jonathan Schaeffer, and Duane Szafron, Poker as an Experimental Testbed for Artificial Intelligence Research, PROCEEDINGS OF AI’98, (Canadian Society for Computational Studies in Intelligence) (1998). 118 • Hand strength – how your hand compares in strength to what your opponents may hold. Hand strength is computed on the flop, turn and river. o o Minimum skill level – assessing your hand strength as a function of your cards and the community cards. Moderate Skill Level - assessing your hand strength as a function of your cards and the community cards while accounting for the number of players still in the game, position at the table, and their history of betting in the hand. Maximum Skill Level - assessing your hand strength as a function of your cards and the community cards while accounting for the number of players still in the game, position at the table, and their history of betting in the hand and the different probabilities for each hidden hand calculating the chance of each hand being played to the current point in the game. Skill levels can be improved even further by varying hidden hand probabilities for each player depending on that player’s model of play. o • Hand potential – the probability of the hand improving (or being overtaken) as additional community cards appear. o o Minimum skill level - assessing your hand strength as a function of your cards and the community cards. Maximum skill level - assessing your hand strength as a function of your cards and the community cards accounting for the possible cards remaining in the deck after assessing the opponent’s model of play. • Betting strategy – whether to fold, call/check, or bet/raise. o o Minimum skill level - assessing your hand strength. Maximum skill level - assessing your hand potential, pot odds, bluffing, opponent modeling and unpredictability. Pot odds are the chances of winning determined by comparing your hand to the expected return from the pot. • Bluffing – allows you to profit from weak hands. Bluffing can create a false impression about your play that can improve the chances of winning subsequent hands. o o Minimum skill level - merely bluffing a certain percentage of all hands. Maximum skill level - predicting the probability that your opponent will call. • Opponent modeling – allows you to determine a likely probability distribution for your opponent’s hidden cards or betting strategy. o o Minimum skill level - uses a single model for all opponents in a given hand. Maximum skill level - modifies the probabilities based on a classification of each opponent (e.g. weak/strong, passive/aggressive), betting history, and collected statistics. • Unpredictability – making it difficult for opponents to form an accurate model of your strategy by varying playing strategy over time to induce opponents to make mistakes based on inaccurate models. Basic Odds and Probabilities The mathematics of poker is both simple and complicated. The simplicity arises from relatively straightforward calculations involved in many situations; the complexity is due to the enormous number of situations that can arise during the course of a poker game. An understanding of the mathematical probabilities and odds associated with the games is a crucial skill in playing poker well. The mathematics of poker has been studied extensively122 and knowledge of the relevant odds is an important skill. A certain modest familiarity with the relevant odds can be considered necessary, though not sufficient, for skilled poker play. As numerous authors have noted, knowledge of mathematical probabilities will not make a good poker player, but total disregard for them will make a bad one.123 Those players who can incorporate the other skill factors into their game – psychology, reading hands, taking advantage of position, bluffing, semi-bluffing, and other strategies – and who recognize the object is to win the most money, not the most pots, have a chance to excel.124 Poker hand rankings are determined by their likelihood of occurrence when five cards are dealt at random from a shuffled deck of 52 cards. The highest-ranking hand is the least likely; the second highest-ranking hand is the second least likely, and so on. The following table summarizes the hand rankings and their probabilities of occurring in a five-card hand dealt from a deck of 52 cards. Poker Hand Probabilities Hand 122 123 Probability Approximately See, e.g., EPSTEIN, supra note 6, at 201-212; SKLANSKY, supra note 105. MCDONALD, supra note 25; DINKIN AND GITOMER, supra note 19, at 49: “In poker and business, you must know the odds and probability first. You don’t always have to go by the odds, but you must at least know them.” Noted expert Lyle Berman makes the related observation: “Poker hones your ability to understand probability and measure risk because the outcomes are so immediate.” Quoted in DINKIN AND GITOMER, supra note 19, at 49. 124 One of the most common mistakes a novice or unskilled player makes in many types of poker, particularly Hold‘em, is to play too many hands. Such a person will end up winning more pots, but will lose a great deal more money in the process. See note 110. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. Royal flush Straight flush* Four of a kind Full house Flush Straight Three of a kind Two pairs One pair High card 0.000002 0.000014 0.000240 0.001441 0.001965 0.003925 0.021129 0.047539 0.422569 0.501177 1 in 649,740 1 in 72,193 1 in 4,165 1 in 694 1 in 509 1 in 255 1 in 47 1 in 21 1 in 2.4 1 in 2 * Excluding royal flushes The probabilities in the above table serve as a reference point, but further knowledge of the odds and mathematics associated with the play of the hands is required for excellence in playing poker. For example, what are the chances of getting two spades on the next two cards to make a flush? In addition to assessing probabilities of getting certain poker hands, proper poker play requires the ability to correctly evaluate the mathematical expectation of the various alternative decisions (bet, fold, call, raise, re-raise, etc.). The expectation, or expected value, of a decision is a function of both the probability of the possible outcomes of the action and the values of these outcomes. In poker, the value of an outcome is the amount of money won or lost. This is where the concept of pot odds, the ratio of the amount of money in the pot to the bet that must be called to continue in the hand, is useful. Better players will also be familiar with effective odds, implied odds, and reverse implied odds. To see how probability calculations operate during poker play, consider a situation that arises fairly often, the flush draw, in today’s most common type of poker, Texas Hold‘em. In Hold‘em (as it is often referred to), each player is dealt two cards face down and, after an initial round of betting,125 three community cards (called the flop) are dealt face up in the center of the table. After a second round of betting, a fourth community card (the turn) is exposed, followed by another round of betting, a fifth and final community card (the river) is exposed, and then a final round of betting.126 To In the typical Hold’em game, two blind bets are posted before the cards are dealt – a small blind by the player to the dealer’s immediate left and a large blind by the next player to the left of the small blind. A blind is a forced bet made before the player sees his cards used to start the pot and stimulate action. The small blind is usually equal to one-half the amount of the big blind. Since the deal rotates around the table (even in a casino where the dealer is not a player, a button used to signify the nominal dealer rotates after each hand), all players participate equally in the posting of any forced blind bets. We will refrain from discussing further details regarding betting amounts and structure as it is not necessary for this example. 126 Each betting round begins with the first active player to the left of the dealer (or in a game dealt by a house dealer, the first active player to the left of the button used to indicate dealer position). Because the first two players to the left of the dealer (or button) have already acted by putting in blind bets, the player one to the left of the big blind is the first with any choices (to call, raise, or fold in the first round of betting) on the pre-flop betting round. 125 illustrate probability calculations, suppose you have four cards to flush after the flop. This would happen if, for example, you held the Ace and Jack of spades and the flop contained the five of spades, the eight of spades, and the two of diamonds. In this case, then, you would make a flush if a spade falls on the turn or river (or both).127 Consider the following three questions: • • • What is the probability he will make the flush on the turn? If he doesn’t make the flush with the turn card, what is the probability he will make it on the river? What is the probability he will make the flush on either the turn or river? To answer these questions, note that since you have seen five cards – your two hole cards and the three flop cards – there are forty-seven remaining unseen cards, of which nine are spades (i.e., there are nine outs, or cards that will complete the flush). Thus the probability you will make the flush on the turn card is 9/47 = .191, for odds against of 38 to 9, or about 4.2 to 1, answering question (a). To answer (b), note that if you do not make the flush on the turn, there are still 9 spades left in the 46 remaining cards, so the probability you make it on the river is 9/46 = .196, for odds against of 37 to 9, or 4.1 to 1. To answer (c), first compute the probability you don’t make the flush on the turn or river, and then subtract this value from one: 1 – (38/47)(37/46) = .350. That is, the probability of making the flush on either the turn or river is 35%, for odds against of 1.86 to 1. The last calculation illustrates how some probabilities can be easier to determine by first computing the probability of the opposite (complement), then subtracting the result from one. This approach is not uncommon. Also, note that the probability that the flush is made with one card to come depends on whether we look at making the flush on the turn card or the river card (having not made the flush on the turn). In the example above, the former probability is .191; the latter is .196.128 The following table shows probabilities and odds of making hands in Texas Hold’em with a given number of outs (cards that will make the desired hand). Odds and Probabilities in Texas Hold‘em 1 Card Making on Turn Number of Outs 21 20 127 1 Card Making on River Probability 45.7% 43.5% Odds Against 1.19 1.30 2 Cards Making on Turn or River Probability 69.9% 67.5% Odds Against 0.43 0.48 Probability 44.7% 42.6% Odds Against 1.24 1.35 For simplicity, we focus only on the flush draw and ignore the possibility of making other hands, such as a pair, three of a kind, etc. 128 This explains apparent discrepancies that may be found when comparing popular books on poker. Some list the probability (or odds) with one card to come, assuming forty-seven cards remain (making the hand on the turn); others with forty-six cards remaining (making the hand on the river, given it was not made on the turn). 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 40.4% 38.3% 36.2% 34.0% 31.9% 29.8% 27.7% 25.5% 23.4% 21.3% 19.1% 17.0% 14.9% 12.8% 10.6% 8.5% 6.4% 4.3% 2.1% 1.47 1.61 1.76 1.94 2.13 2.36 2.62 2.92 3.27 3.70 4.22 4.88 5.71 6.83 8.40 10.75 14.67 22.50 46.00 41.3% 39.1% 37.0% 34.8% 32.6% 30.4% 28.3% 26.1% 23.9% 21.7% 19.6% 17.4% 15.2% 13.0% 10.9% 8.7% 6.5% 4.3% 2.2% 1.42 1.56 1.71 1.88 2.07 2.29 2.54 2.83 3.18 3.60 4.11 4.75 5.57 6.67 8.20 10.50 14.33 22.00 45.00 65.0% 62.4% 59.8% 57.0% 54.1% 51.2% 48.1% 45.0% 41.7% 38.4% 35.0% 31.5% 27.8% 24.1% 20.4% 16.5% 12.5% 8.4% 4.3% 0.54 0.60 0.67 0.75 0.85 0.95 1.08 1.22 1.40 1.60 1.86 2.18 2.59 3.14 3.91 5.07 7.01 10.88 22.50 To fully incorporate the mathematics of gambling into poker play, the odds and/or probabilities in the above table (or analogous values for other poker games) need to be balanced against the amount of money that would be won or lost. This comparison of the winning odds and the pot odds is at the heart of expectation, or expected value. Expectation Generally, the expectation, or expected value, of a wager can be computed by multiplying the possible payoffs by their probabilities and then summing the resulting terms. Mathematically: EV = ∑ (Net Pay i × Pi ) , where Pi is the probability of the ith possible net payoff, Net Pay i . The EV for a bet represents the amount of money the bettor will win or lose on average, or in the long run, from making the bet. As an example, suppose you pay $1 to play a game where a single card is drawn at random from a standard deck of playing cards, and if the selected card is a spade you will win even money; that is, you will be given $1 in addition to the $1 you paid to play the game. It should be clear this is not a smart bet, as you will win only once every four times and therefore will be, on average, down two dollars for every four times you play this game. Your expected value for this wager is negative 50 cents: EV = (+$1)(1/4) + (-$1)(3/4) = -$0.50. This means you will lose 50 cents on average for every time you make this wager. On the other hand, if the net payoff in this game of “Spades” is $4, the wager is now favorable; the expected value is positive $0.25, meaning you will win 25 cents on average every time you make this bet: EV = (+$4)(1/4) + (-$1)(3/4) = +$0.25. The EV is a function of both the probability of winning and the amount you will win. Even if the probability of winning is small, if the payoff is large enough the EV will be positive, making the bet favorable. If we consider only wagers where the outcome is either a single winning value or a loss, as many bets are, then the EV simplifies to: EV = (Win Amount x Prob of Winning) – (Loss Amount x Prob of Losing) Another way to think about whether the EV of a wager is positive or negative is to compare the expected return of the wager to the cost of playing, where the return is the amount paid back to the player for (rather than in addition to) the cost of playing. In the Spades game above where the player is paid $4 in addition to the $1 cost to play the game, the return is $5 if a spade is drawn and $0 is the bet is lost. Using the return values, the expected value can be written as: EV = (+$5)(1/4) + ($0)(3/4) - $1 = +$0.25. This way of looking at the EV adds the cost of playing ($1 in this example) to the net win and net loss and then subtracts it out to compensate (which, of course, it does, since the probabilities of the loss and win total to 1). If we further assume the net loss is equal to the cost of playing (again, the situation with many wagers), then the middle term involving the $0 return need not be included and for bets with only a single win or loss the formula for the wager EV can be written as: EV = (Win Amount x Prob of Winning) – Cost of Playing The win amount multiplied by the probability of winning is the expected return, and for the example above, then, the expected return is +$1.25. Since this is greater than the $1 cost of playing, the wager has positive EV. Expectation and Poker In poker, the cost of playing is the bet needed, and the win amount is the current size of the pot (before you make your bet) plus the bet you need to make to call the hand. Thus the EV can be represented as: EV = [Pot + Bet) x Prob of Winning] – Bet With a few steps of algebra (omitted) this EV formula can be written as: EV = (Pot x Prob of Winning) – [Bet x (1 – Prob of Winning)] Noting that one minus the probability of winning is equal to the probability of losing, and using the symbols P to represent the current size of the pot, B the bet size, W the probability of winning, and L the probability of losing, then the EV is positive when PW – BL > 0. Again using a bit more algebra, the EV is positive when W/L x P/B >1, or when P/B > L/W. The left-hand side of this last expression, P/B, is the ratio of the size of the pot to the amount of the bet needed, or the pot odds. The right-hand side, L/W, is the ratio of the probability of losing to the probability of winning, or the odds against winning. In words, the EV is positive when the pot odds are greater than the odds against winning. To illustrate, suppose you need to call a $20 bet to stay in the hand and the current size of the pot is $60. Further suppose in your current situation the probability you win, if you call the bet, is .20. Then P = 60, B = 20, W = .20, and L = .80. The odds against winning, L/W, are 4 to 1 and the pot odds, P/B, are 3 to 1. Since the odds against winning are greater than the pot odds, the EV is negative and, from a purely mathematical perspective, you will lose money in the long run by calling this bet. Other considerations aside, you should fold in this situation. On the other hand, if in the same situation the current size of the pot is $100, the pot odds (5 to 1) would be greater than the odds against winning and you should make the bet. It is this comparison between what the pot is offering and the chances of winning or losing that lies at the heart of the mathematics of poker. When faced with a decision to bet, fold, or raise, a player who consistently chooses the action with the largest EV will come out a winner. A player who consistently makes decisions with negative expectations will, over the long run, lose money. The present discussion on the mathematics of poker is, by necessity, simplified. In the short term, anything can happen to a single player; a good bet with positive expectation could lose and one with a negative expectation could win. The outcome of any given hand or playing session is uncertain, even when hands are “correctly” played. Skilled players don’t always win and unskilled players don’t always lose; there are statistical fluctuations in the outcomes. In the long run, however, a skilled player – i.e., one who is more skilled than others at the table – is assured of making money, and the general ideas presented here describe the basis of good poker mathematics.129 Mathematical expectation is at the heart of every gambling situation; good poker players consistently make decisions based on expected value.130 In fact, skilled gamblers, poker players in particular, realize that it is the decision that matters, not the outcome.131 129 The relative weight of mathematics in decision-making at poker varies depending on many factors. The mathematics tends to be more important in limit poker, for example, than no-limit, where psychological factors and bluffing can take on a more prominent role. 130 See, generally, SKLANSKY, supra note 105; HENRY STEPHENSON, REAL POKER NIGHT (2005); MASON MALMUTH, GAMBLING THEORY AND OTHER TOPICS (1994). 131 See, e.g., SKLANSKY, supra note 105, at 9-16; MASON MALMUTH, supra note 130, at 9. Although a specific good decision may result in an unfavorable outcome, the overall results associated with good decisions will be favorable in the long run. In some ways, then, the goal of poker is to make correct decisions. Simulations Because poker is a game of skill, it can be useful to observe the results of simulated games in which some of the players are skilled and some are not. If skill is indeed a factor, the unskilled players will tend to lose as the cards “even out” and it will become apparent that the skilled players beat the unskilled players as more and more hands are dealt. An important point here is that such an approach is only viable because player profiles can be designed and set to play poker at different levels of skill. It is impossible, for example, to design a simulation of roulette in which the long-run winnings of players differed. This is because there is no skill in roulette; regardless of how a player places bets, or tries to employ any so-called “system” or strategy, the long-run expected winnings in (double-zero) roulette will be a loss of 5.3% of the money wagered. We present below the results of computer simulations of 1,000,000 hands under a variety of scenarios for the two most popular casino poker games, Texas Hold‘em and Seven-Card Stud.132 Because the simulations allow for different player profiles (as represented by toughness of play, knowledge of odds, ability to bluff, varying play according to position and other players’ moves, etc.) to be loaded into the games, it is possible to see the effects in terms of money won or lost when an unskilled player is playing against skilled players. Texas Hold’em: $20/$40 betting structure, 10% rake, dealer tips. Table 1 gives the results for a Texas Hold’em game with ten players when all player profiles are identical. Since the player profiles are the same, differences in player won/loss figures can be attributed to statistical sampling variability (chance). Final won/loss figures show that all ten players lost money, which can ascribed to the 10% rake, dealer tips, and the fact that players were equally skilled. The player losses ranged from $296,552 to $411,625, which equates to a “win” of -$8.90 to -$12.35 per hour assuming 30 hands per hour. Table 2 shows what happens if one unskilled player is in the game against nine others with identical player profiles. The lack of skill is evident, as this player lost $42.6 million, compared to a win of roughly $4.2 million for each of the skilled players (win amounts for the skilled players ranged from $3.6 million to 4.8 million). This converts to an hourly win rate of approximately $125 for each of the skilled players (range from $107.54 to $143.01) compared to an hourly loss of more than one-thousand dollars ($1,278.25) for the unskilled player. In short, the unskilled player lost ten times as much on average as a skilled player. 132 Simulations were performed using Wilson’s Turbo Texas Hold’em and Seven-Card Stud software. Table 3 shows the results of a similar simulation of nine skilled players and one unskilled player, but differs from Table 2 in that the nine skilled players have different profiles (but all very skilled). The results are similar to those in Table 2, with each of the skilled players winning about ten times more (approximately $140 hourly win) than the unskilled player ($1,447 hourly loss). Table 4 presents the results when two unskilled players are in the game against eight identical-profile skilled players. In this scenario skilled players each won about $8.4 million (or about $250 per hour) compared to a $35.6 million average loss (about $1,069 per hour loss) for the unskilled players. Seven-Card Stud: $6/$12 betting structure, eight players, 10% rake, dealer tips. Table 5 is shows the results of a Seven-Card Stud game with eight identical skilled players. As was the case with the Hold’em scenario, since the player profiles are the same, differences in player won/loss figures can be attributed to statistical sampling variability, or chance. Final won/loss figures show that all players lost money, again this can be ascribed to the rake, dealer tips, and equality in player skill levels. The player losses ranged from $274,097 to $317,587, or an hourly win rate between -$8.22 to $9.53 assuming 30 hands per hour. Table 6 shows the results for a game with one unskilled player against seven other skilled players with identical profiles. As with the Hold’em analysis, the lack of skill is evident. The unskilled player lost $12.5 million, compared to a win of roughly $1.3 million for each of the skilled players (win amounts for the skilled players ranged from $1.2 million to 1.5 million). This converts to an hourly win rate of approximately $40 for each of the skilled players (range from $34.62 to $44.23) compared to an hourly loss of $375 for the unskilled player. In short, the unskilled player lost more than nine times than the average skilled player. Table 7 shows the results of a simulation of seven skilled players and one unskilled player, but differs from Table 6 in that the skilled players have different profiles (but all very skilled). The results are similar to those in Table 6, with each of the skilled players winning about nine times more (approximately $45 hourly win) than the unskilled player ($400 hourly loss). Effect of Number of Hands Played: Texas Hold’em and Seven-Card Stud. Figures 1-4 show the effects of number of hands played on hourly win rate for the first two scenarios in each of the Hold’em and Seven-Card Stud simulations described above. For each figure, the hourly win rate is plotted on the vertical axis and number of hands on the horizontal axis. Figure 1 shows Hold’em results when all ten players are identical in skill; Figure 2 shows the results with one unskilled player in the game against nine identical-profile skilled players. Figures 3 and 4 are the analogous charts for SevenCard Stud (but eight total player rather than nine). As the number of hands increases, there is a stabilizing effect on the group of similarly skilled players. Thus, luck can play a more important role in the short term when skill levels are similar and there is less variance in the win rates for these skilled players as the number of hands increases. It is equally obvious that skill is a dominate factor even after only 100 hands. Figures 5 through 8 are total win (rather than hourly win rate) versions of Figures 1 through 4, respectively. Texas Hold’em, No Rake, No Tokes. For purposes of comparison, Figures 9 through 12 show the win rates for several full-table (Figures 9 and 11) and four-player (Figures 10 and 12) Texas Hold’em games in which there are no rakes and dealer tokes. Without the rake and tokes, the zero-sum nature of poker becomes apparent. In the two figures for which the players are all equally skilled (Figures 9 and 10), the win rate among these skilled players averages out – tends to zero – as the number of hands increases. For the two figures in which there is an unskilled player at a table with other skilled players (Figures 11 and 12), the average win rates among the skilled players tends to the same positive value as the number of hands increases, offsetting the relatively large loss by the unskilled player. These latter two figures make it easy to see how the money in poker shifts from the weaker player(s) to the more skilled player(s). Not All Poker Games are Created Equally Texas Hold’em as described above is a game of skill. But the same can not be said of all poker games. A good comparison is video poker. The house edge on a video poker machine depends on the skill of the player, and reported advantages or payback percentages associated with a video poker machine assume perfect strategy and maximum coin played. Optimal strategy varies depending on the particular machine/game. Playing video poker is easy; playing it well can be challenging.133 There are a great variety of video poker machines, but most are based on the classic five-card draw form of poker where the player is dealt five random cards from a standard 52-card deck (53 cards if the game uses a joker) and then may replace any of these five cards to try to improve his hand. Any discards are replaced by a random selection from the 47 (48 in a game with a joker) remaining cards. The final five-card hand determines the payoff according to the pay schedule for the game. Unlike the traditional cardroom poker game where players are competing against the other players at the table, in video poker the player is not pitted against other players. In video poker, a player wins if his final hand is better than some minimum standard. This minimum standard depends on the particular game. In Jacks-or-Better, the most popular and probably easiest to learn video poker game, the player wins if the final hand is at least a pair of Jacks (or better). The payoff depends on how good the 133 Excellent references on video poker include: Dan Paymar, Video Poker – Optimum Play (1998); Stanford Wong, Professional Video Poker (1993); The Wizard of Odds Website, http://wizardofodds.com/. final hand is – the higher ranking the hand, the larger the payoff. The payoff schedule for a full-pay Jacks-or-Better machine is shown below. Full Pay (9/6) Jacks-or-Better Pay Table Hand Royal Flush Straight Flush Four of a kind Full House Flush Straight Three of a kind Two Pair Pair of Jacks or better 1st coin 250 50 25 9 6 4 3 2 1 2nd coin 500 100 50 18 12 8 6 4 2 3rd coin 750 150 75 27 18 12 9 6 3 4th coin 1,000 200 100 36 24 16 12 8 4 5th coin 4,000 250 125 45 30 20 15 10 5 Note in the above table the bonus for hitting a royal flush when playing five coins – the payoff is 4,000 coins (800-for-1) rather than the 1,250 coins that would result from a 250-for-1 straight multiplier of the single-coin payout. This is why optimal strategy and maximum return demand playing the maximum number of coins. Assuming optimal strategy and maximum coins, the full-pay Jacks-or-Better returns 99.54%. A breakdown of the return contribution by hand type is given in the following table. Full Pay Jacks-or-Better – Return Contribution by Hand Type Hand Payout* Probability Return Royal Flush 800 0.000025 0.0198 Straight Flush 50 0.000109 0.0055 Four of a Kind 25 0.002363 0.0591 Full House 9 0.011512 0.1036 Flush 6 0.011015 0.0661 Straight 4 0.011229 0.0449 Three of a Kind 3 0.074449 0.2234 Two Pair 2 0.129279 0.2586 Pair of Jacks or better 1 0.214585 0.2146 Nothing (Non-winner) 0 0.545435 0.0000 TOTAL RETURN 0.9954 *Royal flush payout assumes max coins played (800-for-1 = 4,000 coins for 5 coins played). The full-pay Jacks-or-Better machine is referred to as a 9/6 machine, so named because of the full house and flush payoffs (9 and 6, respectively). The more common short-pay Jacks-or-Better video poker machines pay only 8-for-1 for a full house and 5for-1 for a flush (8/5 machines); some pay even less. The 8/5 Jacks-or-Better returns 97.30%, the 7/5 Jacks-or-Better (7-for-1 for full house and 5-for-1 for flush) returns 96.15%, and the 6/5 Jacks-or-Better (6-for-1 for full house and 5-for-1 for flush) returns 95.00%. Again, these return figures assume perfect strategy and maximum coins played. When playing perhaps 600 hands per hour, these seemingly small differences in payouts and return percentages can amount to significant dollars lost for the player who fails to seek out machines with the better payoff schedules. Although the player is not competing against other players in video poker, it is still a poker game and skill is relevant. A player who properly uses optimal strategy will fare better than one who plays as if it were a game of pure chance. Straightforward analysis of the standard full-pay Jacks-or-Better video poker machine, for example, shows that the return decreases from 0.9954 when using optimal strategy to 0.3369 when using a random strategy. Put another way, the optimal strategy “skilled” player will lose only 0.46% of the money wagered in the long run, while the random (unskilled) player will lose 66.3% in the long run. Nevertheless, the skill levels between video poker and Texas Hold’em are significant. Skills such as psychology, assessing competition, reading hands, recognizing tells, exploiting position, and money management are conspicuously absent in video poker. As one court noted “Indeed, all the skill elements associated with the ordinary game of draw poker are conspicuously absent in the video version. . . . The player’s only skill is to recognize possible combinations and basic statistical probabilities.”134 As such most courts that have reviewed video poker have concluded that it is a game of chance.135 Another notable difference is that almost all video poker games even when played at optimumal strategy result in the player losing over time. As the North Carolina Court of Appeals recently stated, “(A)lthough a player’s knowledge of statistical probabilities can maximize his winnings in the short term, . . . . (i)n the long run, the video game’s program, which allows only a predetermined number of winning hands, negates even this limited skill element.”136 Public Policy and the Predominance Test A natural question is why is the legality of an activity determined by the predominance test? One answer is tied to the Christian orientation of the United States. Christians approach the subject from two general viewpoints. Some denominations take a deontological viewpoint while others take a teleological viewpoint. Deontology refers to a theory of moral obligation. That is universal and absolute. What is wrong is always 134 United States v. 294 Various Gambling Devices, 718 F. Supp. 1236, 1243 (W.D. Pa. 1989). 135 See United States v. Marder, 48 F.3d 564 (1st Cir. 1995); Score Family Fun Ctr., Inc. v. County of San Diego, 275 Cal. Rptr. 358 (Ct. App. 1990); Games Management, Inc. v. Owens, 662 P.2d 260 (Kan. 1983); Collins CoinMusic Co. v. North Carolina Alcoholic Beverage Control Comm’n, 451 S.E.2d 306 (N.C. Ct. App. 1994); Commonwealth v. Two Elec. Poker Game Machs., 465 A.2d 973 (Pa. 1983). 136 Collins Coin Music Co. v. North Carolina Alcoholic Beverage Control Comm’n, 451 S.E.2d 306, 308 (N.C. Ct. App. 1994) (citation omitted). wrong, under all circumstances, by all people, and despite the results.137 Several Protestant and non-Catholic denominations take the deontological “absolutist” approach toward gambling. Most Protestant teachings concerning gambling emphasize one of the following: A. Work Ethic - Biblical teachings command Christians to use their talents and direct their efforts to productive vocations. They view gambling as the antithesis of the work ethic; where gamblers seek gain for no effort or productive service. B. Poverty Ethic - Christians should use their earnings for God’s purposes, such as supporting one’s family, to relieve poverty, and support just causes. Gambling is a wrongful disposition of one’s earnings. C. An Obsession with Money - A Christian’s devotion should be with God, and not money. Greed, or devotion to money, is contrary to the devotion to God. Typical theological arguments include that gambling “vitiates love for God by exalting the worship of money” and “submits outcome to chance, therefore, subverting a trust in God’s dependable provisions for human needs.” D. Love of One’s Neighbor - Requires the operator to maintain a theoretical advantage over the players. Over time, the operator will necessarily use the advantage to profit at the disadvantage of others. This is contrary to the principle that one should love one’s neighbor. E. Faith in God’s Plan - Most Protestant religions believe that God has a plan based on love and justice. The Church asks that its members work productively in an ordered society. They believe that gambling shows a lack of faith in God’s plan; instead, a trust in luck. These teaching generally translate in a position that all gambling is wrong under any circumstances. For example, the “Social Principles” reflect the position of the United Methodist Church. It reads: Gambling is a menace to society, deadly to the best interests of moral, social, economic, and spiritual life, and destructive of good government. As an act of faith and love, Christians should abstain from gambling and should strive to minister to those victimized by the practice. . .. Community standards and personal lifestyles should be such as would make unnecessary and undesirable the resort to commercial gambling, including public lotteries, as a recreation, as an escape, or as a means of producing public revenue or funds for support of charities or government.138 137 Teleological doctrine is “ends” oriented. It explains phenomena “by final causes.” It is a “worldly” approach to problems. It also relates to utilitarianism: the greatest good to the greatest number. The measure of gambling is the result. If a specific gambling activity results in more good than bad, it is appropriate activity; if it has more bad than good results, it is inappropriate activity. 138 The Social Principles of the United Methodist Church 6-17 (1984, General Conference). Similarly, a leader of the Southern Baptist Convention told the Commission on the Review of the National Policy on Gambling much the same story: In all its resolutions, the Southern Baptist Convention has rejected gambling. Obviously, some forms of gambling are more serious than others, but all forms have been consistently rejected in Southern Baptist statements and resolutions . . . The use of gambling profits for worthy activities has not led Southern Baptists to endorse gambling . . .. The availability of gambling tempts both the reformed gambler and the potential gambler to destruction. For the entire community, gambling is disruptive and harmful. Thus, concerned citizens should work for laws to control and eliminate gambling.139 The Church of Jesus Christ of Latter-Day Saints has been equally vehement in maintaining that gambling is always wrong. In 1925, Church President Heber J. Grant proclaimed, “The Church has been, and now is, unalterably opposed to gambling in any form whatever. (A)ll members of the Church (are urged) to refrain from participation in any games of chance or risky speculation.” As noted in the reference by Heber Grant and the various tenets of the protestant view of gambling, a common element of many of these positions in the positions and teachings is the aspect of luck in the one’s gambling activities. As the United States was primarily a protestant nation in the 1900s, the advent of a rule of law regarding gambling that was closely associated with the country’s dominant religion is an expected outcome. Since the 1900s, however, the demographics of the United States have changed dramatically. Even the past 15 years has seen a shift in religious affiliation. For example, in 1990, __% of the United States population identified themselves as protestant. By 2001, however, this number slipped to ___%. A Shift From A Religious To A Pluralist Condemnation Of Gambling With the decline in protestant religion, the battle over gambling has shifted from one that is primarily religious to one in which the arguments are ostensibly based on pluralist notions with occasional moralist overtures. Two bases for defining the harm justifying government intervention are moralism and pluralism.140 Moralists maintain positions based on subjective personal feelings dictated either by theology or personal notions of social order. The teaching of Patrick Devlin typifies the moralist position. He states: 139 Raymond C. Bell, Moral Views on Gambling Promulgated by Major American Religious Bodies, 171, in Gambling in America: Report of the Commission on Gambling Appendix l. 140 Between the two polars is the pragmatic moral pluralism. While having a particular moral stand against an activity, the pragmatic moral pluralist may argue for legalization only because of the harm caused by making the activity illegal. Id. Societies disintegrate from within more frequently than they are broken up by external pressures. There is disintegration when no common morality is observed, and history shows that the loosening of moral bonds is often the first stage of disintegration so that society is justified in taking the same steps to preserve its moral code as it does to preserve its government and other essential institutions.141 Devlin, reject the notion that government should not interfere in the individual rights of its citizens if to do so prevents harm to society. He advocated a practical approach to enforcement of morals;142 specifically, that government should limit individual freedoms to the extent necessary to prevent public harm.143 Moralists claim that gambling influences the general public’s values and priorities.144 In essence, people may interact with others differently in a community with gambling as opposed to a community without it. Gambling’s emphasis on hedonism, luck, and wealth may affect the nature of these interactions. Undesirable attributes in the community at large may emerge, including that persons are better off being lucky than working hard and that wealth is the most important attribute, therefore, everyone must have a price. Underlying some negative attitudes toward gambling is the fear of any activities that are hedonist, and the idea that pleasure for pleasure’s sake is wrong or shows deviant behavior.145 In contrast to moralist, viewing gambling as an accepted activity can have different origins. Some believe that government should not interfere with a person’s choice on whether to engage in an activity that does not victimize others. This, however, is not to view gambling as necessarily acceptable, but tolerable. Another view is that life contains elements of risk and gambling should be singled out for exclusion. To its opponents, gambling is different from the inevitable risks that people undertake daily, such as crossing the street or flying in a plane. Unlike recognized forms of risk management, such as insurance, the participant is not buying protection against uncertain and potentially catastrophic events.146 Instead, gambling is a consumer good.147 141 Patrick Devlin, The Enforcement of Morals, 13 (1965). 142 Jerome Skolnick, Coercion to Virtue: The Enforcement of Morals, 41 S. Cal. L. Rev. 588, 591 (1968). 143 Id. 144 See William R. Eadington, “The Political Economy of the Legal Casino Gaming Industry in the United States,” Paper 84-1, 18 (1984). 145 V. Abt, et al., Business of Risk 115 (1985). 146 See, e.g., R. King, Gambling and Organized Crime 17 (1969). 147 Peter H. Aranson & Roger LeRoy Miller, Economic Aspects of Public Gaming, 12 CONN. L. REV. 822, (1980). The late Reverend Gordon Moody, an English minister, researched gambling in society for more than four decades. In his last paper, he discussed why people gamble. He summarized it as the desire for “controlled risk.” Put simply, most people enjoy “controlled risk” in some form. Different people are willing to assume various degrees of risk. While a person may not be willing to jump off of a twelve-story building into an air bag, that same person might be willing to risk a roller coaster at the regional amusement park. Casinos market to people who are willing to undertake various levels of “controlled risk” from middle-income tourists with a $500 gambling budget to those who put millions at risk on a typical weekend. What is the common link between these persons? As Reverend Moody points out, gambling within a “controlled risk” environment is just another way in which people experience enjoyment. In effect, it is a form of adult play. Play is the antithesis of work because it creates no direct economic benefit. It may, however, be essential to healthy society and life in industrialized societies because people can use it to express themselves in ways not available in traditional settings, such as the workplace or home. It is a diversion from ordinary life and from societal and personal pressures. It may offer reward through excitement, gratification, and, with gaming, the possibilities of financial reward. Persons who regularly include play in their lives may be better adjusted and greater contributors to society. Gambling is an opportunity by workers to experience risk in a controlled setting. Seminal work on this theory by Edward Devereux also noted that “gambling can revitalize orientations to certain economic goals . . . which play a vital role in our capitalist economy.”148 This includes risk taking, conflict, and adventure. “The Business of Risk,” noted that much of mainstream America’s fear of gaming is the notion that hedonist activity is wrong or deviant behavior.149 When society’s primary struggle was to survive, the condemnation of leisure activities was a natural reaction. Although society has changed, this belief is still with us to some extent. Risk-taking also may be essential to developing character, particularly in the male, and conducive to material advancement.150 A study of South American casinos found that they allow males to escape from their work routines where they may be subordinate, and enter an atmosphere where they can be labeled as “machismo” in socially-acceptable ways. Similarly, the casinos of other continents provide a location for male bonding and bravado.151 148 James H. Frey, Gambling: A Sociological Review, 107, 110 N.7 Annals, AAPSS 474 (July 1984), citing Edward C. Devereux, Gambling and the Social Structure: A Sociological Study of Lotteries and Horseracing in Contemporary America (Ph.D. diss., Harvard University 1949). 149 Abt, et al., supra note 145. 150 Ronald Holloway, Gambling as a Source of Government Revenue, 2 (unpublished paper March 1974) (available at University of Nevada, Las Vegas). 151 William N. Thompson, Machismo: Manifestations of a Cultural Value in the Latin American Casino, 7 Journal of Gambling Studies 143-164 (Summer 1991): 143-164. Pragmatic Amoral Pluralism In contrast to the moralist,152 the pragmatic amoral pluralist assesses whether an activity should be legal based on are objective evaluation that considers many principles and effects.153 For example, Professor William Eadington suggests that governments considering legal gambling should first weigh the benefits, such as taxes, jobs, economic stimulation, and the fulfillment of consumer demands, against costs, such as economic displacement, effects on crime, and dysfunctional gambling. Governments should next consider reasonable cost-effective methods to minimize the costs. Then, according to Eadington, “If, at that point, aggregate benefits do not exceed aggregate costs, or the proposed gambling industry is not economically viable, then creation of a new gambling industry would not be wise.”154 Pluralists that oppose gambling concentrate on externalities. These are the negative consequences or costs of an industry. With most other industries, externalities are tangible by-products of an industry. Air pollution, for example, can be the externality of the steel industry. As early as 1920, economists recognized that externalities created economic considerations. From this perspective, externalities can be addressed through economic solutions. Some economists suggest the use of taxes and subsidiaries on the inflicting industry to deal with them. One approach is for a government to tax a firm for creating an externality at a rate equal to or greater than the damages caused. For example, a steel company might have to pay a tax for releasing pollutants at a rate equal to or greater than the state’s cost to clean the water. If the tax is higher than it would cost to abate the problem, the firm would abate the problem. Another approach is through regulation designed to reduce or eliminate the externality. In the air pollution example, maximum limits may be set on the amount of pollution that an industry can release into the atmosphere. Because games played between persons generally produce few tangible externalities. Instead, the externalities generally concern psychological or economic consequences. Social and economic externalities proffered for a ban on gambling include dysfunctional gambling, crime, adverse economic consequences, and corruption