[legal] poker: public policy, law, mathematics and the future of an american tradition (anthony...

8/14/2019 [Legal] Poker: Public Policy, Law, Mathematics and The Future of an American Tradition (Anthony Cabot, Robert H

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Poker: Public Policy, Law, Mathematics and The Future of an AmericanTradition

Anthony Cabot1

Robert Hannum2

Introduction

Gambling in its many different variants has seen a proliferation across the UnitedStates 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.3In theory, a pragmatic approach to policymaking in the context of gambling

1Anthony 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, aworldwide organization of prominent gaming attorneys devoted to the on-going education of andcommunications within the gaming industry. Mr. Cabot is the co-Editor-in-Chief of theGaming Law Review.He is the founding editor of The Internet Gambling Report Vlll(2005), covering the evolving conflict betweentechnology 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 Vegas1996), 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 contributingauthor of International Casino Law(Institute For the Study of Gambling and Commercial Gaming, Universityof Nevada, Reno, 1991, 3d ed January 1999). Mr. Cabot is listed inBest Lawyers in America.

2Robert 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, anddata mining. His publications include the books Practical Casino Mathand Introductory Statistics: A Self-Study Manual, as well as numerous articles in statistical, gaming, and law journals, including Annals ofProbability, 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

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" ofgambling, the head of a national anti-gambling organization implored a packed meeting room of casinoopponents to work "Women say it's electric morphine," said the Rev. Tom Grey, executive director of theWashington, 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,
http://www.du.edu/~rhannum/PCM.htmlhttp://www.du.edu/~rhannum/PCM.html


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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 opponents side or

natural rights4on the proponents side. When this debate occurs, distinctions between

different types of activities where persons can risk money on the outcome of anuncertain 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 thatVLTs are the 'crack cocaine' of gambling," says a landmark report culled from the 2002 CanadianCommunity 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 "videolottery 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. JamesDobson-via The West End Way, January 17, 1999. (Or that more than 30,000 video poker machines, whichare called the "crack cocaine of gambling", are scattered through South Carolina, and that the governor whoopposed 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-mailto Foxnews.com. "Cyber gambling is the crack cocaine of gambling and will create a new generation ofaddicts unless we stop it."

Scratch-off tickets:State lottery bad economic deal: speaker, 08/27/02, BILL HILES, (Finally, Wright said thepreferred form of lottery ticket sales, machines that vend "scratch-off" tickets, are particularly attractive toteen-agers and are a way of "hooking" them on gambling. ,"The scratch-off card sold in vending machineshas been called the crack cocaine of gambling," he said. "A lottery poses a great danger to our children." )

4Philosophical 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 Lockes notion that allpersons have natural rights, which included the right to pursue happiness. See generally, PeterMcWilliams, Aint Nobodys 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 persons property and to defend thecountry. If a person engages in an activity that is harmful to himself but not to others, governments role, ifany, is to educate the person. Locke viewed persuasion, not government intervention, as the means ofinfluencing others behavior. If smoking leads to cancer, government should warn the public of the risks, notban 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 onlyinterfere 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 himto do so because it will make him happier because, in the opinion of others, to do sowould be wise, or even right. There are good reasons for remonstrating with him, orreasoning with him, or persuading him, or entreating him, but not for compelling him, orvisiting him with any evil in case he does otherwise.

John Stuart Mill, On Liberty (Everymans Library (1992)).
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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 chance5 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.

5Prohibition of Funding of Unlawful Internet Gambling Act, Sect. 5361(1) (2005)


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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 Americas national game,8 the national vying

game of the United States,9and the most popular international card game in history.10Its

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 As-

Nas, a game whose origin and age are in dispute,12and 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

6Playing 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. Playingcards originating in Asia evolved from symbols and paraphernalia associated with ancient divinatorypractices. DAVID M.HAYANO,POKER FACES 8 (1982). In the same way that dice came into existence withreligious ritual, cards appeared alongside the divinatory use of the arrow around the twelfth century. GERDAREITH,THE AGE OF CHANCE 49 (1999). The cards of Asia and Europe were miniature pieces of artwork withthe social and cultural life of their country of origin embodied in the exquisite detail of their design. Theywere as individual and faithful a mirror of the taste and temperament and traditions of the people as otherbraches of their arts. CATHERINE HARGRAVE,HISTORY OF PLAYING CARDS 170 (1966). During the late thirteenthand early fourteenth centuries cards were introduced, along with paper money, and gunpowder, into Europethrough 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 andcourt figures kings, queens, and knaves. Originally the hand-crafting of cards made their cost prohibitive tothe majority of the population; it was not until the invention of the printing press in the fifteenth century thatcards 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 GAMES115 (1991).9

PARLETT, supranote 8, at 86.10

JOHN SCARNE,SCARNES GUIDE TO MODERN POKER, 13 (1980).11


Parlett describes the conclusions of Michael Dummett (THE GAME OF TARO, 1980), who conductedpainstaking 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 fiveeach 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 themas in non-draw poker, based on combinations of pairs, triplets, fulls, and quartets. Contrary to some whoclaim amazing antiquity regarding As-Nas, there is no evidence of the game being mentioned in Persianliterature at any date earlier than the oldest surviving cards, nor do we have any rules of the game earlierthan the nineteenth century. The kinship of As-Nas to other games can be more plausibly explained as aborrowing from European games than vice versa, especially when it is observed that As is not itself arelevant Farsi (Persian) word, but does happen to be the French for Ace. PARLETT, supranote 8, at 112-113.


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Poque13, Bouillotte14, Prima15and As-Nas,16Poque 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 pok-

ah.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 inthe 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.19Today 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

13Poque 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 wererestricted to one pair, two pair, triplets, and four of a kind,athttp://www.pagat.com/stops/poch.html #18-1914

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 Carr was three cards of the same rank that matched aturned up card. The Brelan was a hand of three cards of the same rank, different from the turned up card. Ifmore than one player has a Brelan, the hand with the highest rank would win. If no one has a Brelan Carror 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, Ninesworth 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,supranote 7.17

The word Poker can be traced back via French Poque to one or more fifteenth-century German gamesvariously recorded as Boeckels, Bocken, Bogel, Bockspiel, etc., which, when not denoting one of similar titleplayed with balls or stones was the original of the still-played game of Poch, or Pochen. Its basic meaning isbash or knock, and, by extension, knock, provoke, brag, vie, and suchlike. PARLETT, supra note 7, at 86.18

PARLETT, supranote 8, at 112-113.19

For information on the origins and history of poker see, e.g., ALVAREZ, supranote 2, at 32-44; EPSTEIN,supranote 6, at 201; SCARNE, supranote 9, at 23-25.20

See, e.g., GREG DINKIN AND JEFFREY GITOMER,THE POKER MBA, xi (2002); ALVAREZ, supranote 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, SUCKERS PROGRESS (1938), at 23-25.
http://hands/http://hands/


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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, iscalled 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, "Im 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 1829.23In 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

Pokers position as Americas national card game in the twentieth century may

not have been foreseeable towards the end of the nineteenth. Citing Fosters 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.26Quoting Blackbridges The

Complete Poker Playerof 1880:27

22

JOE COWELL, THIRTY YEARS PASSED AMONG THE PLAYERS IN ENGLAND AND AMERICA (New York, 1844).23

The game was similarly described by JONATHON GREEN in EXPOSURE OF THE ARTS AND MISERIES OFGAMBLING (1843). See alsoJAMES HILDRETH, DRAGOON CAMPAIGNS TO THE ROCKY MOUNTAINS;BEING A HISTORYOF 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 hundredslast night at poker..."), at 128-130. More generally,seePARLETT, supranote 8, at 111-115; DAVID SPANIER,TOTAL POKER 58 (2002); A.ALVAREZ, POKER:BETS,BLUFFS, AND BAD BEATS 36-38 (2001); HERBERT ASBURY,SUCKERS PROGRESS 23-25 (1938).24

It is noteworthy that the top hand in this old Poker is, unlike modern Poker, an unbeatable hand.25


The Honorable Robert Schenck, American ambassador to Great Britain is often credited with theintroduction of Poker into English society in 1872 and perhaps the first codification of poker in history.Parlett, supranote 8, at 114-115; JOHN MCDONALD, STRATEGY IN POKER,BUSINESS, AND WAR 37 (1950).27

Parlett, supranote 8, at 115.


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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, witha 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.28The

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 Bohns New Handbook of Games.29 The

draw was the most substantial innovation that turned poker from a gamble into a game

of skill.30Other 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.

28An early working description of the 52-card game appears in a supplement to the 1850 reprint of a

Philadelphian Hoyleunder the title Poker, or Bluff, and a Boston Hoyleof 1857. Parlett, supranote 8, at111. 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

Bohns New Handbook of Games38430

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 Pokerfrom a gamble to a science. Parlett, supranote 8, at 112.31

Parlett, supranote 8; David Parlett, A History of Poker, at www.pagat.com/vying/pokerhistory.html.


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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, its 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 Holdem. Thegame 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 Holdem, 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

32Wikipedialists 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_poker33

Wikipedialists 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

Wikipedialists 15 variants such as Texas Holdem, Pineapple, Tahoe, Double-board hold'em, Omahahold'em, Manila and Pinatubo. http://en.wikipedia.org/wiki/Community_card_poker


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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 limitgames 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-limitgames, bets or raises are limited only by the amount of money in the pot

at the time the wager is made. In no-limitgames, 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 (no-

limit 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 Holdem 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 theybecame 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).
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"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.38In 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.40Despite

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 skill-

based "contests," but because state legislatures want to eradicate these types of

36 See Darlington Theatres, 190 S.C. at 291, 2 S.E.2d at 786 (referringto 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.

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. See15 U.S.C. 77a et seq. (2000). Seealso Richard A. Brealey, Fundamentals of Corporate Finance 257 (1995) ("Commodity futures allow firms tofix 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 partiesunderstood 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 equityownership, 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 gamblingtransactions); Morris v. Norton, 75 F. 912 (6th Cir. 1896) (holding similarly and stating that such gamblingcontracts are void).
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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 opinionagainst them, most states adopted specific constitutional prohibitions against lotteries in

the nineteenth century.46Whether 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 Times-Star Co., 72 Ohio St. 112, 73 N.E. 1058,106 Am.St.Rep. 586.

50 See id.
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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 tosee 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.2d662, (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)).


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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 of control over events

or an uncertainty as to the occurrence of those events.55

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 frequentlyfound poker to be of sufficient skill as not to be a lottery game. 56When 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 Black's Law Dictionary 231 (6th ed. 1990) (definition of"chance").

56 See, e.g., Harris v. Missouri Gaming Comn, 869 S.W.2d 58 (Mo. Sup. Ct. 1994). See also, e.g., BellGardens 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 RecreationEnterprises, 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 Gardens opinion, the court was tasked with determining whether a game called jackpot poker wasvariation on poker that maintained the skill elements of poker or whether it was a prohibited lottery stylegame. The court concluded that the underlying poker game remained a skill game; however, the jackpotfeature was a prohibited lottery tacked on to the poker game. Nevertheless, the Bell Gardens court also heldthat jackpot poker is not a game of skill. Part of its reasoning was that the rules of jackpot poker aredifferent than regular poker. Specifically, unlike the pot distributed in each "regular" poker game, in jackpotpoker, 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 sametime). See Bell Gardens Bicycle Club, 36 Cal.App.4th at 747. In California, video poker was also found to bea 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. Atty


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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 onlotteries was applicable to video poker, in light of a lower court opinion that equated

video poker with licensed traditional poker.61The 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.64An 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 constitutions 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 Henshaws 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 agame 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. Atty Gen. 1969-9 (WA 1969).

66 See Harris v. Missouri Gaming Comn, 869 S.W.2d 58 (Mo. Sup. Ct. 1994). Cf. Thole v. Westfall, 682S.W.2d 33 (Mo. 1984)(holding that, in video poker, while skill plays a part, the outcome depends in amaterial degree upon chance). See Harris v. Missouri Gaming Comn, 869 S.W.2d 58 (Mo. Sup. Ct. 1994).

67 See State v. Cannon, 134 S.W. 513 (Mo. Sup. Ct. 1911).


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substantial skill and judgment.68A 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 FCCs enforcement statutes and regulations.70In 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 thenprovided an exception for bona fide contests . . . of skill or strength in which prizes are

awarded, this exception probably does not apply to poker.74The 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.76The 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-skillequation 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 anillegal 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 theIndoor 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 noanalysis 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, whenplayed electronically, was a game of chance. Ill. Op. Atty 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.2d234 (City Crim. Ct. 1941).


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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.82In an older Minnesota case, without any analysis of the skill issue, the

court held that the plaintiffs 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.84in 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, applyingMassachusetts law, held that chance predominated over skill in the playing of a video poker game. SeeUnited States v. Marder, 48 F.3d 564 (1st Cir. 1995). Previously, however, the Massachusetts Court ofAppeals 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 generals opinion thatcites the Indian Gaming Regulatory Act nearly in its entirety, which includes a list of games of chance thatcontains poker, though poker is never analyzed in the attorney generals opinion. See Op. Atty. Gen. Wis. 3-90 (1990).


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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. 94Likewise, 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.97Casino games involving skill include Blackjack, Video Poker, many of the newerpoker-based casino games such as Caribbean Stud Poker, Let It Ride Poker, and Three

Card Poker.98In games involving skill, decisions and strategies can affect the outcome

and in a gambling environment, a players 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 gamblingdevices. (In Double-Up, the player is essentially playing poker, where the game is programmed "with aminimum standard for a winning hand such as jacks or better.) The court found the fact that the cardsequences are electronically programmed in each machine to be significant. Thus, the court concluded thatthe small amount of skill used to play such game is overshadowed by pure chance. Id. at 449.

94 Ark. Op. Atty Gen No. 98-141, 1998 WL 549232 *1 (June 26, 1998). More recently, however, theSupreme Court of Arkansas held that video poker was a game of chance. See Sharp v. State, 88 S.W.3d848, 852 (Ark. Sup. Ct. 2002).

95 See Op. Atty. Gen. (May 23, 1997).

96See, for example, ROBERT C.HANNUM AND ANTHONY N.CABOT, PRACTICAL CASINO MATH, 2

nded. (2005).

97For 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, inWRITING IN RESTAURANTS, 93 (1986); Luck has an influence, but skill has a more pronounced effect. BASILNESTOR, THE SMARTER BET GUIDE TO POKER13 (2003). One author explains further: It should be pointed outhere that the analytical distinction between games of chance and games of skill is somewhat artificial. Asnoted earlier, all games, even those most amenable to the skillful prediction of the player, contain anelement of chance. The distinction outline above is therefore not an absolute separation, for even in gameslike 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


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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. Forabove 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

Theres 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 skillelement 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

105

DAVID SKLANSKY, THE THEORY OF POKER 2-4 (1999).106

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 versuschance in poker, 29-37.109

GARY CARSON, THE COMPLETE BOOK OF HOLDEM POKER, 4-5 (2001).


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and they would alter their strategy to exploit them. One cannot be a strong poker player

without modeling your opponents 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 Holdem, the most popular form of

poker played today, the authors of a leading artificial intelligence software package

considered the following aspects of poker:121

118

Aaron Davidson, Opponent Modeling in Poker: Learning and Acting in a Hostile and Uncertain

Environment (2002) (M.Sc. thesis, University of Alberta, available athttp://www.cs.ualberta.ca/~games/poker/).119

Jonathan Schaeffer, Darse Billings, Lourdes Pea, and Duane Szafron, Learning to Play Strong Poker,ICML-99,PROCEEDINGS OF THE SIXTEENTH INTERNATIONAL CONFERENCE ON MACHINE LEARNING (1999).120

Lourdes Pea, Probabilities and Simulations in Poker (1999) (M.Sc. thesis, University of Alberta,available athttp://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 Testbedfor Artificial Intelligence Research, PROCEEDINGS OF AI'98, (Canadian Society for Computational Studies inIntelligence) (1998).
http://www.cs.ualberta.ca/~jonathan/Grad/davidson.htmlhttp://www.cs.ualberta.ca/~jonathan/Grad/davidson.htmlhttp://www.cs.ualberta.ca/~darse/Papers/ML99.htmlhttp://www-ai.ijs.si/SasoDzeroski/ICML99/icml99.htmhttp://www.cs.ualberta.ca/~jonathan/Grad/pena/thesis.htmlhttp://www.cs.ualberta.ca/~jonathan/Papers/Papers/ai98.poker.htmlhttp://www.cs.ualberta.ca/~jonathan/Papers/Papers/ai98.poker.htmlhttp://www.cs.ualberta.ca/~jonathan/Papers/Papers/ai98.poker.htmlhttp://www.cs.ualberta.ca/~jonathan/Papers/Papers/ai98.poker.htmlhttp://www.cs.ualberta.ca/~jonathan/Grad/pena/thesis.htmlhttp://www-ai.ijs.si/SasoDzeroski/ICML99/icml99.htmhttp://www.cs.ualberta.ca/~darse/Papers/ML99.htmlhttp://www.cs.ualberta.ca/~jonathan/Grad/davidson.htmlhttp://www.cs.ualberta.ca/~jonathan/Grad/davidson.html


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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 Minimum skill level assessing your hand strength as a function

of your cards and the community cards.

o 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.

o 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 beimproved even further by varying hidden hand probabilities for

each player depending on that players model of play.

Hand potential the probability of the hand improving (or being

overtaken) as additional community cards appear.

o Minimum skill level - assessing your hand strength as a function of

your cards and the community cards.

o 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 modelof play.

Betting strategy whether to fold, call/check, or bet/raise.

o Minimum skill level - assessing your hand strength.

o 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 falseimpression about your play that can improve the chances of winning

subsequent hands.

o Minimum skill level - merely bluffing a certain percentage of all

hands.

o Maximum skill level - predicting the probability that your opponent

will call.


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Opponent modeling allows you to determine a likely probability

distribution for your opponent's hidden cards or betting strategy.

o Minimum skill level - uses a single model for all opponents in a

given hand.

o Maximum skill level - modifies the probabilities based on aclassification 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 Probability Approximately

122See, e.g., EPSTEIN, supranote 6, at 201-212; SKLANSKY, supranote 105.

123MCDONALD, supra note 25; DINKIN AND GITOMER, supranote 19, at 49: In poker and business, you must

know the odds and probability first. You dont always have to go by the odds, but you must at least knowthem. Noted expert Lyle Berman makes the related observation: Poker hones your ability to understandprobability and measure risk because the outcomes are so immediate. Quoted in DINKIN AND GITOMER,supranote 19, at 49.124

One of the most common mistakes a novice or unskilled player makes in many types of poker,particularly Holdem, is to play too many hands. Such a person will end up winning more pots, but will lose agreat deal more money in the process. Seenote 110.


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1. Royal flush 0.000002 1 in 649,740

2. Straight flush* 0.000014 1 in 72,193

3. Four of a kind 0.000240 1 in 4,165

4. Full house 0.001441 1 in 694

5. Flush 0.001965 1 in 509

6. Straight 0.003925 1 in 255

7. Three of a kind 0.021129 1 in 47

8. Two pairs 0.047539 1 in 21

9. One pair 0.422569 1 in 2.4

10. High card 0.501177 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 todays most common type of poker,

Texas Holdem. In Holdem (as it is often referred to), each player is dealt two cards face

down and, after an initial round of betting,125three 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

125In the typical Holdem game, two blind bets are posted before the cards are dealt a small blind by the

player to the dealers immediate left and a large blind by the next player to the left of the small blind. A blindis a forced bet made before the player sees his cards used to start the pot and stimulate action. The smallblind is usually equal to one-half the amount of the big blind. Since the deal rotates around the table (even ina casino where the dealer is not a player, a button used to signify the nominal dealer rotates after eachhand), all players participate equally in the posting of any forced blind bets. We will refrain from discussingfurther 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 ahouse dealer, the first active player to the left of the buttonused to indicate dealer position). Because thefirst two players to the left of the dealer (or button) have already acted by putting in blind bets, the player oneto the left of the big blind is the first with any choices (to call, raise, or fold in the first round of betting) on thepre-flop betting round.


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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).127Consider

the following three questions:

What is the probability he will make the flush on the turn?

If he doesnt 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 remainingcards, 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 dont 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 exampleabove, the former probability is .191; the latter is .196.128

The following table shows probabilities and odds of making hands in Texas

Holdem with a given number of outs (cards that will make the desired hand).

Odds and Probabilities in Texas Holdem

1 CardMaking on Turn

1 CardMaking on River

2 CardsMaking on Turn or River

Number ofOuts Probability

OddsAgainst Probability

OddsAgainst Probability

OddsAgainst

21 44.7% 1.24 45.7% 1.19 69.9% 0.43

20 42.6% 1.35 43.5% 1.30 67.5% 0.48

127For 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. Somelist the probability (or odds) with one card to come, assuming forty-seven cards remain (making the hand onthe turn); others with forty-six cards remaining (making the hand on the river, given it was not made on theturn).


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19 40.4% 1.47 41.3% 1.42 65.0% 0.54

18 38.3% 1.61 39.1% 1.56 62.4% 0.60

17 36.2% 1.76 37.0% 1.71 59.8% 0.67

16 34.0% 1.94 34.8% 1.88 57.0% 0.75

15 31.9% 2.13 32.6% 2.07 54.1% 0.85

14 29.8% 2.36 30.4% 2.29 51.2% 0.9513 27.7% 2.62 28.3% 2.54 48.1% 1.08

12 25.5% 2.92 26.1% 2.83 45.0% 1.22

11 23.4% 3.27 23.9% 3.18 41.7% 1.40

10 21.3% 3.70 21.7% 3.60 38.4% 1.60

9 19.1% 4.22 19.6% 4.11 35.0% 1.86

8 17.0% 4.88 17.4% 4.75 31.5% 2.18

7 14.9% 5.71 15.2% 5.57 27.8% 2.59

6 12.8% 6.83 13.0% 6.67 24.1% 3.14

5 10.6% 8.40 10.9% 8.20 20.4% 3.91

4 8.5% 10.75 8.7% 10.50 16.5% 5.07

3 6.4% 14.67 6.5% 14.33 12.5% 7.01

2 4.3% 22.50 4.3% 22.00 8.4% 10.88

1 2.1% 46.00 2.2% 45.00 4.3% 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 bymultiplying the possible payoffs by their probabilities and then summing the resulting

terms. Mathematically:

, = )( ii PPayNetEV

where Pi is the probability of the ith possible net payoff, . 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 onceevery 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:

iPayNet

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


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now favorable; the expected value is positive $0.25, meaning you will win 25 cents on

average every time you make this

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