# United States v. Dicristina

> District Court, E.D. New York · August 21, 2012 · 886 F. Supp. 2d 164

URL: https://www.frixlaw.com/law-library/cases/8701527

## Case

- **Full name:** United States v. Lawrence DICRISTINA
- **Court:** District Court, E.D. New York
- **Decided:** August 21, 2012
- **Citations:** 886 F. Supp. 2d 164; 2012 WL 3573895
- **Precedential status:** Published
- **Opinion:** Opinion of the court by Weinstein
- **Judges:** Weinstein
- **Cited by:** 3 later opinions in the Frix Law Library

## Citator (automated)

- No negative treatment found by the automated citator. That is not the same as a confirmation that the case is good law; read the citing cases.
- Full citator and citing cases: https://www.frixlaw.com/law-library/cases/8701527

## How later opinions describe it (automated extraction)

- noting that Di-Cristina had waived the argument that poker was not gambling under New York law and explaining that it has no merit

## Opinion text

MEMORANDUM, ORDER, & JUDGMENT
JACK B. WEINSTEIN, Senior District Judge.
Table of Contents
I. Introduction..............................................................168
II. Facts........................ 170
A. Procedural History....................................................170
B. Evidence on Poker....................................................171
1. Poker in the United States .........................................171
2. Game Play Generally..............................................172
3. Expert Testimony.................................................173
a. Defense Expert...............................................173
b. Government Expert............................................185
c. Defense Expert’s Supplemental Report...........................189
*167 4. Other Evidence...................................................198
5. Conclusions of Other Courts and the States...........................194
6. Compared to Video or “Joker” Poker................................197
C. Evidence at Trial.....................................................198
III. Federal Rule of Criminal Procedure.........................................198
IV. Rules of Statutory Construction ............................................199
A. Generally............................................................199
B. Rule of Lenity........................................................199
V.Federal Gambling Laws ...................................................200
A. Illegal Gambling Business Act..........................................200
1. Statutory Language...............................................200
2. Dictionary Definitions..............................................202
3. Common Law.....................................................202
4. Legislative History................................................203
a. Purpose of the Statute.........................................203
b. Definition of Gambling Generally................................205
c. Discussion of Particular Games..................................207
5. Commission on the Review of the National Policy Towards Gambling.....210
6. Subsequent Mafia Involvement in Poker Games.......................211
B. Other Gambling Statutes...............................................212
1. Contemporary with the IGBA.......................................212
2. Pre-IGBA........................................................213
a. Transporting Gambling Materials................................213
b. Gambling Ships ...............................................215
c. Wire Act.....................................................215
d. Travel Act....................................................215
3. Post-IGBA.......................................................216
a. Indian Gambling Regulatory Act ................................216
b. National Gambling Impact Study Commission Act.................217
c. Unlawful Internet Gambling Enforcement Act of 2006 ..............219
VI.Proof Needed That Business Engaged in “Gambling” Under the IGBA..........219
A. Limited Case Law Interpreting 18 U.S.C. § 1955 (b)(2).....................219
B. Statutory Text and Legislative History are Ambiguous ....................221
1. Text.............................................................221
2. Legislative History................................................223
3. Other Federal Statutes.............................................224
C. Rule of Lenity Weighs in Favor of the Defendant.........................224
VIL Poker is Not Gambling Under IGBA........................................224
A. No Controlling Federal Cases..........................................225
B. Only “Games of Chance” Are Gambling Under IGBA......................226
1. Statute is Ambiguous..............................................227
a. Text.........................................................227
b. Dictionary and Common Law Definitions.........................227
e. Legislative History............................................227
d. Other Federal Statutes.........................................228
2. Gambling Not Limited to House-Banked Games ......................229
3. Gambling is Limited to Games Predominated By Chance...............229
C. Poker is Predominated By Skill Rather than Chance ......................231
D. Poker is Not Gambling Under IGBA....................................234
VIII. Conclusion 235
*168
Table of Figures
Fig. 1: Winning through time (April 2010 through March 2011) for the top and bottom ten players in terms of total dollar amounts won or lost at $5/$10 stakes.................................................................177
Fig. 2: Win rate comparison: Queen Jack suited (e.g.QA JA)........................180
Fig. 3: Win rate comparison: King Nine offsuit (e.g.KA 9A ).........................181
Fig. 4: Average win rate for players of different predicted skill, for $5/$10 stakes players in the prediction group ...........................................183
Fig. 5: Percentage of the time a higher skilled player (top 50% of skill) would predominate over a lower skilled player (bottom 50% of skill) after a given number of hands at $0.50/$1.00 stakes.....................................184
Fig. 6: Percentage of the time a higher skilled player (top 50% of skill) would predominate over a lower skilled player (bottom 50% of skill) after a given number of hands at $l/$2 stakes..........................................187
Fig. 7: Simulated Cumulative Winnings of Top 10 Winners and Losers (1,000 players, 100,000 trials each)..............................................188
Fig. 8: Average win rates for players of different predicted skill, for $5/$10 stakes, adding rake back in player results.........................................190
Fig. 9: Contribution of skill to poker...............................................193
I. Introduction
Defendant Lawrence Dicristina is charged with operating an illegal gambling business involving poker games in violation of the Illegal Gambling Business Act (IGBA), 18 U.S.C. § 1955 , and conspiring to do so. See Second Superseding Indictment, Doc. Entry 25, Dec. 9, 2011. The type of poker alleged and proved, to have been played in defendant’s establishment was “Texas Hold’em,” a game described in Part 11(B)(1), infra. When reference is made to “poker” in this memorandum, this is the variant of pokerreferred to.
Mr. Dicristina moved to dismiss the indictment on the grounds that a poker room does not fall under the definition of an illegal gambling business proscribed by the federal statute because poker is predominately a game of skill rather than chance. Def.’s Mot. to Dismiss the Indictment, Doc. Entry 69, June 29, 2012. He also contended that whether poker is a game of chance or skill is a mixed question of law and fact to be determined by the jury. Id.
Following pretrial oral argument and expert testimony, the court ruled that whether poker constituted gambling under the applicable federal criminal statute would be decided as a matter of law. See Tr. of Daubert Hr’g 89:1-5, July 6, 2012 (“Def. Expert Daubert Hr’g Tr.”). Decision on the motion to dismiss was reserved. The case proceeded to trial, the jury being instructed that poker constituted gambling under the IGBA. Defendant was convicted on both counts. He then renewed his motion for a judgment of acquittal. See Def.’s Mem. of L. in Supp. of his Mot. for a Judgment of Acquittal Under Rule 29 of the Federal Rules of Criminal Procedure, Doc. Entry 92, July 19, 2012.
Although the defendant initially raised the issue of whether poker as played in this case is gambling under New York law, see Def. Expert Daubert Hr’g Tr. 85:5-86:1 — the violation of which is an element of the federal offense, see 18 U.S.C. § 1955 (b)(l)(i) — he has not renewed this *169 aspect of his motion. See Def.’s Mot. to Dismiss the Indictment, Doc. Entry 69, June 29, 2012. The argument is waived. In any event, it has no merit. New York courts have long considered that poker contains a sufficient element of chance to constitute gambling under that state’s laws. See N.Y. Penal Law § 225.00 (2) (“ ‘Gambling.’ A person engages in gambling when he stakes or risks something of value upon the outcome of a contest of chance or a future contingent event not under his control or influence, upon an agreement or understanding that he will receive something of value in the event of a certain outcome.”); N.Y. Penal Law § 225.00 (1) (“ ‘Contest of chance’ means any contest, game, gaming scheme or gaming device in which the outcome depends in a material degree upon an element of chance, notwithstanding that skill of the contestants may also be a factor therein.”); In re Plato’s Cave Corp. v. State Liquor Auth., 115 A.D.2d 426 , 496 N.Y.S.2d 436, 438 (1st Dep’t 1985), aff'd 68 N.Y.2d 791 , 506 N.Y.S.2d 856 , 498 N.E.2d 420 (1986) (holding that a Joker Poker video game fell under § 225.00’s definition of gambling in partial reliance on its similarity to poker; “[ajlthough there is a degree of skill and concentration involved in playing poker, ‘the outcome depends in a material degree upon an element of chance,’ i.e., the draw of the cards”); see also Dalton v. Pataki 11 A.D.3d 62 , 780 N.Y.S.2d 47 , 64 n. 5 (3d Dep’t 2004) (noting that “the term ‘game of chance’ or ‘contest of chance’ ... has been interpreted to include such games as ‘stud’ poker”), aff'd 68 N.Y.2d 791 , 506 N.Y.S.2d 856 , 498 N.E.2d 420 (1986); People v. Turner, 165 Misc.2d 222 , 629 N.Y.S.2d 661, 662 (N.Y.Crim.Ct.1995) (“Games of chance range from those that require no skill, such as a lottery ..., to those such as poker or blackjack which require considerable skill in calculating the probability of drawing particular cards. Nonetheless, the latter are as much games of chance as the former, since the outcome depends to a material degree upon the random distribution of cards.... The skill of the player may increase the odds in the player’s favor, but cannot determine the outcome regardless of the degree of skill employed.”); People v. Dubinsky, 31 N.Y.S.2d 234 , 237 (Bronx Cnty. Ct.Spec.Sess.1941) (“There is no doubt that playing ‘Zstud’ poker for money is a game of chance and constitutes gambling.”); id. at 238 (“[T]he courts of many states including our own seem to be unanimous in their holding that where a host receives some consideration or some payment for permitting a card game to be played or other gaming to take place in his premises, that constitutes gambling.”); cf. Katz’s Delicatessen, Inc. v. O’Connell, 302 N.Y. 286 , 97 N.E.2d 906, 907 (1951) (holding that “a social game of poker played in a basement room” of a liquor store violated a law which provided that “[n]o person licensed to sell alcoholic beverages shall suffer or permit any gambling on the licensed premises, or suffer or permit such premises to become disorderly”). This series of New York State decisions do not decide the issue now posed: whether a business involving illegal poker games violates the federal IGBA.
The defendant’s argument in favor of dismissal is two-fold. First, he claims that even if poker is “gambling” under New York law, not all violations of state gambling laws constitute “gambling” prosecutable under the IGBA. The federal statute defines gambling as “including] but ... not limited to pool-selling, bookmaking, maintaining slot machines, roulette wheels or dice tables, and conducting lotteries, policy, bolita or numbers games, or selling chances therein.” 18 U.S.C. § 1955 (b)(2). He submits that this definition limits which state gaming laws trigger prosecution under the IGBA: a business must involve games sufficiently similar to the nine *170 games enumerated in the federal definition in order to be prosecuted as a “gambling business” under the IGBA. Second, he contends that the poker room he operated does not constitute a “gambling business” under this narrow definition — that is to say, that a game run by a “gambling business” must be both house-banked and predominated by chance in order to be sufficiently similar to those enumerated, and that his poker enterprise was neither.
The government counters that § 1955(b)(2) does not, by its plain language, restrict what kinds of games constitute gambling under the IGBA. Urged is that the goal of the federal statute was to curb the influence of organized crime, which derived substantial revenues from illegal gambling, and that the federal law was passed to bolster states’ efforts on this front. It follows, so the argument goes, that any gambling activity that is illegal under state law is “gambling” under the IGBA. Gov’t Response in Opp. to Def.’s Mot. to Dismiss the Indictment and Mot. to Preclude Expert Testimony, Doc. Entry 76, July 5, 2012.
Both the defendant’s and the government’s interpretations of the statute are plausible. It is unclear from the text and legislative history of the IGBA whether every state gambling offense would permit a federal conviction. See Part VI, infra. It is equally uncertain whether, in enacting the statute, Congress foresaw that poker businesses would be prosecutable under it. See Part VII, infra.
In light of these ambiguities, the rule of lenity requires that the defendant’s interpretation be adopted, and his conviction be dismissed. His acts did not constitute a federal crime.
Declaring that the federal gambling statute does not cover poker games of the type operated by the defendant does not prevent federal law enforcement agencies from achieving the goals of the statute, as put forward by the government, or encroach on any states’ ability to proscribe these card games. In poker games controlled by the Mob, a violation of state gambling laws would permit federal prosecution under the Racketeer Influenced and Corrupt Organizations Act (RICO). See 18 U.S.C. §§ 1961-1968 . Even if the gambling business is not Mob — controlled—as it was not in this case — New York State gambling laws would permit prosecution in state court. See, e.g. N.Y. Penal Law § 225.05 .
For the reasons stated below, the defendant’s conviction is vacated, and the indictment dismissed.
II. Facts
A. Procedural History
On December 9, 2011, defendant Lawrence Dicristina was charged in a second superseding indictment with operating an illegal gambling business involving poker games in violation of the IGBA (Count Two) and conspiring to do so (Count One). See Second Superseding Indictment, Doc. Entry 25, Dec. 9, 2011. He initially pled guilty to Count Two, the substantive IGBA offense. See Tr. of Guilty Plea, Doc. Entry 40, Dec. 12, 2011. At his sentencing hearing, he moved to withdraw his plea. Doc. Entry 50, May 1, 2012. The plea was withdrawn, and a trial date was set. Id.
A week before trial, the defendant moved under Federal Rule of Criminal Procedure 29(b) to dismiss the indictment, contending that poker did not constitute gambling as defined by the IGBA. See Def.’s Mot. to Dismiss the Indictment, Doc. Entry 69, June 29, 2012. An amicus brief in support of his argument was filed by the Poker Players Alliance (PPA). See PPA Mot. to File an Amicus Br. in Supp. of Def.’s Mot. to Dismiss, Doc. Entry 74, July 1, 2012. The defendant also sought to introduce expert testimony at trial to show *171 that poker was a game of skill rather than chance and thus outside the purview of the statute. See Doc. Entry 73, July 3, 2012.
Following a Daubert hearing, defendant’s witness was permitted to present his opinion as an expert, but his testimony was excluded from the trial as irrelevant. See Def. Expert Daubert Hr’g Tr. 84:1-2. It was ruled that whether poker constituted gambling was a matter of law that would be decided by the court, rather than by the jury. Id. 89:1-5 .
Decision on defendant’s motion to dismiss was reserved. Id. He renewed his motion at the close of the government’s case, Tr. of Trial 264:2-3, July 10, 2012, and at the close of evidence, id. 325:18-23 , with decision again reserved.
After it was instructed that running a poker establishment was illegal, the jury convicted the defendant of both Counts One and Two. See Doc. Entry 91, July 12, 2012. Additional briefing on the motion to dismiss was submitted following the verdict.
The government submitted evidence at a post-trial Daubert hearing held on August 10, 2012. See generally Tr. of Daubert Hr’g, Aug. 13, 2012 (“Gov’t Expert Daubert Hr’g Tr.”). Experts for the government and the defendant testified independently and in a joint discussion with the court, submitting reports supplemented by extensive briefs and letters. See id.; Def. Letter Attaching Expert Report App. (Report of Dr. Randall Heeb), Doc. Entry 77, July 6, 2012 (“Def. Expert Report”); Report of Dr. David DeRosa, Doc. Entry 103, Aug. 10, 2012 (“Gov’t Expert Report”); Def.’s Letter Addressing Issues Raised at Aug. 10 Daubert Hearing App. (Supplemental Report of Dr. Randal D. Heeb), Doc. Entry 104, Aug. 13, 2012 (“Def. Expert Supp. Report”); Gov’t Reply to Def.’s Letter Addressing Issues Raised at Aug. 10 Daubert Hearing, Doc. Entry 107, Aug. 17, 2012 (“Gov’t Reply Letter”); Def.’s Letter Reply to Gov’t Aug. 17, 2012 Letter, Doc. Entry 108, Aug. 20, 2012.
B. Evidence on Poker
Central to the issue of whether poker falls within the ambit of the statute is: 1) whether Congress, at the time of its enactment of the IGBA, understood “gambling” to include poker; and 2) whether poker is, like the other games enumerated in that statute, a game predominated by chance.
1. Poker in the United States
Poker has a long history in the United States. See, e.g., “The National Game,” N.Y. Times, Feb. 12, 1875 (describing the spread of literature on poker). The game first appeared in roughly its modern form in the early nineteenth century in New Orleans. James McManus, Cowboys Full: The Story of Poker 51 (2009). It has been embraced by many of our political leaders and other public figures. For example, “Justice Douglas was a regular at President Franklin Roosevelt’s poker parties; Chief Justice Vinson played poker with President Truman.” Cheney v. U.S. Dist. Court for Dist. of Columbia, 541 U.S. 913, 917 , 124 S.Ct. 1391 , 158 L.Ed.2d 225 (2004) (citing J. Simon, Independent Journey: The Life of William O. Douglas 220-221 (1980); D. McCullough, Truman 511 (1992)). Driven in part by the Internet, which allows for online poker playing, and cable television, which frequently broadcasts poker tournaments, the game has surged in popularity in recent years. Anthony Holden, Bigger Deal: A Year Inside the Poker Boom 1, 10 (2007). In 2006, 8,773 players entered the “main event” in the World Series of Poker, the most prestigious poker tournament in the United States, and more than 44,500 players participated in the tournament at large. Id. at 1.
*172 2. Game Play Generally
While there are several major variants of poker, the defendant’s business involved “No-Limit Texas Hold’em,” a game of increasing popularity. See Def. Expert Dauberb Hr’g Tr. 14:24-15:4; Part 11(C), infra. No-Limit Texas Hold’em is currently the most popular variant of poker. See Def. Expert Daubert Hr’g Tr. 14:12-22.
Texas Hold’em poker has been described as follows:
The game is usually played with at most 10 (and at least 2) players. Like most variants of poker, the objective in hold’em is to win pots, where a pot is the sum of the money bet by all players in a hand. A pot is won either at the showdown by forming the best five card poker hand out of the seven cards available, or by betting to cause other players to fold and abandon their claim to the pot. The objective of a player is not to win the maximum number of individual pots, but rather to make mathematically correct decisions in order to maximize the expected net amount won in the long run.
Hold’em is often played using small and big blind bets. A dealer button is used to represent the player in the dealer position; the dealer button rotates clockwise after each hand, changing the position of the dealer and blinds. The small blind is posted by the player to the left of the dealer and is usually equal to half of the big blind. The big blind, posted by the player to the left of the small blind, is equal to the minimum bet.
A play of a hand begins with each player being dealt two cards face down from a standard deck of 52 cards. These cards are the player’s hole or pocket cards, they are the only cards each player will receive individually, and they will only (possibly) be revealed at the showdown, making hold’em a closed poker game. After the pocket cards are dealt, there is a “pre-flop” betting round, beginning with the player to the left of the big blind (or the player to the left of the dealer, if no blinds are used) and continuing clockwise. A round of betting continues until every player has either folded, put in all of their chips, or matched the amount put in by each other active player.
After the pre-flop betting round, assuming there remain at least two players taking part in the hand, the dealer deals a flop; three face-up community cards. The flop is followed by a second betting round. This and all subsequent betting rounds begin with the player to the dealer’s left and continue clockwise.
After the flop betting round ends a single community card (called the turn) is dealt, followed by a third betting round. A final single community card (called the river) is then dealt, followed by a fourth betting round and the showdown, if necessary.
If a player bets and all other players fold, then the remaining player is awarded the pot and is not required to show his hole cards. If two or more players remain after the final betting round, a showdown occurs. On the showdown, each player plays the best five-card hand he can make from the seven cards comprising his two pocket cards and the five community cards. A player may use both of his own two pocket cards, only one, or none at all, to form his final five-card hand. If the five community cards form the player’s best hand, then the player is said to be playing the board and can only hope to split the pot, since each other active player can also use the same five cards to construct the same hand.
*173 If the best hand is shared by more than one player, then the pot is split equally among them. The best hand is determined according to the ranking described below. If the significant part of the hand involves fewer than five cards, (such as two pair or three of a kind), then the additional cards (called kickers) are used to settle ties. Note that only the card’s numerical rank matters; suit values are irrelevant in Hold’em.
PPA Mot. for Leave to File an Amicus Br. Ex. B (Noga Alon, Poker, Chance and Skill 2-3 (unpublished manuscript)), Doc. Entry 74, July 3, 2012.
The government does not dispute that skill plays some role in poker, particularly in “no-limit” poker games. As one writer has described the matter:
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.... 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)....
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 a player’s chips from hand to hand are all skills....
Anthony Cabot & Robert Hannum, Poker: Public Policy, Law, Mathematics, and the Future of an American Tradition, 22 T.M. Cooley L. Rev. 443 , 450-54 (2005).
A skilled player should be able to assess the strength of his hand as a function of his hole cards, the community cards, the number of players still in the game, their betting strategy and the position at the table. He should be able to assess the model of play of the other players, estimate the probability of improving his hand once the next community cards are revealed, and should be able to hide his strategy by bluffing and leaving his behavior unpredictable.
PPA Mot. for Leave to File an Amicus Br. Ex. B (Noga Alon, Poker, Chance and Skill 16 (unpublished manuscript)), Doc. Entry 74, July 3, 2012.
Unlike other games commonly considered gambling, such as roulette, craps, or blackjack, the house does not participate in game play during poker games. Cabot & Hannum, supra, at 452.
Instead, players compete against each other, and money won or lost is merely transferred from one player to another. The casino provides a dealer, who does not play, and the casino makes 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 the most common; a “rake” (percentage extracted) of 5% to 10% is typical.
Cabot & Hannum, supra, at 452-53.
3. Expert Testimony
a. Defense Expert
At a July 6, 2012 pretrial hearing, Dr. Randal D. Heeb, a respected economist, statistician, and player in national poker tournaments, testified as an expert on game theory. See Def. Expert Daubert Hr’g Tr. 12:7-8. He highlighted the number of skilled strategic choices, such as how much to wager, made by poker players in the course of playing a single hand:
[Tjhere’s a very large number of decisions that need to be made by a poker player playing any given hand.... The simplest and most obvious choice that a player has to make is simply whether to play a particular hand____ [For example, a hand with a King and a Nine in *174 different suits] is a hand which is particularly easy for unskillful players to play badly, and for skillful players to play well. And the very first decision that a player has to make is simply whether or not to play and how much to bet, and less skillful players seeing a King and a Nine, which seem like relatively high cards, and when the King comes, they will have a pair of Kings, which seems like a relatively strong hand, and yet unskillful players tempted to play that hand are very likely to bet too much and to lose to players with even better hands. Because even though it seems like a good hand, when you happen to get another King, you make a strong hand, it seems like you are likely to win. In fact, you may win relatively many hands. You are not going to win very much money with that hand, and when you lose, you are likely to lose a lot of money. So unskillful players tend to play that hand poorly, and make bad decisions, not only the decisions you play, but also how much to bet, .how to respond to other players, when other players raise them, for example.
So a more skillful player would recognize that the only way to win with that hand would be, for example to get a pair [of] Kings, and if nobody else has anything that is a very good hand, you are likely to win almost nothing with that pair of Kings. On the other hand, if another player, instead of starting with a King Nine, had a King Ace, and now when all of the common cards are dealt subsequently in the game, a King appears, both players would have a pair of Kings, but the player with the Ace King would have a much stronger hand and therefore win much more often and much more. The less skillful player would have a tendency to bet too much with the King Nine early, and would also tend to call too often later.
Tr. of Hr’g 26:22-28:12, July 6, 2012.
Bluffing, raising, and folding require honed skills to maximize the value of the cards dealt by Lady Luck:
[Wagering is] also used to try, for example, to force an opponent to fold their hand, and there are two relevant aspects of that strategic play. One would be a bluff. If I think you have the best hand and I want to bet an amount that is going to induce you to give up your hand, you know, that’s one element of the wager. And what’s important about that wager is not that I am betting on the outcome of some outside event, but rather the amount that I choose to bet is carefully strategically chosen in order to influence your behavior, and I choose an amount based on what I think [you] will do, given the amount that I bet, and it can go two different ways. Sort of the novice way to think about this is the more that I bet, the more likely you are to fold, because it’s harder for you to put up more money to call my bet. With more expert players, they would anticipate that effect. And, so, there’s a bluff that has a name among poker players called a “post oak bluff’ where you bet a small amount to make your opponent think you are trying to make them call. So they think about that with their model of how you play, and they decide to fold because of the small amount that I bet. And so the amount that you bet becomes incredibly important.
There’s a second way that the amount that you bet, whether or not to bet becomes important. Even if I’m pretty sure I got the best hand, I may want you to fold because, for example, if you have a flush draw and I have the best current hand, I may not want you to get your chance to make your flush. So I *175 will bet an amount designed to make it uneconomic for you to make the call, and if you are a good player, you will recognize that and you will fold. If you are a bad player, you will make an unskillful play that actually wins me money over time. So by making that correct amount of the bet, I’ve influenced the outcome, both immediately in the single hand and over the long haul, the amount that I win over time playing against either skillful or unskillful players. So ... whether or not to bet, whether or not to raise, which is going to bet zero, let the other person bet and raise after the fact, these are all strategic elements which are the essence of poker, and in that sense there’s nothing analogous to that in a game of chance like betting on a football game or betting on the roll of the dice.
Id. 50:8-51:24.
Position at the table and the habits of fellow players must be taken into account to play successfully.
[AJnother very simple thing to notice that unskillful players don’t tend to notice ... is that the position at the table matters. So the person [who] has to act first is at a disadvantage, because they don’t know what the other players are going to do. So the person that acts last, and because you act in turn around the table in a clockwise fashion, the person that acts last has a big advantage. They got to see what other players did before they made their choices. So a skillful player recognizes that advantage and ... changes their strategy, plays more hands, and plays them more aggressively in later positions, but at the same time folds their hands and plays more conservatively, if other players have acted with strength in front of them.
So if a player has a bet in an early position, that is a relatively strong play. And so a player that gets to play later, would take that into account if they are a skillful player, and would only play a very strong hand.
Yet another way that a skillful player can use relatively simple information is to recognize how skillful their opponents are and change their strategy based on who they are playing against. So if a skillful player bets in an ... early position — and I know that that is a skillful player because I have observed how they played the rest of their hands — I know that they know that that early position is a dangerous position for them to be in. So if a skillful player bets in that position, I ... think they ... have a stronger hand, I react accordingly. Unskillful players don’t even notice this. So, again, that’s a relatively easy play that can be learned in one day of training and a couple of days of practice, which would dramatically improve a player’s results.
Id. 37:3-38:9; see also id. 49:7-16 (“In poker, you don’t know the cards that [the other players] have, but they know what cards they have. They don’t know the cards that you have. So you have a model of your opponent and how they react to the situation that they see. They have a model of you in their mind, and how well the players play, make their decisions to use this information, which is generated by the chance mechanism, the way in which they then use the information that they do have to make their strategic choices is what makes poker such an ... interesting game.”). When poker is played live, as it was in the instant case, rather than on a computer, additional skills come into play, such as “the ability to read their opponent, to detect from their opponent’s betting behavior, from their tone of voice, from their reactions, whether or not they have a good hand.” Id. 42:1-4.
Dr. Heeb opined that poker differs from other forms of gambling, such as sports *176 betting, because the player .can rely on sophisticated skills to change the outcome of the game. • Id. 49:17-20.
[T]he player in a poker game is making all of the decisions, making all the plays, which include whether or not to wager on a particular hand and how much. And, in fact, the act of wagering itself is the essence of the decision. So in one sense in a gamble over any other mechanism, whether it was a bet on a baseball game or a bet on the roll of the dice, the wager itself is completely independent of the event being wagered on. Whereas, in poker, the wager is not in the same sense a wager on the outcome. It is the strategic choice that you are- making. You are trying to influence the outcome of the game, either by the amount that you are wagering, trying to build up and win more money.
Id. 49:21-50:8.
According to Dr. Heeb, “many people make a living playing poker and win consistently over time” whereas “it is impossible to make a living and to win consistently playing casino games such as roulette” where chance predominates. Def. Expert Report at 11. This fact alone was an independent foundation for his opinion that skill predominates over chance in poker. Id.
As shown in Figure 1 below, prepared by Dr. Heeb, the ten most proficient players earn dramatically more money than the ten least proficient players over the course of a year. The most skillful professionals earn the same celestial salaries as professional ball players.
The expert for the government, Dr. DeRosa, demonstrated — and Dr. Heeb conceded — that a figure similar to Figure 1 could be obtained by chance tosses of a coin. See Part II(A)(B)(3)(b), infra; Gov’t Reply Letter at 3. But, while Dr. Heeb showed that the same poker players would consistently come out on top in the play of a new set of multiple hands of poker, this consistency could not be demonstrated in a new set of coin tossers by the same tossers. See Part 11(B)(3)(c), infra.
*177 [[Image here]]
According to Dr. Heeb, Figure 1 shows that the ten best players “win consistently” and that “these players’ cumulative amounts won are nearly always increasing,” even though they may have “a few losing days or weeks.” Id. By contrast, the ten worst players “are consistently losing throughout the year. Id. He posits that “[t]he fact that the winning players tend to win consistently and the losing players tend to lose consistently demonstrates that there is a skill differential between these groups.” Id.
*178 Dr. Heeb acknowledged that poker also involves an element of chance. Def. Expert Daubert Hr’g Tr. 58:12-13. “On any given hand ... the probabilities are certainly finite.” Id. 62:14-15. The following hypothetical posed by the government to Dr. Heeb on cross-examination is illustrative:
Q. ... The lower skilled player has seven deuce offhand, which is ... statistically the wors[t] starting hand in poker; is that correct?
A. Yeah, probably.
Q. And the higher skilled player has two aces, which is the best starting hand ... in hold’em poker; is that right?
A. That’s right. That’s right.
Q. And when the hand starts, the high skilled player with the two aces is about an 87 percent to 12 percent favorite....
A. That sounds right.
Q. So ... the lower skill player perhaps demonstrating his lack of skills goes all in for $500 with his seven deuce off suit and the higher skill player calls that. Just as a matter of percentage, the lower skilled player has about a 12 percent chance of actually winning that hand, correct?
A. At the point that they both made the bet and called the be[t], yes.
Q. So about one out of ten times, give or take, in that scenario, the lower skilled player will actually win?
A. That’s right, one out of eight actually.
Q. ... And at that point the lower skilled player can take his money and go home, right?
A. There’s nothing to stop a player from quitting, I guess.
Q. And the fact that the higher skilled player is higher skilled, doesn’t get him his money back, right?
A. That’s right
Id. 70:4-71:10; see also 57:18-24 (“For example, a bad beat [a subjective term for a hand in which a player with what appear to be strong cards nevertheless loses], ... might be a hand in which after the play of the hand, the betting has all been made, I believe that I have or I may even know exactly that I have an 85 percent chance of winning and a 15 percent chance of losing, and a bad beat would be a hand on which the 15 percent chance occurs.”).
He acknowledged that poker falls in between chess, which he characterized as an almost pure game of skill, and roulette, which he characterized as a pure game of chance. Id. 44:8-45:9. According to Dr. Heeb:
[T]he question then is: How do you know if skill predominates over chance in poker? And the right way to analyze that question is to ask: Over how long does it take for skill to essentially show itself and predominate over the element of chance? And the answer is that it’s sufficiently few number of hands, that a player could reach that number of hands in a few playing sessions. And, again, depending on how skillful that player is, an extremely skillful player, that player’s skill would manifest itself in that player’s results relatively quickly.
Id. 45:9-18.
Based on his research, Dr. Heeb concluded that skill predominated over chance in determining the outcome of a poker game. He summarized the results of his study of 415 million hands of No Limit Texas Hold’em that were played on-line at the PokerStars website from April 2010 to March 2011. Id. 13:3-9. To verify the reliability of the data he received from PokerStars, he obtained publicly available data from HandHQ, a company that tracks hands played on PokerStars and other online poker sites. Def. Expert Report at 10. Using this outside source, he confirmed that the data received from Pok *179 erStars was an accurate records of hands played. Id. Although his information came from internet poker, rather than face-to-face games, Dr. Heeb concluded that the data set he chose was appropriate:
The game is a game of skill in exactly the same way, whether it’s played live or played over the internet----So my conclusions ... carry over exactly to when the exact same game is played, whether it is played in person, played with cards, ... or played electronically over the internet. The only difference between playing live and playing in person is that the live game brings in some additional elements of skill which are not available to the internet player.
Def. Expert Daubert Hr’g Tr. 41:13-24. Using this sizable data set, Dr. Heeb conducted two different analyses to evaluate the relative effect of skill and luck on players’ success rate in poker.
First, he looked at whether a player’s average win rate on all other hands was predictive of their success in a particular kind of hand — for example, a King and a Nine in different suits (the King Nine hand). Id. 22:14-23:3. He divided players into two groups: those whose success rate was above the median, and those whose success rate was below the median. Id. 24:13-22. Players whose success rate was above the median were more successful with the King Nine hand than players whose success rate was below the median. Id. 24:23-25:3. As summarized in Figures 2 and 3, more highly skilled players won more — or lost less — than lower-skilled players when dealt the same hand.
*180 [[Image here]]
*181 [[Image here]]
Dr. Heeb concluded that a player’s skill had a statistically significant effect on the amount of money won or lost in a particular hand in poker. Id. 25:15-19; 26:11-18; see also id. 28:21-29:3 (The fact that “players who tended to play poorly with all the rest of their cards, also played poorly and lost, or [won] less, with any particular hand, would be sufficient onto itself to demonstrate that the actions of the skillful players are skill, not luck, because if they were lucky, of course the fact that they were lucky on one set[] of cards, would have no influence on how they did with other cards.”). While Dr. Heeb acknowledged that “in a single hand, what cards are dealt is going to be an even more important factor, ... regardless of which hand a player is dealt,” he explained that “when players are dealt the same hand, *182 the more skillful player plays it much better and achieves a better result.” Def. Expert Daubert Hr’g Tr. 39:6-15. But see Gov’t Reply Letter at 6 (contending that “what hand a player is dealt is the predominant determinant of how much he will profit or lose from that hand ”).
Second, he randomly divided the same data set into two groups. Id. 30:21-24. He used regression analysis on the first group to create “a skill index that related how skillfully the player played to what their actual win rates were.” Id. 31:19-21. His skill index included “240 statistics about their play. [It wo]uld be equivalent — if I could draw another analogy, and I hope that this isn’t stretching it too far, but a baseball player that decides how often they swing at the first pitch or whether they are waiting for a curve ball or a strike.” Gov’t Expert Daubert Hr’g Tr. 103:4-8. He then applied the skill index to the second analysis group to see whether players who were predicted to be of high skill actually won significantly more money than players predicted to be of low skill. Def. Expert Daubert Hr’g Tr. 33:1-5. He found that “[t]he lowest skill players according to the predicted skill index in fact achieve much worse results. Average players still don’t do very well. Very good players are winning players.” Id. 33:7-10.
As illustrated in Figure 4, a player’s win rate increases as his skill level increases. Win rate is calculated as a fraction of the big blind won per hand, on average.
*183 [[Image here]]
Dr. Heeb explained Figure 4 as follows:
The line slopes upward to the right, indicating that players with higher predicted skill on average have higher win rates. If poker were a game of chance, there would be no relationship between predicted skill and results. The slope of the line reflects the much higher expected win rate of skillful players compared to less skillful players. This relationship characterizes games of skill.
Def. Expert Report at 36.
Dr. Heeb then divided the analysis group into players with skill below the median and players with skill above the median. Def. Expert Daubert Hr’g Tr. 33:19-23. As shown in Figure 5 below, he found that “it takes about 900 hands of *184 poker for the high skill group to predominate over the low skill group with 90 percent confidence” and about “1400 hands for 95 percent confidence.” 13. C4 CO CO
[[Image here]]
Dr. Heeb testified that this number of hands is “quite reasonably played in a relatively short amount of time by players that are playing poker seriously” and that “over a longer period of time, skill predominates even more.” Id. 34:19-23; see also Gov’t Expert Daubert Hr’g Tr. 92:22-93:8 (“90 percent of the time the top half [in a $l/$2 game, see Fig. 6, infra] would be ahead after 880 hands, which is about 30 hours of play.... [A]t the World Series [of Poker], a typical one day of play is 10 hours, excluding breaks, so it actually takes about 13 hours to play 10 hours of play. That’s a standard day. A standard tournament takes three days. So in the amount of time it takes players to play one poker tournament,. 90 percent of the more skillful half of the players would be ahead of the less skillful half of the players.”).
*185 Based on these analyses, this expert concluded that skill predominates over chance in poker. Id. 18:4-5. He also noted that the “topic ... has been addressed by a number of other researchers, none of whom had the data I have available with the whole cards available to me. All of the results that I have seen, both in published and unpublished papers, are all consistent with the result that skill predominates over chance.” Id. 40:20-25; see also Part 11(B)(4), infra.
b. Government Expert
The government’s expert, Dr. David DeRosa, who is also a well-qualified econometrician, testified at a post-verdict Daubert hearing on August 10, 2012. See generally Gov’t Expert Daubert Hr’g Tr. Dr. Heeb was present at the hearing to answer questions regarding his report and participate in a technical discussion with Dr. DeRosa and the court. See generally id.
Unlike Dr. Heeb, Dr. DeRosa neither has any personal experience with poker, see id. 6:7-14, nor has he independently analyzed the game. Moreover, he noted that he had “not been provided with any of the data or statistical analyses summarized in Dr. Heeb’s report.” Gov’t Expert Report at 2. His testimony was thus limited to a critique of whether “Dr. Heeb’s stated results support his overarching conclusion, namely that skill predominates over chance in poker.” Id. He did not offer any opinions as to the validity of Dr. Heeb’s calculations or his general methodology. Id.
Dr. DeRosa acknowledged that “the actions of [poker] players ha[ve] some impact on the outcome [of the game] and poker is not a game of pure chance.” Id. at 10. Nevertheless, he had several criticisms of Dr. Heeb’s work.
First, he argued that Dr. Heeb’s analysis erroneously relied on “relative skill rather than likelihood that a player will earn a profit.” Id. at 4. According to Dr. DeRosa:
Poker players play poker to win money. A player will consider himself a winner if he earns a profit. The fact that he may lose less money than another player is likely to be of cold comfort. I believe that the proper metric for determining success at a session of poker is whether or not a player profits from playing the game.
Id. at 6; see also Gov’t Reply Letter at 1-2 (emphasizing this point). Yet Dr. Heeb’s own data shows that most players lose money at poker. Dr. DeRosa pointed to Figure 4, supra, which he said shows that:
[P]layers in the 51st to 75th skill percentile lost approximately .15 to .45 [of the big blind] per hand. In the $5/$10 game Dr. Heeb analyzes [in Fig. 4, supra], this equates to a loss of approximately $1.50-$4.50 per hand.
Even top players in the 90th skill percentile appear to have, on average, suffered losses from their poker playing. Only between the 90th and 95th skill percentile does it appear that “skillful” players begin to experience a positive win rate (i.e. have a positive expected return).
Gov’t Expert Report at 6-7; see also Gov’t Reply Letter at 3.
Dr. DeRosa concluded from the fact that so many players lose money that “if a player were to make a profit at any given session in a game where he faced a negative expected rate of return, such profit would have to be primarily as the result of luck.” Gov’t Expert Report at 7. Because so few players win money, he contended, skill cannot predominate over luck in poker. See Gov’t Expert Daubert Hr’g Tr. 9:7-17 (“I go in with a certain amount of money, and I leave with more money. And if I don’t do that, I am a loser. I’m a loser. So a lot of this ranking stuff is *186 irrelevant because skill should be winning money. And as I read the report and as I read Dr. Heeb’s testimony, probably 95 percent of the people who play this online poker lose money so I don’t understand where the skill is. How could it be skillful playing if you’re losing money? And I don’t consider it skill if you lose less money than the unfortunate fellow who lost more money.”); id. 24:25-25:5 (“But the other striking thing that I found was the idea that 95 percent of these people lose money. So for 95 percent — according to the report that I read. That win rate is a negative number so 95 percent of them lose money. So, Your Honor, isn’t then poker a game of chance, not skill, just on that alone?”).
Second, Dr. DeRosa disagreed with Dr. Heeb’s use of cumulative data — i.e., his examination of results over a large number of hands — to evaluate whether skilled players outperform unskilled players. Dr. DeRosa instead stated that the relevant frame of reference for determining whether skill or chance predominates is a single hand. Gov’t Expert Daubert Hr’g Tr. 27:12-18 (“[Tjhere’s no requirement that you have to play forever. It’s not like a game of golf where you have to play all 18 holes. It’s not like a game of tennis where you have to play three sets. You can drop out any time you want. So the fact that if you play one hand chance is the material decider, I would say that says it right there.”).
[N]o matter how long a player sits at a table, the probability of receiving any given hand is the same on the next hand before the cards are dealt as it was for every other hand in the game. This is reminiscent of a famous paradigm from basic probability theory. If red has come up 20 times in a row in roulette, it does not mean that “black is due.” The probability of getting red or black (or green) with each spin of the wheel is independent of prior history. From this point of view, Dr. Heeb’s analysis of long-term results is of limited value....
Gov’t Expert Report at 10; see also Gov’t Reply Letter at 2-3. Moreover, he argued, without independent factual support, that the number of hands required for skill to predominate over chance in poker to a reasonable degree of statistical confidence exceeded the number played by an average player. For example, as shown in Figure 6, in order for a skilled player to beat an unskilled player with 95% confidence in a game with $l/$2 stakes, the player would have to play 1,399 hands. *187 “Assuming an average of 30 hands per hour, a player would have to play more than 46.6 hours with no breaks” to reach that number of hands. Gov’t Expert Report at 9.
[[Image here]]
Third, Dr. DeRosa argued that the presence of persistent winners and losers, as illustrated by Dr. Heeb’s chart (shown as Figure 1, supra) does not prove that skill predominates over chance in poker, because “persistent winners and losers (selected after the fact) result normally from random chance variation.” Id. at 11.
If one were to chart the performance of players involved in a game whose outcome was determined by purely by chance, one might expect to see similar results. Some players are seen — after *188 the fact — to have consistently won. This does not prove or disprove that their winning was a result of skill.
Id. at 12. To demonstrate this point, Dr. DeRosa ran a simulation that produced results similar to having 1,000 players each flip a coin 100,000 times. Id. As with a coin flip, each player had “an equal chance of either winning or losing an equal amount of money on any given trial.” Id. As shown below in Figure 7, his results appear strikingly similar to those of Dr. Heeb in Figure 1.
[[Image here]]
According to Dr. DeRosa, “[t]his experiment shows that in a game of pure chance, in the long run, the top winners exhibit the behavior of persistently winning while the *189 top losers appear to be consistently losing.” Gov’t Expert Report at 13; see also Gov’t Reply Letter at 3-4; Figure 1 and accompanying text, supra.
Finally, Dr. DeRosa questioned the validity of Dr. Heeb’s data set, as well as his methodology. Since the data came from an online poker website, Dr. DeRosa was concerned that it might not represent “real hands played by real players” and might include false data points representing instances in which live players — who may have believed that they were playing against another, similarly-situated person — were playing against either a computer or a confederate of the gaming company. See id. at 17; Gov’t Expert Daubert Hr’g 32:5-10; 73:22-74:20; see also Gov’t Reply Letter at 10 (“It should be noted that Dr. Heeb admitted that he never performed any test to determine whether players were colluding or had more information than they should have had (such as knowing what the community cards would be before they were dealt). In a game based on imperfect information, knowledge of even a single card, whether held by an opponent or included in the community cards[,] would be massively valuable.”). He also questioned Dr. Heeb’s decision to categorize “[pjlayers with too few hands played to calculate statistics for all the various hand and position combinations” as “the lowest skill level” in his analysis of whether skilled players played particular hands better than unskilled players. Def. Expert Report at 36 n.7. According to Dr. DeRosa:
These players could be ‘skilled’ players who only played a few ... hands and then quit because they were losing.... The assumption ... could cause a self-serving bias in Dr. Heeb’s analysis. A player only plays a few hands because he loses. He is then assumed to be unskilled and therefore the expected loss of unskilled players increases.
Gov’t Expert Report at 16.
Dr. DeRosa concluded that Dr. Heeb has not proven that skill predominates over chance in poker. Gov’t Expert Report at 3. He did not discuss Dr. Heeb’s analysis of the relative performance of skilled versus unskilled players in playing the same hand. See Fig. 2-3, supra, and accompanying text.
c. Defense Expert’s Supplemental Report
Following the August 10, 2012 Daubert hearing, Dr. Heeb submitted a supplemental expert report responding to Dr. DeRosa’s critiques and providing additional support for his conclusion that skill predominates over chance in poker. See generally Def. Expert Supp. Report.
First, Dr. Heeb argued that his definition of skill, and his evaluation of relative skill levels, was appropriate. He conceded that only “10 percent to 20 percent of the players in any given game are good enough to win consistently.... And that’s represented by the top 6 to 8 percent of players on” Figure 4, supra. Gov’t Expert Daubert Hr’g Tr. 86:5-9. He contested the view, however, that poker players can only demonstrate skill by winning money. Instead, as Dr. Heeb put it, “the question of whether skill predominates requires only an examination of the relative importance of skill.” Def. Expert Supp. Report at 1. Moreover, he added, “[a] big part of the reason that more poker players have losing results than have winning results on a cumulative basis is that in most circumstances, including the data I studied, player pay a fee to the operator of a poker game in the form of a ‘rake,’ which is a small percentage deducted from each pot.” Id. at 2. To demonstrate this, Dr. Heeb adjusted Figure 4, supra, to add the rake payments back to the players’ winnings. *190 In his initial analysis, which included the payment of the rake, as shown in Figure 4, only 28% of players in the $5/$10 game have a positive profit over the course of a year. When the rake is added back, 37% of players have a positive profit, as shown in Figure 8. As before, win rate is calculated as fraction of the big blind won per hand, on average.
[[Image here]]
Dr. Heeb further explained that “[t]he reason that less than half the players earn a profit is that the best players (with or without the rake) win more than their prorata share of the profits, so there are fewer winners than losers.” Id. But see Gov’t Reply Letter at 2 (“[A]nalyzing the data without the rake is misleading because poker is a game where winning or losing is determined by monetary performance in an absolute sense. Unlike games such as chess or golf, wagering money is *191 an integral part of a poker game. Whether a player is successful depends on how much money he has won or lost, but by how well he has faired against the other players.”)/
Dr. Heeb also defended his assignment of players who play very few hands to the low skill group, explaining that, in his experience as a poker player, “players who play only a few hands and quit” — even if they win money before leaving the game, as some do — “are almost always low skill players.” Id. at 7. He noted that, because “the outcome of players’ hands are effectively weighted by the number of hands that they played, ... a player who played only a few hands would get very little weight in the simulation.” Id.
Second, Dr. Heeb explained his reliance on cumulative results, and particularly his dependence on results involving large numbers of hands played:
In order to assess whether poker is a game in which skill predominates, it is essential to consider the cumulative outcome after a sufficient number of hands. Consider baseball or gold. Baseball is a game of skill on every pitch, even those pitches on which something “lucky” or “unlucky” happens. Nonetheless, it would not be possible to determine with statistical confidence that baseball is a game of skill from a single pitch, or even a single game, even though the score is known and can change with each pitch. Similarly, each stroke in gold can change the score. Poker is a game of skill on every hand that is played, but proving this statistically requires a sufficient number of hands....
... Typical poker players, even in social games, play multiple sessions at regular intervals, such as playing once or twice weekly. Even after only an eight-hour session of poker (about 240 hands), skillful play can already be distinguished from less skillful play.... [When the 50% most skilled players are compared to the 50% least skilled players] 76% of higher skill players are already ahead after just 240 hands. If I focus on the top 10% of players, compared with the bottom 30% of players, 88% are ahead after just 240 hands. More than 90% are ahead after just 300 hands.
This number of hands can easily be played in a single session of poker, even by casual players in a social game.... A serious poker player, even an amateur, can easily play thousands of hands a month in live play.
Id. at 3^4. See also Gov’t Expert Daubert Hr’g Tr. 78:22-79:22 (“Dr. Heeb: ... [I]f I look over a large number of plays, a large number of a statistical sample, what I learn from the sample after enough observations is arbitrarily close to the absolute truth. And it’s just a question of how many you have to look at to know what the true underlying distribution or any underlying statistic would be. So depending on how closely you want to know the truth, you may have to look at more and more — a larger and larger sample, more and more observations. But the underlying truth hasn’t ever changed. So we’re trying to detect whether or not this is a game of sMll with a degree of precision.... After enough information, we can determine that the probability of players getting different results, the skillful players’ better results, the less skillful players’ less successful results, the probability of that happening by anything other than a difference in skill between the players becomes ... smaller and smaller the more observations on the data, the more hands that we play. It’s still a game of skill even on one hand. But to say that we have shown that with statistical certainty requires more and more information the more precisely we want to measure it.”); see id. 77:20-78:6 (“Dr. Heeb: The way that I would think about it *192 is that the question is whether or not the game is a game of skill. How many hands do you need to look at in order to discern that with statistical certainty? A more familiar example might be baseball. One pitch in baseball is a skillful event, both skillful by the pitcher and skillful by the hitter. If you wanted to demonstrate that skill, you would look at a lot of pitches, games, for the season. And based on a statistical analysis of a lot of events, you would be able to determine whether or not that was a skillful act. But it’s a skillful act in the execution of just one swing or one pitch.”).
Third, Dr. Heeb provided additional charts and calculations to support his contention that winning persists in poker, and that the trends shown in Figure 4 are the result of skill rather than chance. He showed that, in general, winning players persisted in winning, and losing players persisted in losing, prospectively — i.e., after they had been identified as winners and losers. Def. Expert Supp. Report at 4-5. The same was not true for players in a pure game of chance, such as the coin toss modeled by Dr. DeRosa in Figure 7, supra. Dr. Heeb concluded that “[tjhis clearly demonstrates that it is the relative skills of these [poker] players and not chance that is leading to their winning and losing.... The contrast between [the performance of poker players and coin tossers] illustrates the degree to which skill is predominant over chance.” Id. at 5.
Finally, Dr. Heeb calculated the relative proportions that skill and chance contribute to the outcome of poker. He explained his methodology as follows:
If the proportion of the game attributable to skill is 0%, then the probability of prevailing should be the same for all contestants. As a result, in a matchup of a “higher skilled” and a “lower skilled” player in a game in which skill contributes 0% to the outcome, the “higher skilled” player will win about 50% of the time. If the proportion of skill in the game is 100%, then a perfectly skilled contestant would win 100% of the time. However, even in a game of 100% skill, the more skillful player could make an error, leading to a win by the less skillful player. If skill and chance are equally important, and therefore equally likely to contribute to the probability of prevailing, then half the time skill is decisive, and half of the time chance is decisive. When skill is decisive, the skillful contestant wins. When chance is decisive, the players have an equal probability of winning. This implies that a contest between two players or teams that is exactly 50% skill and 50% chance will result in the skillful contestant winning 75% of the time. Of course, the poker games I studied were not two player games, but the experiment that I conducted pitted a group of more skilled players against a group of less skilled players, so this is the appropriate measure to use.
Id. at 8.
As “the proper duration of a test of the fraction of skill and chance in any game must be a function of the game itself,” Dr. Heeb chose several benchmarks that were representative of different kinds of game play, ranging from a social game to the world championship contest.
An eight hour poker session, typical of some social games, would involve about 240 hands, since in an hour of live play, players will play about 30 hands. A typical poker day at a poker tournament would last ten hours, excluding breaks, and involve about 300 hands. Events at the World Series of Poker last three, ten-hour days, for a total of about 900 hands of play. The winner of the World Series of Poker’s main event is widely recognized as the world champion. That event is conducted over ten days, so the *193 poker World Champion is crowned after about 3,000 hands.
Id. at 9. The formula relied upon by Dr. Heeb is as follows:
P(W@H) = PS * P(W@S,H) + PC * P(W@C,H)
= PS * P(W@S,H) + (1-PS) * P(W@C,H)
= PS * 1 + (1-PS) * 0.5
= 0.5 + 0.5PS
Where:
P(W@H) = Probability of Winning for the High Skill Player
PS = Portion of the Game Contributed By Skill
PC = Portion of the Game Contributed By Chance
P(W@S,H) = Probability of Winning if Skill is Decisive, for the High Skill Player
P(W@C,H) = Probability of Winning if Chance is Decisive, for the High Skill Player
Id. at 8.
Using this formula, he compared the performance of the top 10% of players to the bottom 30% of players in a $5/$10 stake game, and the performance of the top 50% of players to the bottom 50% of players based upon $l/$2 stakes, at these benchmarks. Id. at 10. In as few as 240 hands, skill accounted for more than 50% of the outcome in the games.
Fig. 9: Contribution of skill to poker
[[Image here]]
Dr. Heeb opined, “[T]he above analysis establishes that skill in poker predominates over chance overwhelmingly, based on a standard of 3,000 hands of play. If the Court were to rule using a benchmark involving fewer hands of play, under all benchmarks proposed above, poker is a game in which skill predominates over chance.” Id. The government contests the conclusions Dr. Heeb draws from this chart, but not the calculations themselves. See Gov’t Reply Letter at 8-10.
4. Other Evidence
A number of other studies were properly relied on by the defendant without objection, providing additional empirical support for the fact that skill determines the outcome in poker. See Fed.R.Evid. 703 (“If experts in the particular field would reasonably rely on those kinds of facts or data in forming an opinion on the subject, they need not be admissible for the opinion to be admitted.”).
One study found, in an analysis of 103 million hands of Texas Hold’em poker, that seventy-five percent of poker hands conclude when one player bets and induces his opponents to fold; the cards are never revealed or compared. See PPA Mot. for Leave to File an Amicus Br. Ex. A (Paco Hope & Sean McCulloch, Statistical Analysis of Texas Hold’em 6 (Mar. 4, 2009) (unpublished article)), Doc. Entry 74, July *194 3, 2012. In the remaining hands, at least half the time the player who would have had the best hand does not win because he has folded. Id. The authors concluded that “in the sampled data, the vast majority of games are determined by something other than the value of the cards, since no player reveals any cards to determine the winner.” Id. at 14.
Other studies have found that skilled players defeated unskilled players both in simulations and in real-world play. See PPA Mot. for Leave to File an Amicus Br. Ex. B (Noga Alon, Poker, Chance and Skill 15-16 (unpublished manuscript)), Doc. Entry 74, July 3, 2012 (concluding, based on analysis of a simplified model of poker, that “although like in essentially almost any other game there is some influence of chance in poker, the game is predominantly a game of skill,” and that “the significance of skill increases dramatically as the number of hands played grows”); PPA Mot. for Leave to File an Amicus Br. Ex. C (Rachel Croson, Peter Fishman, & Devin G. Pope, Poker Superstars: Skill or Luck? Similarities between golf — thought to be a game of skill — and poker, Chance, vol. 21, no. 4 (2008)), Doc. Entry 74, July 3, 2012 (comparing the effect of chance and skill on golf and poker and concluding that poker is as much a game of skill as golf); PPA Mot. for Leave to File an Amicus Br. Ex. D (Steven D. Levitt & Thomas J. Miles, The Role of Skill Versus Luck in Poker: Evidence from the World Series of Poker 12-14 (May 2011) (unpublished manuscript)), Doc. Entry 74, July 3, 2012 (finding, based on an analysis of data from the 2010 World Series of Poker, that “[p]layers classified as high skill [based on past performance in other tournaments] are 12 percent more likely to make money than the average player, and 19 percent more likely to make the final table” and that “in some crude sense, the predictability of outcomes for pairs of players in a poker tournament is similar to that between teams in Major League Baseball”).
The government counters that “expert poker players recognize the critical role that luck plays in the game.” Gov’t Mem. of L. in Opp. to Def.’s Rule 29 Mot. 31, Doc. Entry 96, July 27, 2012. For example, one professional poker player, Phil Gordon, has observed, “Change ten river cards [i.e., the final card dealt in any Texas Hold’em hand] in any poker player’s tournament career, and I would bet that they would be a losing tournament player for their career.” McManus, supra, at 342. Similarly, Dan Harrington, a prominent and accomplished expert poker player, has acknowledged, “The volatility in [no-limit Texas Hold’em] tournaments is out of sight ... Sure, you see some names repeating as winners. They are truly great players. But the problem is, there are lots of other truly great players you haven’t seen at all. And it’s not because they are paying badly. It’s the variance. You need to be extremely-lucky.” Id. at 343.
The government also contests the conclusions the defendant draws from one of the studies cited. It contends that “the fact that [most poker] players fold” before the showdown “demonstrates that chance is the dominant factor in poker. Every decision a player makes is a reaction to a chance event (the random distribution of cards) or another player’s reaction to a chance event over which the player has no control.” Gov’t Reply Letter at 6.
5. Conclusions of Other Courts and the States
Whether poker is a game of chance or a game of skill is a matter of some public and judicial debate. See, e.g., DeeDee Correll, Taking their chances on poker’s legality: Is Texas Hold’em about the luck of the draw, or the skill of the player? The question is being played out in courts *195 around the country, L.A. Times, Sept. 3, 2009, at 14.
When the first wave of anti-gambling laws was passed by state legislatures across the country in the nineteenth century, they frequently prohibited poker along with other gambling activities. McManus, supra, at 83-84. In early cases, poker players were described as “gamblers,” and poker was described as “gambling.” See, e.g., Utsler v. Territory, 10 Okla. 463 , 62 P. 287, 288 (Ok.1900) (upholding defendant’s conviction under state statute making it “unlawful for any dealer in intoxicating liquors in this territory to have or permit any gambling, game of chance, or gambling carried on, or to have or keep any gambling table or gaming device of any kind, in a room where intoxicating liquors are sold” and noting that the witness McKay and “[t]he witness Fisher ... testified that [they] saw gambling carried on in the room with cards, being known as ‘stud poker,’ and he also testified that liquor was sold in the same room”); In re Selling’s Estate, 2 N.Y.S. 634, 635 (1888) (denying respondent the right to administer the estate of a deceased on the grounds that “[t]he proof submitted by the petitioner also shows the respondent Joseph Selling to be a man of utterly worthless and irresponsible character; that he is a professional gambler, know[n] as ‘Poker Joe’ ”).
Several state gaming laws explicitly include “poker” — apparently including Texas Hold’em — in their definition of gambling or define it as a game of chance. E.g. Wis. Const. Art. IV, § 24(6)(c) (prohibiting the legislature from authorizing particular games as a state-run lottery, including poker); Idaho Const. Art. Ill § 20(2) (prohibiting casino gambling, including poker); Ark.Code § 5-66-112 (prohibiting betting money or something of value on card games, including “poker”); Conn. Gen. Stat. § 53 -278a(2) (“ ‘Gambling’ means risking any money, credit, deposit or other thing of value for gain contingent in whole or in part upon lot, chance or the operation of a gambling device, including the playing of a casino gambling game such as ... poker.”); Ohio Rev.Code Ann. § 2915.01 (“‘Game of chance’ means poker, craps, roulette, or other game in which a player gives anything of value in the hope of gain, the outcome of which is determined largely by chance, but does not include bingo.”); Idaho Code § 18-3801 (defining gambling as including poker and excluding “[b]ona fide contests of skill, speed, strength or endurance in which awards are made only to entrants or the owners of entrants”); Iowa Code § 99B.11 (“A poker, blackjack, craps, keno, or roulette contest, league, or tournament shall not be considered a bona fide contest” of skill exempt from gambling license requirements; “[c]ribbage, bridge, chess, checkers, dominoes, pinochle and similar contests, leagues or tournaments” are exempted.); Okla. Stat. tit. 21 § 941 (“Except as provided in the Oklahoma Charity Games Act, every person who opens, or causes to be opened, or who conducts, whether for hire or not, or carries on ... poker ... for money, checks, credits, or any representatives of value, or who either as owner or employee, whether for hire or not, deals for those engaged in any such game, shall be guilty of’ opening, conducting or carrying on gambling game.); Tenn. Code Ann. § 39-17-501 , Sentencing Commission Comments (“The definition of ‘gambling’ includes ... poker.”); cf. Cal. Penal Code § 337j(e) (including poker in the definition of a controlled game which is unlawful to operate without a license except when played “in private homes or residences, in which no person makes money for operating the game, except as a player”). Others implicitly include poker in their definition of gambling. See Fla. Stat. §§ 849.08-849.085 (2)(a) (prohibiting “any game at cards, keno, roulette, faro or other game of chance, at any *196 place, by any device whatever, for money or other thing of value” but stating that gambling on poker is not a crime when played for “penny ante”); id. § 849.086(1) (authorizing poker games at racetracks if those games are played in compliance with Florida law); Mich. Comp. Laws Ann. § 750.314 (making it unlawful for any person “by playing at cards ... or by betting or putting up money on cards ... [to] win or obtain any sum of money or any goods”).
State courts which have ruled on the issue are divided as to whether poker constitutes a game of skill, a game of chance, or a mixture of the two. See Cabot & Hannum, supra, at 456-64 (surveying state court decisions); Bennett M. Liebman, Poker Flops Under New York Law, 17 Fordham Intell. Prop. Media & Ent. L.J. 1 , 19-21 (2006) (“[M]ost courts find that poker is a game of chance.... [E]ven the jurisdictions that recognize the great level of skill involved in playing poker nonetheless conclude that the degree of chance involved in the playing of the game renders poker an activity constituting gambling.”). Compare Garrett v. Alabama, 963 So.2d 700, 700-01 (Ala.Crim.App.2007) (unpublished) (affirming decision that poker is a game of chance); Indoor Recreation Enterprises, Inc. v. Douglas, 194 Neb. 715 , 235 N.W.2d 398, 401 (1975) (holding that poker and bridge are predominately games of chance); Joker Club, L.L.C. v. Hardin, 183 N.C.App. 92 , 643 S.E.2d 626, 629-31 (N.C.Ct.App.2007) (holding that poker is a game of chance under the predominate factor test); and Commonwealth v. Dent, 992 A.2d 190, 196 (Pa.Super.2010) (applying predominate factor test and finding that Texas Hold’em is a game of chance); with Chames v. Cent. City Opera House Ass’n, 773 P.2d 546, 551 (Colo.1989) (holding that, although card games played at an event, including poker, do require skill, it also involves an element of chance, and that this element is sufficient to qualify it as gambling under state law); State ex rel. Schillberg v. Barnett, 79 Wash.2d 578 , 488 P.2d 255, 257-59 (1971) (same); and PPA Mot. for Leave to File an Amicus Br. Ex. E (Town of Mount Pleasant v. Chimento, No. 98045DB (Mt. Pleasant (S.C.) Muni. Ct. Feb. 19, 2009), Doc. Entry 74, July 3, 2012 (stating that poker is a game of skill but nevertheless finding defendants guilty of a state gambling offense since that criteria was not clearly relevant to state law definition of gambling), appeal filed, No. 2009-CP10-001551 (S.C.Ct.App. Oct. 1, 2009). Cf. State v. Coats, 158 Or. 122 , 74 P.2d 1102 (1938) (“Poker, when played for money, is a gambling game, but, since it involves a substantial amount of skill and judgment, it cannot reasonably be contended that it is a lottery.”). But see Def.’s Letter Reply to Gov’t Aug. 17, 2012 Letter 1, Doc. Entry 108, Aug. 20, 2012 (citing foreign cases finding that poker is -a game of skill).
Many states which do not explicitly include poker in their definition of gambling have nevertheless found that poker is gambling. See, e.g., Garrett, 963 So.2d at 700 (holding that poker is covered by a state gambling statute); State v. Duci, 151 Ariz. 263 , 727 P.2d 316, 319 (1986) (holding that poker is covered by a state gambling statute which defines gambling as betting on the result of any game of skill or chance); People v. Mitchell, 111 Ill.App.3d 1026 , 67 Ill.Dec. 669 , 444 N.E.2d 1153, 1155 (Ill. App.Ct.1983) (same); State v. Schlein, 253 Kan. 205, 218 , 854 P.2d 296 (1993) (holding that a location which hosts a poker tournament is a “gambling place” under state law “and an individual who enters the premises where gambling is occurring, with the intent to participate in the poker tournament, has entered into a gambling place”); Joker Club LLC, 643 S.E.2d at 630-31 (holding that poker is gambling under state law); Dent, 992 A.2d at 196 (same); Barnett, 488 P.2d at 258 (same); cf. Emer *197 son v. Townsend, 73 Md. 224 , 20 A. 984 (1890) (money loaned for poker was loaned for “gambling”).
Federal courts have generally treated poker as a game of chance and characterized it as gambling. See, e.g., Johnson v. Collins Entm’t Co., Inc., 199 F.3d 710, 720 (4th Cir.1999) (“The regulation of lotteries, betting, poker, and other games of chance touch all of the above aspects of the quality of life of state citizens.”); Mashantucket Pequot Tribe v. Connecticut, 913 F.2d 1024 , 1027 n. 5 (2d Cir.1990) (“The games of chance that Connecticut permits at the ‘Las Vegas nights’ include blackjack, poker, dice, money-wheels, roulette, baccarat, chuck-a-luck, pan game, over and under, horse race games, acey-ducey, beat the dealer, and bouncing ball.”); Percifield v. United States, 241 F.2d 225, 226 (9th Cir. 1957) (“[Ajppellant operated a gambling casino at Rangely, Colorado, known as the Ace-High Club. This contained a bar, a lounge, a cafe, and a casino room where games of chance were played, including blackjack or ’21’, poker, craps or dice, as well as slot machines.”); Mich. Gambling Opposition v. Norton, 477 F.Supp.2d 1, 19 (D.D.C.2007) (“Class II gaming [under the Indian Gaming Regulatory Act, see Part V(B)(3)(a), infra] includes games of chance such as bingo or poker.”); Valley Broadcasting Co. v. United States, 820 F.Supp. 519, 522 (D.Nev.1993) (“Plaintiffs desire to broadcast commercials related to legal gaming activities located in Nevada such as blackjack, craps, poker, roulette, slot machines, and other lawful games of chance.”); cf. United States v. Gotti 459 F.3d 296, 342 (2d Cir.2006) (finding that Joker Poker machines were gambling devices under New York law based upon their similarity to poker, as the defendant “concedes that the games in question had the theme of poker, and he has not contended in his brief that chance does not play a material role in the outcome of a poker game”), cert. denied sub nom., Ciccone v. United States, 551 U.S. 1144 , 127 S.Ct. 3001 , 168 L.Ed.2d 726 (2007).
6. Compared to Video or “Joker” Poker
Courts have also been asked to rule on the legality of activities involving video or “Joker Poker” machines. “A video poker machine is an electronic device with a video screen at the top and buttons to operate its functions. The object of playing a video poker machine is to obtain the best poker hand possible on the video screen. The machine awards points for winning poker hands.” United States v. Conley, 92 F.3d 157 , 159 n. 1 (3d Cir.1996). While game play on these mechanical devices is somewhat similar to playing “live” poker, “video poker machine gambling entails less skill and hence ■ more chance.” United States v. Conley, 859 F.Supp. 864, 869 (W.D.Pa.1994) (referencing the affidavit of an FBI agent), aff'd, Conley, 92 F.3d 157 ; see also United States v. 294 Various Gambling Devices, 718 F.Supp. 1236, 1243 (W.D.Pa.1989) (“[Ajll the skill elements associated with the ordinary game of draw poker are conspicuously absent in the video version. In video poker there is no raising, no bluffing, no money management skills. The player’s only skill is to recognize possible combinations and basic statistical probabilities.... Even a player with minimal experience can discard the least desirable cards and retain those cards which provide the greatest likelihood for a winning combination, but the cards drawn are produced at random and only chance determines whether a player wins or loses. Furthermore, even this limited skill element is countered in the long run by what is called a retention ratio. Over time the video poker machine is programmed to retain a set percentage of all credits played, so that over the long haul even the astute player cannot defeat the retention ratio.”). Unlike live poker or internet pok *198 er, video poker is house-banked; players play against the machine (the house) rather than other players.
C. Evidence at Trial
The essential facts of the case are largely undisputed. The defendant, in partnership with two others, operated a poker club in the back room of a warehouse out of which he conducted a legitimate business selling electric bicycles. Tr. of Trial 277:12-281:19 (Testimony of Jacek Meekelberg), July 10, 2012. Games were generally held on Mondays and Thursdays, see, e.g. Tr. of Trial 47:9-10 (Testimony of Joseph George Monteleone), July 9, 2012, although there was some evidence to suggest that this schedule was not adhered to with full regularity. Tr. of Trial 305:8-23 (Testimony of Jonathan Seda), July 10, 2012 (indicating that sometimes there were not enough players to get a poker game started). Games were advertised via word-of-mouth and text messages sent to potential participants by the partnership. E.g. id. 63:7-12 (Testimony of Joseph George Monteleone). The club contained two tables, at which No Limit Texas Hold’em was played. Id. 57:23-58:1 (Testimony of Joseph George Monteleone). A “1-2” game was played at one of the tables; a “5-5” game was played at the other. Id. In a 5-5 game, one designated player would have to bet $5 (the “small blind”), and another designated player would have to bet $5 (the big blind), regardless of what cards they held in their hand. Id. 32:17-33:10. In the 1-2 game, the small blind was $1, and the big blind was $2. Id. 58:2-5. The average amount of chips purchased by the players, or “buy-in,” ranged from $100 for the 1-2 game, Tr. of Trial 182:6-8 (Testimony of Deborah Berardi), July 10, 2012, to $300 for the 5-5 game, Id. 182:9-10 (Testimony of Deborah Berardi). See also Tr. of Trial 58:7-12 (Testimony of Joseph George Monteleone), July 9, 2012 (stating that the average buy-in for the 1-2 game was $100-300); id. 303:15-19 (Testimony of Jonathan Seda) (“A. If it was a one-two game, the minimum buy-in would be 60 bucks. The max you can come into the game with is 300. Q. Was there a bigger table, as well? A. Rarely. If it was, it was a five-five, and I think the max would be like 500.”). Games could last as long as eight hours. Tr. of Trial 47:7-8 (Testimony of Joseph George Monteleone), July 9, 2012 (“Q: And about how many times did you gamble [at the defendant’s establishment]? A: From December of 2010 ‘til February 2011 twice a week.’ ”); id. 59:12-21 (“Q: When did you typically arrive when you played games at [the defendant’s establishment]? A: Usually, give or take, 10:00 p.m. Q: How long did you typically play? A: Four to five hours. Usually, I would leave around 2:00, between 2:00 and 3:00 a.m. Q: Was the game breaking up when you left? A: No. Q: Do you know when it ended? A: Various nights, 6:00, 6:00 a.m., 7:00 a.m.”).
Players were plied with free food and drinks by a waitress to induce them to stay and play longer. E.g. Tr. of Trial 96:12-17 (Testimony of UC4783), July 9, 2012. A five percent “rake” for the house was collected by the dealers from each pot. Id. 105:15-20. Dealers were paid twenty-five percent of the rake. Tr. of Trial 317:8-11 (Testimony of Jonathan Seda), July 10, 2012. The remaining funds from the rake were used for expenses relating to the operation of the business and for profits. See id. 322:17-323:3; id. 284:24-25 (Testimony of Jacek Meckelberg).
Other than the operation of these games, no unlawful conduct by the defendant — such as money laundering or loansharking — was shown. No connection to organized crime was suggested.
III. Federal Rule of Criminal Procedure 29
Under Federal Rule of Criminal Procedure 29, “[a]fter the government clo *199 ses its evidence or after the close of all the evidence, the court on the defendant’s motion must enter a judgment of acquittal of any offense for which the evidence is insufficient to sustain a conviction.” Fed. R.Crim.P. Rule 29(a). Decision may be reserved until after the jury returns a verdict of guilty. Id. 29(b).
A defendant challenging his conviction on the basis of the insufficiency of evidence “bears a heavy burden.” United States v. Henry, 325 F.3d 93, 103 (2d Cir.2003). His conviction must be affirmed if “any rational trier of fact could have found the essential elements of the crime beyond a reasonable doubt.” United States v. Florez, 447 F.3d 145, 154 (2d Cir.2006) (emphasis in original). The evidence must be viewed in the light most favorable to the government. United States v. Pizzonia, 577 F.3d 455, 462 (2d Cir.2009).
Even though the rule speaks only of insufficiency of evidence, it obviously covers a case where the alleged or proved conduct does not violate the statute charged. “In a criminal case, a failure of the indictment to charge an offense may be treated as a jurisdictional defect.” United States v. Foley, 73 F.3d 484, 488 (2d Cir.1996), overruled in part on other grounds, Salinas v. United States, 522 U.S. 52 , 118 S.Ct. 469 , 139 L.Ed.2d 352 (1997). A court will grant a motion under Rule 29 where the conduct does not constitute a crime.
IV. Rules of Statutory Construction A. Generally
“[Statutory construction must begin with the language employed by Congress and the assumption that the ordinary meaning of that language accurately expresses the legislative purpose.” United States v. Albertini, 472 U.S. 675, 680 , 105 S.Ct. 2897 , 86 L.Ed.2d 536 (1985); see also, e.g. United States v. Piervinanzi, 23
F.3d 670, 677 (2d Cir.1994). Where a term in a criminal statute is undefined, courts resort to dictionaries to determine its “ordinary meaning.” See, e.g., United States v. Santos, 553 U.S. 507, 511 , 128 S.Ct. 2020 , 170 L.Ed.2d 912 (2008) (plurality op.) (relying on the Oxford English Dictionary, the Random House Dictionary of the English Language, and Webster’s New International Dictionary to define the term “proceeds”); see also United States v. Broxmeyer, 616 F.3d 120, 125 (2d Cir. 2010) (consulting the Random House Dictionary of the English Language to determine the meaning of “persuade,” “induce,” and “entice”; although these terms were not defined in the statute, they are “words of common usage that have plain and ordinary meanings”). Should Congress use a common-law term in a statute, it is assumed that the “term ... comes with a common law meaning, absent anything pointing another way.” Safeco Ins. Co. of America v. Burr, 551 U.S. 47, 58 , 127 S.Ct. 2201 , 167 L.Ed.2d 1045 (2007). “The meaning of doubtful terms or phrases may [also] be determined by reference to their relationship with other associated words or phrases.” United States v. Dauray, 215 F.3d 257, 260, 262 (2d Cir.2000). Moreover, “where general words” are accompanied by “a specific enumeration of persons or things, the general words should be limited to persons or things similar to those specifically enumerated.” Id. When the plain language and canons of statutory interpretation fail to resolve statutory ambiguity, reference will be made to legislative history. See, e.g., Lee v. Bankers Trust Co., 166 F.3d 540, 544 (2d Cir.1999).
B. Rule of Lenity
Interpretation of criminal statutes is guided by unique considerations. As the Supreme Court has explained:
Athough it is not likely that a criminal will carefully consider the text of the law *200 before he murders or steals, it is reasonable that a fair warning should be given to the world in language that the common world will understand, of what the law intends to do if a certain line is passed. To make the warning fair, so far as possible the line should be clear.
McBoyle v. United States, 283 U.S. 25, 27 , 51 S.Ct. 340 , 75 L.Ed. 816 (1931). If a criminal statute remains unclear even when viewed in context, “[t]he rule of lenity requires ambiguous criminal laws to be interpreted in favor of the defendants subjected to them.” Santos, 553 U.S. at 514 , 128 S.Ct. 2020 . The Supreme Court declared:
This venerable rule not only vindicates the fundamental principle that no citizen should be held accountable for a violation of a statute whose commands are uncertain, or subjected to punishment that is not clearly prescribed. It also places the weight of inertia upon the party that can best induce Congress to speak more clearly and keeps courts from making criminal law in Congress’s stead.
Id.
While questions of burdens of proof generally apply to factual matters, the rule of lenity, in essence, places a burden of proof on the government with respect to statutory interpretation. In order to prevail, the government must show that it is more probable than not that the meaning that it relies upon is the appropriate interpretation of the statute. A state of equipoise on the issues requires favoring the defendant’s view. See id. at 513-14 , 128 S.Ct. 2020 (stating that, where two competing definitions of a critical statutory term are equally plausible, “the tie must go to the defendant”). The government bears the burden of proving by a preponderance standard any factual propositions that underlie its interpretation of the statute.
The rule of lenity “is especially appropriate in construing ... predicate offenses under the Racketeer Influenced and Corrupt Organizations Act, 18 U.S.C. § 1961 (1) (1994 ed., Supp. IV),” such as illegal gambling under the IGBA. Skilling v. United States, — U.S. -, 130 S.Ct. 2896, 2932 , 177 L.Ed.2d 619 (2010).
A statute in not “ ‘ambiguous’ for purposes of lenity merely because it [i]s possible to articulate a construction more narrow than that urged by the Government.” Moskal v. United States, 498 U.S. 103, 108 , 111 S.Ct. 461 , 112 L.Ed.2d 449 (1990). Lenity is “reserved ... for those situations in which a reasonable doubt persists about a statute’s intended scope even after resort to ‘the language and structure, legislative history, and motivating policies’ of the statute.” Id. (quoting Bifulco v. United States, 447 U.S. 381, 387 , 100 S.Ct. 2247 , 65 L.Ed.2d 205 (1980)). It is a “doctrine of last resort.” United States v. Hescorp, Heavy Equip. Sales Corp., 801 F.2d 70, 77 (2d Cir.1986); see also United States v. Granderson, 511 U.S. 39, 54 , 114 S.Ct. 1259 , 127 L.Ed.2d 611 (1994) (applying the rule of lenity “where text, structure, and history fail to establish that the Government’s position is unambiguously correct”).
V. Federal Gambling Laws
A. Illegal Gambling Business Act
1. Statutory Language
Close reading of the IGBA reveals that it requires both a violation of an applicable state law and proof of additional federal elements. The IGBA provides, in pertinent part, that:
(a) Whoever conducts, finances, manages, supervises, directs, or owns all or part of an illegal gambling business shall be fined under this title or imprisoned not more than five years, or both.
*201 (b) As used in this section—
(1) “illegal gambling business” means a gambling business which—
(i) is a violation of the law of a State or political subdivision in which it is conducted;
(ii) involves five or more persons who conduct, finance, manage, supervise, direct, or own all or part of such business; and
(iii) has been or remains in substantially continuous operation for a period in excess of thirty days or has a gross revenue of $2,000 in any single day.
(2) “gambling” includes but is not limited to pool-selling, bookmaking, maintaining slot machines, roulette wheels or dice tables, and conducting lotteries, policy, bolita or numbers games, or selling chances therein.
(3) “State” means any State of the United States, the District of Columbia, the Commonwealth of Puerto Rico, and any territory or possession of the United States.
(e) This section shall not apply to any bingo game, lottery, or similar game of chance conducted by an organization exempt from tax under paragraph (3) of subsection (c) of section 501 of the Internal Revenue Code of 1986, as amended, if no part of the gross receipts derived from such activity inures to the benefit of any private shareholder, member, or employee of such organization except as compensation for actual expenses incurred by him in the conduct of such activity.
18 U.S.C. § 1955 (emphasis added).
The structure of the IGBA is similar to that of RICO, which was passed as part of the same act. See Organized Crime Control Act of 1970, Pub. L. No. 91-452, 84 Stat. 922 (codified in scattered sections of the U.S.C.). While the IGBA “declares] that certain gambling activities violate federal as well as state law,” Iannelli v. United States, 420 U.S. 770, 788 , 95 S.Ct. 1284 , 43 L.Ed.2d 616 (1975), it does not merely federalize state gambling crimes. In order to run afoul of the IGBA, the defendant must operate an “illegal gambling business” as defined by federal law. See Sanabria v. United States, 437 U.S. 54, 70 , 98 S.Ct. 2170 , 57 L.Ed.2d 43 (1978) (holding that, although a “gambling business” may violate multiple provisions of state law, the “allowable unit of prosecution” under the statute for the purposes of double jeopardy is participation in a particular “gambling business”). To show that the defendant did so, the government must prove not only that the gambling activities conducted by the business violated state law, 18 U.S.C. § 1955 (b)(1)®, but also two additional, uniquely federal elements. Id. § 1955(b)(1) (ii) - (iii); see also Sanabria, 437 U.S. at 70 , 98 S.Ct. 2170 (“Congress did not assimilate state gambling laws per se into the federal penal code, nor did it define discrete acts of gambling as independent federal offense.”). These elements' — that the business must (1) include five or more employees, § 1955(b)(1)(h), and (2) be in operation for thirty days or earn more than $2,000 in one day, § 1955(b)(l)(iii) — limit the reach of the statute to enterprises of a particular size. Thus, even if poker were to constitute gambling under the IGBA, most “kitchen table” poker games would not satisfy either or both of these requirements.
The IGBA does not define the federal component of gambling precisely. Though games of chance run by tax exempt organizations are excluded from prosecution under § 1955(e), § 1955(b)(2) makes no mention of chance, skill, or any other characteristic defining gambling. While it enumerates a list of activities that constitute gambling, this list is not exclusive. *202 See Organized Crime Control: Hearings Before Subcomm. No. 5 of the H. Comm, on the Judiciary, 91st Cong. 325 n.66 (1970) (hereinafter “House Judiciary Hr’gs”) (Committee on Federal Legislation, The Association of the Bar of the City of New York, The Proposed Organized Crime Control Act of 1969 (S. 30) (1970)) (“The term ‘gambling’ is said to ‘include’ certain specified activities ... without indicating whether the list is supposed to be all-inclusive.”). Nor does the statute explicitly state how this list of gambling activities in subsection (b)(2) relates to the crime of running an illegal business as defined by subsection (b)(1). Resort to techniques other than plain meaning is necessary to determine the meaning of the term and its relation to the rest of the statute.
2. Dictionary Definitions
Dictionary definitions of gambling vary widely. Some broadly include “play[ing] a[ny] game for money or property.” Gamble, Merriam-Webster Online Dictionary, http://www.merriam-webster.com/ dictionary/gamble (last visited July 10, 2012); see also Gambling, Black’s Law Dictionary 748 (9th ed. 2009) (“The act of risking something of value, esp. money, for a chance to win a prize.”). Others define gambling as limited to playing games of chance for money. Gamble, The Oxford English Dictionary (2d ed. 1989) (“To play games of chance for money, esp. for unduly high stakes; to stake money (esp. to an extravagant amount) on some fortuitous event.”), available at http://oed.com/ view/Entry/76447; Gambling, Webster’s Third New International Dictionary 932 (1971) (“1: the act or practice of betting: the act of playing a game and consciously risking money or stakes on its outcome; 2: the act of risking something on an uncertain event”); Gamble, Webster’s Third New International Dictionary 932 (1971) (“1: a: to play a game of chance for money or other stakes; b: to wager money or stakes on an uncertain outcome (as of a horse or an athletic game); 2: to stake something of value on an uncertain event or contingency”); Gamble, Merriam-Webster’s Collegiate Dictionary 478 (10th ed. 1999) (“1: a: to play a game for money or property b: to stake something on an uncertain outcome; 2: to stake something on a contingency; to take a chance”); Gamble, American Heritage Dictionary of the English Language, http://ahdictionary.com/ word/search.html?q =gambling (last visited July 20, 2012) (“[t]o bet on an uncertain outcome, as of a contest,” or “[t]o play a game of chance for stakes”).
Poker is sometimes treated as a synonym both for gambling generally and for the games enumerated in the IGBA. See Roget’s International Thesaurus § 514.7 (3d ed. 1962) (listing, as synonyms for “gamble,” “(games of chance) ... horse racing, keno, lotto, ... roulette, ...; poker, faro, etc. (card games)).
3. Common Law
Most states find that an “activity is ... illegal gambling if a person risks something of value on an activity predominately determined by chance for the opportunity to win something of greater value than he or she risked.” Cabot & Hannum, supra, at 445 (emphasis added); see also, e.g., Morrow v. State, 511 P.2d 127, 129 (Alaska 1973). But see, e.g., Ariz. Rev. Stat. Ann. § 13-3301 (4) (“‘Gambling’ or ‘gamble’ means one act of risking or giving something of value for the opportunity to obtain a benefit from a game or contest of chance or skill or a future contingent event but does not include bona fide business transactions which are valid under the law of contracts including contracts for the purchase or sale at a future date of securities or commodities, contracts of indemnity or guarantee and life, health or accident insurance.”); 720 111. Comp. Stat. § 28-1 (“A person commits gambling when he ... *203 [p]lays a game of chance or skill for money or other thing of value.... ”); Chames, 773 P.2d at 551 (“While poker and perhaps some of the wagering games might involve some skill, these games certainly are contingent ‘in part’ upon chance, and when, as here, the games involve risking a thing of value for gain, they constitute a form of ‘gambling’ in its commonly understood sense.”); Barnett, 488 P.2d at 257-59 (Wash.1971) (holding that a game which involves an element of chance, even if skill is also involved, is sufficient to qualify it as gambling under state law).
4. Legislative History
a. Purpose of the Statute
Concerns about organized crime appear to have been the major driving force behind the Organized Crime Control Act of 1970 generally, as well as the IGBA specifically. The goal of 18 U.S.C. § 1955 was “to give the Federal Government a new substantive weapon, a weapon which will strike at organized crime’s principal source of revenue: illegal gambling.” S. Rep. No. 91-617, at 71 (1969); see also Organized Crime Control Act of 1970, Pub. L. No. 91-452, 84 Stat. 922, 923 (codified in scattered sections of 18 U.S.C.) (stating that the purpose of the act was “to seek the eradication of organized crime in the United States by strengthening the legal tools in the evidence-gathering process, by establishing new penal prohibitions, and by providing enhanced sanctions and new remedies to deal with the unlawful activities of those engaged in organized crime”). As President Nixon explained in his Message to Congress regarding the bill:
While gambling may seem to most Americans to be the least reprehensible of all the activities of organized crime, it is gambling which provides the bulk of the revenues that eventually go into usurious loans, bribes of police and local officials, “campaign contributions” to politicians, the wholesale narcotics traffic, the infiltration of legitimate businesses, and to pay for the large stables of lawyers and accountants and assorted professional men who are in the hire of organized crime.
115 Cong. Rec. 10,043 (Apr. 23, 1969) (Organized Crime Message from the President of the United States).
Prior to its enactment, the existing interstate-nexus requirement permitted large intrastate gambling rings to escape federal prosecution. See House Judiciary Hr’gs at 156-57 (statement of Att’y Gen. John N. Mitchell) (“Federal jurisdiction under existing law ... depends upon the establishment of a specific link to interstate commerce on a case-by-case basis. As a result, many large-scale and lucrative illegal gambling operations, which we have reason to believe are dominated by the Cosa Nostra, escape prosecution.”). Through the IGBA, Congress sought to close this “loophole” by obviating the need for proof of an interstate nexus in each case. Measures Relating to Organized Crime: Hearings Before the Subcomm. on Crim. Laws & Procedures of the S. Comm, on the Judiciary, 91st Cong. 382-83 (1969) (hereinafter “Senate Judiciary Hr’gs ”) (statement of Assistant Att’y Gen. Will Wilson); see also 116 Cong. Rec. 605 (Jan. 21, 1970) (statement of Sen. Allott). Federal enforcement was seen as particularly necessary in light of what was perceived as a failure to prosecute gambling offenses due to the widespread corruption of state officials by organized crime. S. Rep. No. 91-617, at 72 (“The effect of ... police corruption is stultifying on Federal-State cooperation in the campaign against organized gambling. This inability of Federal agencies properly to enforce the statutes within their jurisdiction is an important basis for the Congress to take action in this area.”); Senate Judiciary Hr’gs at 448 (Message from the President of the United States Relative to the Fight Against Orga *204 nized Crime) (“For most large scale illegal gambling enterprises to continue operations over any extended period of time, the cooperation of corrupt police or local officials is necessary.”); 115 Cong. Rec. 10,736 (Apr. 29, 1969) (statement of Sen. Hruska) (“There are two reasons for this continued growth of this gambling industry: first, the inability, and second, the unwillingness of local authorities to take action against it.”); 116 Cong. Rec. 591 (Jan. 21, 1970) (statement of Sen. McClellan) (“[Something must be done to stop this flow of money to organized crime from gambling operations, and we must stop the corruption of local officials and law enforcement 'by organized crime.”); 116 Cong. Rec. 604 (Jan. 21, 1970) (statement of Sen. Allott) (The IGBA will permit “the Federal Government to intervene where local and State governments have been rendered powerless because of the corruption of responsible officials.”).
The IGBA was not designed to “define discrete acts of gambling as independent federal offenses.” See Scmabria, 437 U.S. at 70 , 98 S.Ct. 2170 . The debates focused not on prohibiting particular kinds of gambling, but on targeting particular kinds of criminals — i.e., reaching “those who are engaged in an illicit gambling business of major proportions.” S. Rep. 91-617, at 73; H.R. Rep. 91-1549, at 53 (1970), reprinted in 1970 U.S.C.C.A.N. 4007, 4029 (“The intent of section 1511 and section 1955, below, is not to bring all illegal gambling activity within the control of the federal government, but to deal only with illegal gambling activity of major proportions. It is anticipated that cases in which their standards can be met will ordinarily involve business-type gambling operations [of] considerably greater magnitude than simply meet the minimum definitions. The provisions of this title do not apply to gambling that is sporadic or of insignificant monetary proportions. It is intended to reach only those persons who prey systematically upon our citizens and whose syndicated operations are so continuous and so substantial as to be of national concern, and those corrupt state and local officials who make it possible for them to function.”); Senate Judiciary Hr’gs at 449 (Message from the President of the United States Relative to the Fight Against Organized Crime) (“The purpose of this legislation is to bring under federal jurisdiction all large-scale illegal gambling operations which involve or affect interstate commerce.”). See also United States v. Cook, 922 F.2d 1026, 1034 (2d Cir.1991), cert. denied 500 U.S. 941 , 111 S.Ct. 2235 , 114 L.Ed.2d 477 (1991) (noting that the federal interest underlying the IGBA is the eradication of large-scale gaming); United States v. Farris, 624 F.2d 890, 895 (9th Cir.1980), cert. denied, 449 U.S. 1111 , 101 S.Ct. 919 , 66 L.Ed.2d 839 (1981), superceded by statute, Indian Gaming Regulatory Act of 1988, Pub. L. No. 100-497, 102 Stat. 2467, as recognized in United States v. E.C. Investments, Inc., 77 F.3d 327 (9th Cir.1996) (“The policy underlying § 1955 is that large-scale gambling is dangerous to federal interests wherever it occurs [including on an Indian reservation].”). Congress found that, where a state had outlawed a particular form of gambling, “organized crime had developed complex channels” to capitalize on the opportunity presented. United States v. Sacco, 491 F.2d 995 , 1000 & n. 6 (9th Cir.1974) (citing President’s Comm’n on Law Enforcement and Administration of Justice, Report: The Challenge of Crime in a Free Society 189 (1967); Task Force Report: Crime and its Impact — an Assessment 52-53 (1967)).
Congress did not propose to supplant the traditional role of states in regulating gambling. Iannelli, 420 U.S. at 788 , 95 S.Ct. 1284 (noting that Congress “recognize[ed] that gambling activities normally are matters of state concern” in limiting *205 the scope of the federal statute to large-scale gambling operations); House Judiciary Hr’gs at 194 (statement of Assistant Att’y Gen. Will Wilson) (“[W]e are not trying to bring the whole gambling enforcement problem into the Federal jurisdiction, the Federal courts.”). Rather, “[t]he purpose of the statute is simply to make the Federal Government a more effective member of the established State-Federal law enforcement partnership which has long been waging a common war on organized crime and illegal gambling.” 116 Cong. Rec. 604 (Jan. 21, 1970) (statement of Sen. Allott); see also, e.g., House Judiciary Hr’gs at 170 (statement of Att’y Gen. John Mitchell) (stressing that the IGBA “does not proscribe gambling which is legitimate under state law, nor does it prohibit lotteries and bingo games conducted for charitable purposes. The federal proposal will not interfere with a State’s right to regulate the conduct of citizens within its jurisdiction.”); 116 Cong. Rec. 601 (Jan. 21, 1970) (statement of Sen. Hruska) (stating that the IGBA gives “the Attorney General broad latitude to assist local and state government in cracking down on illegal gambling, the wellspring of organized crime’s reservoir”) (quoting Organized Crime Message from the President of the United States, April 23, 1969); 116 Cong. Rec. 591 (Jan. 21, 1970) (statement of Sen. McClellan) (“[The IGBA] would give the Federal Government two new means to aid the States in combating large-scale gambling.”),
b. Definition of Gambling Generally
In its original form, the IGBA did not include a separate definition of gambling. The statute’s scope did not encompass all state gambling crimes, but only “betting, lottery, or numbers activity”:
(a) Whoever conducts, finances, manages, supervises, directs, or owns all or part of an illegal gambling business shall be fined under this title or imprisoned not more than five years, or both.
(b) As used in this section, the term ‘illegal gambling business’ means betting, lottery, or numbers activity which
(1) is a violation of the law of a State or political subdivision thereof;
(2) involves five or more persons who operate, work in, participate in, or derive revenue from said betting, lottery, or numbers activity; and
(3) has been or remains in operation for a period in excess of thirty days or has a gross revenue of $2,000 in any single day.
(d) This section does not apply to any bingo game, lottery, or similar game of chance conducted by an organization exempt from tax under section 501(c)(3) of the Internal Revenue Code of 1954, as amended, if no part of the gross receipts derived from such activity inures to the benefit of any private shareholder, member, ' or employee of such organization except as compensation for actual expenses incurred by him in the conduct of such activity.
Illegal Gambling Business Control Act of 1969, S. 2022, 91st Cong., 1st Sess. § 201; see also H.R. 10683, 91st Cong., 1st Sess. § 201 (“[T]he term ‘illegal gambling business’ means betting, lottery, or numbers activity ... [and] involves five or more persons who operate, work in, participate in, or derive revenue from said betting, lottery, or numbers activity....”); H.R. 10789, 91st Cong., 1st Sess. § 201(b) (same); H.R. 10944, 91st Cong, 1st Sess. § 201(b) (same); H.R. 11026, 91st Cong, 1st Sess. § 201(b) (same); H.R. 11345, 91st Cong, 1st Sess. § 201(b) (same); H.R. 13331, 91st Cong, 1st Sess. § 201(b) (same). No discussion of why a separate definition of gambling was included in the final version of the bill could be found. *206 Nor could it be determined why that definition was changed to specify the nine enumerated games.
Descriptions of the statute’s definition of an illegal gambling business varied. One of the bill’s sponsors declared that “[a]n illegal gambling business is defined as, first, violating State law,” possibly implying that the IGBA did not include a separate federal definition of gambling. 116 Cong. Rec. 601 (Jan. 21, 1970) (statement of Sen. Hruska); see also Senate Judiciary Hr’gs at 381 (statement of Assistant Att’y Gen. Will Wilson) (“[W]e have defined, for purposes of this title, an illegal gambling business as one which is in violation of state or local law....”); House Judiciary Hr’gs at 156 (statement of Att’y Gen. John Mitchell) (“[The IGBA] will make it a Federal offense to engage in a gambling operation which is illegal under State law....”); 116 Cong. Rec. 35196 (Oct. 6, 1970) (statement of Sen. Poff) (same); 116 Cong. Rec. 35304 (Oct. 6, 1970) (statement of Sen. Railsback) (“[The IGBA] enlarges Federal jurisdiction over illegal gambling activities, which are defined as violating a law, involving 5 or more persons, operating for more than 30 days or having a gross income of $2,000 in one day.”). Similarly, another senator stated that “[t]he approach of the bill is to define an ‘illegal gambling business’ in terms of the number of people involved and in terms of gross receipts and length of operation,” rather than in relation to a federal gambling definition. 116 Cong. Rec. 602 (Jan. 21, 1970) (statement of Sen. Yarborough). Yet other members of Congress highlighted the fact that the statute targeted particular games. See 116 Cong. Rec. 603 (Jan. 21, 1970) (statement of Sen. Allott) (“The statute defines an ‘illegal gambling business’ as one including such forms of betting as bookmaking or numbers and which first, is a violation of state law ....” (emphasis added)); House Judiciary Hr’gs at 287 (statement of Rep. Halpern) (“[The IGBA and 18 U.S.C. § 1511 ] define ‘illegal gambling business’ so as to exclude bingo, lotteries, or games of chance conducted by religious or charitable organizations but would include any other betting, lottery or numbers activity in violation of State or local law....”).
In its report, the Senate Committee on the Judiciary indicated that the definition of gambling was limited to particular games. S. Rep. No. 91-617, at 73 (“It defines an ‘illegal gambling business’ as including ‘pool selling, bookmaking, maintaining slot machines, numbers, and other gambling activity’ which — (1) is a violation of State law .... ”); id. (“Sections 1955(b)(l)-(3) define an ‘illegal gambling business,’ as above, as gambling or numbers activity. ... See proposed section 1511, above [discussed infra at Part V(B)(1) ].”). While the Senate Committee went on to say that “State” and “gambling” are also defined “comprehensively,” it is unclear whether it meant that the terms were defined broadly, or merely defined thoroughly.
Congress never discussed the meaning of “gambling” in the IGBA more generally. It did not address whether it encompassed games of some skill, or merely games predominated by chance. The New York City Bar Association’s Committee on Federal Legislation, however, assumed, in its report to Congress, that the statute “define[d] ‘gambling’ broadly to include virtually all games of chance.” House Judiciary Hr’gs at 323 n.61 (Committee on Federal Legislation, The Association of the Bar of the City of New York, The Proposed Organized Crime Control Act of 1969 (S. 30) (1970)).
Nor did Congress debate whether a game would have to be house-banked to constitute gambling — although one senator expressed concern at the ability of organized crime to make large amounts of *207 money from non-house-banked games. See Senate Judiciary Hr’gs at 495 (“[In a numbers game, b]ets are placed on any three-digit numbers from one to 1,000. The mathematical odds are 1,000 to one. Yet seldom, however, is the payoff over 500 to one, and then, on cut numbers ... it is even less. The gambler thus seldom gambles. In addition, he hedges his bet in a complicated layoff system.... The professional bookmaker ... seldom gambles either. He gives track odds or less without track expenses, pays no taxes, is invariably better capitalized or ‘lays off a certain percentage of his bets with other gamblers, takes credit bets to stimulate the play, and may even fix the event by corrupting private and professional sports.”).
c. Discussion of Particular Games
In debating the IGBA, Congress stated that, at the time of the statute’s enactment, the Mafia played a significant role in organizing a wide array of gambling activities.
Law enforcement officials agree almost unanimously that gambling is the greatest source of revenue for organized crime. It ranges from lotteries, such as ‘numbers’ ... to off-track horse betting. ... In large cities where organized criminal groups exist, very few of the gambling operators are independent of a large organization.... ’ Most large-city gambling is established or controlled by organized crime members through elaborate hierarchies. ‘There is no accurate way of ascertaining organized crime’s gross revenue from gambling in the United States. Estimates of the annual intake have varied from $7 to $50 billion. Legal betting at racetracks reaches a gross annual figure of almost $5 billion, and most enforcement officials believe that illegal wagering on horse races, lotteries, and sporting events totals at least $20 billion each year. Analysis of organized criminal betting operations indicates that the profit is as high as one-third of gross revenue — or $6 to $7 billion each year. While the Commission cannot judge the accuracy of these figures, even the most conservative estimates place substantial capital in the hands of organized crime leaders.’
Report of the President’s Commission on Law Enforcement and Administration of Justice, The Challenge of Crime in a Free Society 188-189 (1967) (cited in Iannelli, 420 U.S. at 788 , 95 S.Ct. 1284 ); see also 115 Cong. Rec. 10,041 (Apr. 23, 1969) (Organized Crime Message from the President of the United States) (“Many decent Americans contribute regularly, voluntarily and unwittingly to the coffers of organized crime — the suburban housewife and the city slum dweller who place a twenty-five cent numbers bet; the bricklayer and college student who buy a football card; the businessman and secretary who bet illegally on a horse.”); 116 Cong. Rec. 590 (Jan. 21, 1970) (Statement of Sen. McClellan) (“Organized crime, of course, does not limit its illegal gambling operations to horse racing and sporting events. It also includes gambling in the form of lotteries, dice games, and illegal casinos.”). According to the Attorney General, “In an area which organized crime has invaded, there are few independent gamblers. Even if competitors have the capital required to ‘make it’ on their own, the syndicate has methods of persuading them to join up, or to go into business elsewhere.” House Judiciary Hr’gs at 153 (statement of Att’y Gen. John N. Mitchell).
Debates focused primarily on Mafia-run numbers rackets — intrastate lotteries that offered lopsided odds and thus leached significant sums from poor communities. See Senate Judiciary Hr’gs at 495 (statement of Sen. McClellan) (“Most large slum areas, for example, have within them some form of a lottery known as numbers.... *208 Assuming an honest payoff — often not the case — the ultimate effect of the racket is to drain the work income of slum residents away from food, clothing, shelter, health, and education.”); House Judiciary Hr’gs at 87 (statement of Sen. McClellan) (“Cosa Nostra informant Joe Valachi ... described well the impact of organized gambling on its direct victims when he said: ‘It’s poor people that play the numbers; and if you want the truth, most of them play because they are desperate for money and have no other way to get it.’ ”).
In his message to Congress on Organized Crime, the President singled out “the numbers racket” as a particularly significant and pernicious form of gambling. See Senate Judiciary Hr’gs at 444 (1969) (Message from the President of the United States Relative to the Fight Against Organized Crime). Statements by other public officials echoed the sentiment. Id. at 158 (statement of Sen. Tydings) (“The greatest single source of revenue for organized crime is its gambling activities, which net an estimated seven (7) to fifty (50) billion dollars a year.... A great portion of this is gained through numbers rackets, draining from the poorest inhabitants of our ghettos and slums and their families precious dollars which should be spent for food, shelter and clothing.”); id. at 425 (statement of William Hundley, former head of the Organized Crime and Racketeering Section at the Department of Justice) (“[PJrobably the only area where [the IGBA] would be helpful would be in getting at big numbers rackets, because in my experience in the Justice Department any gambling operation that was worth Federal concern had an interstate aspect, and that you could proceed under [the Paraphernalia Act] and the other bills. But some of the really big numbers operations, particularly in a place like New York, can be, by the nature of the operation, self-contained ... and you could use this new [statute] against those. I don’t see that it would be really of much use otherwise in the gambling area.” (emphasis added)); id. at 382-83 (statement of Assistant Attorney Gen. Will Wilson) (stating that “[v]ery few numbers operations have been prosecuted at a Federal level because seldom are state lines crossed” and that the IGBA is designed to close this “loophole”).
Also of particular concern was bookmaking, which often relied on national crime syndicates. 116 Cong. Rec. 596 (Jan. 21, 1970) (statement of Sen. McClellan) (“Boo

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Source: Frix Law Library, https://www.frixlaw.com/law-library/cases/8701527. Public record. Not legal advice.