
516 F.3d 634 (2008)
UNITED STATES of America, Plaintiff-Appellee,
v.
Fuat USENI and Phillip. J. Cozzo, Defendants-Appellants.
Nos. 06-1978, 06-2107.
United States Court of Appeals, Seventh Circuit.
Argued September 19, 2007.
Decided February 21, 2008.
*635 *636 *637 *638 Shoshana Gillers, Office of the United States Attorney, Chicago, IL, for Plaintiff-Appellee.
Shelly B. Kulwin, Jeffrey R. Kulwin, Kulwin, Masciopinto & Kulwin, Jeffrey B. Steinback, Chicago, IL, for Defendants-Appellants.
Before BAUER, MANION, and WOOD, Circuit Judges.
MANION, Circuit Judge.
Under Illinois law, only charitable organizations are allowed to run certain gambling games such as bingo games, pull-tab games, and raffles as fundraisers for their organizations. In this case, the operators of the Grand Palace Bingo Hall (the "Grand Palace") in Northlake, Illinois, used the Italian American War Veterans (the "IAWV"), a charitable organization, as a front to pocket nearly three million dollars in gambling proceeds. Both Fuat "Frank" Useni and Phillip Cozzo worked at the Grand Palace from its inception until it was sold to a group of IAWV members. A jury convicted Useni and Cozzo of conspiring to commit racketeering offenses and operating an illegal gambling business, as well as several counts of mail fraud and tax fraud. Following their convictions, Useni and Cozzo appealed, challenging various aspects of their respective convictions and sentences. On appeal, the principal question in their challenges to their convictions and sentences is the *639 extent of their involvement in the illegal gambling that occurred at the Grand Palace. We affirm.

I.
Because the jury returned a verdict in favor of the government in this case, we summarize the evidence in the light most favorable to the government. The people who comprised the central witnesses at trial were: Polly Kirby, the manager of the Illinois Department of Revenue's office of bingo and charitable games; Patrick Marotta, the former president and CEO of Gore & Kaye, a wholesale distributor of charitable gaming supplies that was the Grand Palace's primary supplier; Carmen Trombetta and Steven Mariani, IAWV members who were involved in the preparation and operation of the Grand Palace; Carole Johnson, Useni's former girlfriend and a worker at the Grand Palace; Lorraine Mazzei, Cozzo's former girlfriend; Aaron Levitanksy, the Grand Palace's accountant; Donna Dombrowski, the live-in girlfriend of Fred Bingham, the Grand Palace's bookkeeper; and Richard Lexby, an agent for the Internal Revenue Service (the "IRS"). We refer to those witnesses, as well as any other of the witnesses at trial, when their testimony is relied upon in our narrative of the evidence in this case.
A. Illinois Gambling Laws
Illinois has a network of laws and regulations designed to allow charitable organizations to raise money through limited forms of gambling while, at the same time, strictly limiting the use of the money and facilities involved in the gambling in order to prevent fraud and abuse. At trial, Illinois Department of Revenue employees Polly Kirby, Lisa Roberts, and Randi Kaplan testified about Illinois's regulatory scheme for charitable gambling. According to those witnesses, only certain charitable organizations, such as the IAWV, are permitted to run bingo halls. A charitable organization must have a license issued by the state, to conduct bingo or pull-tab games.[1]See 230 ILCS 20/2; 230 ILCS 25/1. A license, which must be renewed annually, allows the charitable organization to hold bingo or pull-tab games once a week. Illinois law also requires that a charitable organization have a license to conduct raffles, but the licensing of raffles is left to each individual municipality rather than the state. In addition, Illinois law prohibits conducting raffles and bingo games on the same premises. 230 ILCS 25/2(11).
A company or person that is not affiliated with a charitable organization may obtain a supplier's license, which allows that company to sell gambling supplies to the charitable group running the games; or a provider's license, which allows the company to rent a facility to a charitable group conducting games. See 230 ILCS 20/3.1; 230 ILCS 25/1.4  .5. The provider's license, like the bingo and pull-tab licenses, has to be renewed yearly by the state of Illinois. Neither the supplier nor the provider may receive any revenue from the games other than a reasonable sum in exchange for providing their services; the net proceeds of the gambling must go to the charitable organization running the games. See 230 ILCS 20/4; 230 ILCS 25/2. Furthermore, only the members of the charitable organization are allowed to participate in operating the games, including selling bingo *640 cards or pull-tabs, calling numbers, confirming and paying winners, and handling or counting the proceeds from the sale of cards and pull-tabs. Most importantly, only members of the charitable organization are allowed to handle the money earned from the games. Significantly, the members of the charitable organization involved in operating the games must be volunteers and are themselves prohibited from being compensated for their work in running the games. See 230 ILCS 20/4(3); 230 ILCS 25/2(3).
Supplier, pull-tab, and bingo licensees have reporting obligations to the state. Suppliers must file quarterly reports listing such information as the manufacturer's serial number for each pull-tab box sold, the date of the sale, the type of tickets sold, serial numbers for the tickets, and what the ideal gross proceeds would be for each box of pull-tabs. Pull-tab and bingo licensees are required to report quarterly to pay their taxes.[2] On a bingo report, a licensee must list the date, the amount of prizes awarded, and the number of players participating for each bingo session held, as well as the gross proceeds from the games that quarter and the amount of tax owed to the state. In contrast, a pull-tab return must report, among other things, each pull-tab game played, the date the particular pull-tab game was played, the manufacturer's serial number for that game, the gross proceeds from the game, the gross proceeds for the sale of pull-tabs that quarter, and the amount of tax owed.
B. Birth of the Grand Palace
While the network of laws, rules, and regulations were designed to prevent fraud, a gambling operation nevertheless presented a lucrative attraction to someone willing to skirt the law. The Grand Palace was the brainchild of William Shlifka,[3] a man who had no affiliation with the IAWV. Shlifka planned to have several IAWV posts each apply for separate bingo and pull-tab licenses, which would allow Shlifka to run several sessions of gaming a week. In turn, Shlifka would have the Grand Palace apply for provider's and supplier's licenses so that it could supply the gambling equipment and host the sessions. Shlifka would pay each veteran who worked a nightly gaming session $50 per session and would pay each IAWV post $100 for every gaming session they hosted.
From the beginning, Shlifka involved Cozzo, who was also not a member of the IAWV, in the planning of the Grand Palace. Prior to the opening of the Grand Palace, Shlifka, together with Cozzo, met with several people who would be key to the Grand Palace's success: Steven Mariani, a high-ranking IAWV member who would recruit IAWV posts and members; Patrick Marotta, the president of bingo-supply distributor Gore & Kay who would be the main supplier of gambling equipment to the Grand Palace; and Aaron Levitansky, who would do the accounting work for the Grand Palace. According to Mariani's testimony, Shlifka and Cozzo approached Mariani and asked him to recruit IAWV posts to sponsor the games and offered Mariani $100 for each gaming session hosted by an IAWV post recruited by Mariani. Shlifka also introduced Mariani to "Frank" Useni, another non-IAWV member, as someone who would help run the kitchen and do the janitorial work for the bingo hall. Shlifka and Cozzo next met with Marotta about providing gaming *641 supplies. Marotta testified that Shlifka and Cozzo sought Marotta's advice as to the type of games to run and pull-tabs to use. At that meeting with Marotta, Shlifka referred to Cozzo as his "partner." Shlifka and Cozzo then met with Levitansky about the hall. Levitanksy testified that Shlifka told him that the Grand Palace would make money by renting the hall and selling bingo cards to the IAWV posts, as well as by selling concessions to hall patrons. At that meeting no mention was made of the Grand Palace ever profiting off of the revenue from the games.
After securing the aid of Mariani, Marotta, and Levitansky, Shlifka applied for a provider's license in February 1994, using the names of his wife and daughter as purported officers of the Grand Palace. Several applications for bingo and pull-tab licenses for IAWV posts were also submitted. Donna Dombrowski, Fred Bingham's live-in girlfriend, testified that. Bingham, the Grand Palace's bookkeeper and a non-IAWV member, completed the applications for the posts. Each application listed the address of the Grand Palace as the address of the IAWV post submitting the application, though no IAWV post had its place of business at the Grand Palace. Mariani testified that Shlifka, gave the money for the license application fees to him, who in turn had money orders made out to be submitted with the applications.
According to the testimony of Lorraine Mazzei, Cozzo's former girlfriend, Cozzo had one of the bingo license applications signed by Mazzei and his sisters. The bingo application required. Mazzei and Cozzo's sisters to make several certifications, including that they were bona fide members of the charitable organization and that they had a copy of the rulebook for conducting charitable games and would "be responsible for the conduct of the games in accordance with the provisions of the laws of the State and the rules and regulations of the department governing the conduct of such games." When the bingo and pull-tab license applications were rejected because they were not signed by members of the IAWV, Mariani testified that Shlifka had him obtain the signatures of veterans on amended license' applications. After they were submitted, the amended applications were accepted and bingo and pull-tab licenses issued. No license to conduct raffles was ever obtained.
While the licenses were being pursued, Shlifka held two planning meetings. Both meetings occurred before the operation of the games commenced, the first being held in January 1994 and the second in May 1994. Mariani and Carmen Trombetta  an IAWV member who, like Mariani, became deeply involved in the Grand Palace  testified that Useni and Cozzo attended both meetings. At the May meeting, Shlifka instructed the IAWV veterans working the games to deny that they were getting paid, if asked.
C. Operation of the Grand Palace
Once the games commenced, each IAWV post was ostensibly running one of the weekly gambling sessions. In reality, though, the veterans had little control over the games; their contribution was limited to selling pull-tabs, bingo cards, and raffle tickets to the hall's patrons. According to the IAWV members who testified at trial, the veterans did not control which games were played. They were not allowed to count the money generated by the games or be in the back room where the money was kept. They had no idea how much money was generated by the business. And they did not have any control over the checking accounts where the proceeds for the games were deposited.
*642 The real power over the games  and, most importantly, over the revenue generated from the games  was exercised by those who had access to the Grand Palace's back office, all of whom were non-veterans: Shlifka, Bingham, and Shlifka's daughter Laura Dostal, as well as Cozzo and Useni. Shlifka and Cozzo would determine which games would be played. After a veteran had completed selling his allotment of pull-tabs, raffle tickets, or bingo cards, someone from the back office would collect the gaming proceeds from the veteran and take the money to the back room. There, the money was collected and taken by Fred Bingham, the bookkeeper for the Grand Palace and a non-veterans, to deposit in accounts he controlled. Besides handling the money, Bingham, along with Dombrowski, filled out the quarterly bingo and pull-tab returns for the IAWV posts. On those returns, the number of pull-tab games being played was vastly under-reported, as was the revenue generated by the pull-tab games.
Cozzo, along with Shlifka, appeared to be running the hall. According to the testimony of the veterans who worked at the Grand Palace, as well as one of the undercover state revenue agents sent to investigate the Grand Palace's operations, Cozzo announced the rules of bingo prior to the session, sold bingo cards, verified winning bingo numbers, administered the raffles, sold pull-tabs, announced the pull-tab numbers, took the pull-tab proceeds to the back office, brought out new boxes of pull-tabs to sell, paid the veterans, and controlled the pull-tab machine on the wall, removing money from it and fixing it when it malfunctioned. In contrast, Useni worked primarily in the concession area of the Grand Palace. However, witnesses testified that he also verified winning bingo cards, sold pull-tabs and raffle tickets, provided raffle tickets to the veterans to sell, paid the veterans, walked around observing the workers and players, and installed, restocked, and removed the money from the pull-tab machine.
Both Useni and Cozzo were involved in obtaining the pull-tabs from Marotta. Marotta testified that Cozzo often ordered the pull-tabs from Marotta and picked them up at Marotta's place of business. Marotta stated that Useni also picked up the pull-tabs on occasion. Marotta further testified that he sold a tremendous volume of pull-tabs to the Grand Palace  massive in comparison to other bingo operations. Undercover state revenue agents sent to investigate the Grand Palace observed that the number of pull-tab games played at the Grand Palace exceeded the number allowed by law, which varied depending on the type of game played and total payout for the session. Since pull-tabs are required to be registered with the state, Cozzo, along with Shlifka, approached Marotta at one point and asked him to supply them unregistered pull-tabs. Marotta testified that he agreed to provide them with unregistered pull-tabs but that, unbeknownst to Cozzo and Shlifka, he continued to sell them registered pull-tabs.
D. Useni's Ownership of the Grand Palace
In June 1995, Useni purchased the Grand Palace from Shlifka. After the purchase, Useni and Cozzo were in charge of the hall, and they informed the others of the change in leadership. Marotta testified that Cozzo told him that "the heat was on" and that Shlifka was stepping down. Cozzo then told Marotta that he was in charge and, if there were any problems, to contact him. According to Levitanksy's testimony, Cozzo and Useni also met with him and told him that he should direct any questions about the Grand Palace to them. Additionally, Marian testified that Useni *643 talked to him and told him that he had bought out Shlifka; going forward, Mariani was to take orders from Useni.
Useni applied for a provider's license shortly after purchasing the Grand Palace. On that license, Useni signed a certification which read: "I . . . certify that no employee of mine shall manage or operate the games. I also state that I have read the applicable bingo or charitable games rulebook." Despite that certification, the games continued to be operated the same as they were under Shlifka's regime. Carole Johnson, Useni's girlfriend, testified that, when she asked Useni where the money from the games was going, Useni told her that it was going into a "slush fund" and that he was planning on retiring early.
During his ownership of the Grand. Palace, Useni hired Cesar Valera to work in the kitchen of the concession area. The kitchen had been Useni's primary area of responsibility before he purchased the Grand Palace. Valera testified that Useni paid him, like the veterans, in cash and he was not given a W-2.
E. Sale of the Grand Palace to Bingo Partners
Useni's ownership of the Grand Palace did not last long. Just eleven months after purchasing the hall, Useni sold it in May 1996 to Bingo Partners, Inc. ("Bingo Partners"), a group of veterans consisting of Mariani (the organizer), Trombetta, James Sarno, Rosario DiMarco, Sam Lenoci, and Michael. Riccio. Mariani testified that Useni had said that he needed to sell "right away."[4] According to Johnson, right before Useni sold the Grand Palace to Bingo Partners Useni told Johnson not to talk to anyone who came into the Grand Palace in a suit because Useni thought that might be an FBI agent. Useni also told Johnson that he thought the hall was bugged. Useni and Cozzo, along with Johnson, began shredding the pull-tabs, both the winning and losing tickets, placing the remains in opaque green bags.
The sale to Bingo Partners did not end Useni's and Cozzo's involvement with the Grand Palace. In addition to a $120,000 payment up front in exchange for the Grand Palace, Bingo Partners promised Useni and Cozzo further payments in a series of installments. Mariani testified that Cozzo and Useni repeatedly called Bingo Partners looking for those payments, which were made out of the money collected from the pull-tab machine. Trombetta testified that Cozzo and Useni lent Bingo Partners the money to operate the games to help Bingo Partners get established. Trombetta also testified that Useni promised to let Bingo Partners use his provider's license in exchange for $1000 a week. In addition, Mariani testified that Bingo Partners received help from Bingham, from whom Mariani sought advice on several occasions as to how to operate the hall.
Although Bingo Partners was now in charge, the operation of the Grand Palace did not differ significantly from when Useni owned the hall. Bingo Partners continued to pay the workers in cash and run the same games as the previous regime. A big change, however, was that the FBI began electronically monitoring the back room of the Grand Palace. As a result, the FBI was able to uncover evidence that the veterans comprising Bingo Partners were diverting a substantial portion of the *644 proceeds from the gambling into their own pockets. At the height of operation, Trombetta testified that each member of Bingo Partners took $800 to $1000 per week from the proceeds of the gambling. In order to prevent discovery of the skimmed proceeds by the state, the number of patrons attending the bingo sessions was significantly under-reported. As a consequence, the amount of proceeds from the bingo games went substantially underreported. Bingo Partners also did not report to the state the proceeds from the pull-tab machines or the raffles; instead, the members of Bingo Partners pocketed those funds.
F. Indicted
More than a year after Cozzo and Useni relinquished control of the Grand Palace to Bingo Partners, Cozzo became aware of an FBI investigation and took steps to head off prosecution. Cozzo attempted to ensure that Marotta kept quiet. (Recall that Marotta had been, the Grand Palace's biggest supplier and therefore knew the extent of the Grand Palace's operation.) In October 1997, Cozzo met with Marotta at Finkel's Deli. Cozzo told Marotta that the heat was on and that they were being investigated by the FBI. Cozzo warned Marotta to keep his mouth shut and to say nothing or else he would be a "dead man." Cozzo later repeated his threat to Marotta, this time over the phone after Marotta had met with the FBI, again telling Marotta that he was a "dead man."
Cozzo's efforts to stave off a federal prosecution were unsuccessful, though he was not formally charged until April 2002, when the government indicted him, Useni, Shlifka, Mariani, Trombetta, Sarno, DiMarco, Lenoci, Riccio, and James Prebis, who had replaced Bingham as the Grand Palace's bookkeeper during the tenure of Bingo Partners.[5] In count one of the indictment, Cozzo and Useni were charged with conspiring to conduct an enterprise's affairs through a pattern of racketeering activity in violation of 18 U.S.C. § 1962(d). The government alleged that Useni and Cozzo agreed to conduct and participate in the conducting of the affairs of an association-in-fact enterprise consisting of the Grand Palace, Cozzo, Useni, Shlifka, Mariani, Bingo Partners, and the members of Bingo Partners, through a pattern of racketeering activity that included operating an illegal gambling business and mail fraud. Count two of the indictment alleged that Cozzo and Useni conducted an illegal gambling business in violation of 18 U.S.C. § 1955. Counts three through nine alleged that Cozzo and Useni committed mail fraud in violation of 18 U.S.C. §§ 1341 and 2 because the bingo and pull-tab license applications Bingo Partners had submitted to the state on behalf of the IAWV posts in 1997 were part of a scheme to defraud. Count twenty-five alleged that Cozzo and Useni had conspired to commit tax fraud in violation of 18 U.S.C. § 371 by concealing income from the gambling at the Grand Palace. Counts twenty-six and twenty-seven alleged that Useni wilfully understated the Grand Palace's corporate income on the two corporate tax returns he signed as the Grand Palace's owner in violation of 26 U.S.C. § 7206(1).
G. Trial
Shlifka died after the indictment was handed down. Mariani, Trombetta, and DiMarco all pleaded guilty and agreed to testify against Useni and Cozzo.[6] In return, the government agreed to recommend that Trombetta receive a one-third *645 reduction in his sentence and that DiMarco receive a two-thirds reduction. In Mariani's case, the government agreed that Mariani could ask the district court for a sentencing departure based on his cooperation.
Useni and Cozzo proceeded to trial. The witnesses at the six-day trial included Mariani, Trombetta, and DiMarco, as well as Marotta, the Grand Palace's supplier who testified under a grant of immunity; Johnson, Useni's girlfriend who had previously testified before the grand jury under a grant of immunity[7]; and Agent Richard Lexby of the IRS, who testified as the government's summary witness, Lexby noted that during the period Useni owned the Grand Palace, pull-tab returns submitted to the state showed that 654 pull-tab games were played during the 259 sessions at the Grand Palace. However, Illinois revenue agents conducting surveillance at the Grand Palace observed 742 pull-tab games played over the 54 sessions the agents attended in the same time period. From that information, as well as testimony from the IAWV members who worked at the Grand Palace and the bingo and pull-tab returns filed with the state, Lexby estimated the total amount of money that had been diverted from the IAWV from 1994 to 1997 at $ 2,986,365.[8] According to Lexby, that figure was a conservative estimate because he did not attempt to include any calculation of the diverted proceeds from the pull-tab machines or the raffles held during the time period before the sale of the Grand Palace to Bingo Partners.
A jury found Useni and Cozzo guilty on all counts in which they were charged: the racketeering conspiracy count, the § 1955 illegal gambling business count, the mail fraud counts, and the tax counts. The district court sentenced Cozzo to ninety-six months of imprisonment and Useni to sixty months. Both Useni and Cozzo appeal.

II.
A. Sufficiency of the Evidence
We begin with the appellants' challenges to the sufficiency of the evidence *646 supporting their convictions. In challenging their convictions this way, both Useni and Cozzo bear "a heavy burden," since we must examine "[t]he evidence and all reasonable inferences that can be drawn from it . . . in the light most favorable to the government." United States v. Gardner, 238 F.3d 878, 879 (7th Cir.2001); see also United States v. England, 507 F.3d 581, 588 (7th Cir.2007) ("[A]n appeal does not deputize this Court as the ultimate trier of fact."). We will find the evidence insufficient "only if no rational trier of fact could have found guilt beyond a reasonable doubt." United States v. Hendrix, 482 F.3d 962, 966 (7th Cir.2007) (quoting United States v. Leahy, 464 F.3d 773, 794 (7th Cir.2006)).
1. RICO Conspiracy
Both Useni and Cozzo challenge the sufficiency of the evidence supporting their conviction under 18 U.S.C. § 1962(d). They argue that the evidence, even taken in the light most favorable to the government, does not show that they knew of the illegal gambling operation being conducted at the Grand Palace, nor that they agreed to join in the conspiracy.[9]
To be convicted of conspiracy under § 1962(d), one must knowingly agree to facilitate the activities of those who are operating an enterprise. United States v. Swan, 250 F.3d 495, 499 (7th Cir.2001); see also Brouwer v. Raffensperger, Hughes & Co., 199 F.3d 961, 967 (7th Cir.2000). While the government must show that there was an agreement between the members of the conspiracy; direct evidence need not be shown since "an agreement can be inferred from the circumstances." United States v. Campione, 942 F.2d 429, 438 (7th Cir.1991). However, "mere association with conspirators, knowledge of a conspiracy, and presence during conspiratorial discussions is not sufficient to convict a person of conspiracy." United States v. Percival, 756 F.2d 600, 610 (7th Cir.1985). The government has to show that the defendant was aware of the essential nature and scope of the enterprise and intended to participate in it. United States v. Stephens, 46 F.3d 587, 592 (7th Cir.1995).
The government has presented sufficient evidence to show that both Useni and Cozzo were aware of the scope of the enterprise and intended to participate in it. The evidence the government presented of the planning before the Grand Palace even commenced operation supported the jury's finding that Cozzo was aware of the scope of the enterprise and the illegalities that the enterprise was prepared to perpetrate. These illegalities included the submission of false and misleading license applications to the state and the routine, systematic violation of Illinois gambling laws. The evidence clearly showed that Cozzo intended to actively participate in their perpetration. Cozzo was present at the initial meeting with Marotta and was represented to Marotta as Shlifka's "partner." He was also present when Shlifka offered Mariani $100 for each gaming session hosted by an IAWV post recruited by Mariani. And he *647 was present at the two initial planning meetings in 1994, including the meeting where the IAWV veterans were instructed to deny that they were getting paid for working the games. From Cozzo's presence at those meetings, a jury could rationally conclude that Cozzo could not possibly have been unaware of how the Grand Palace was going to be doing business. Moreover, Cozzo had his sisters and girlfriend sign the application representing that they were IAWV members, even though they obviously were not. A reasonable jury could have interpreted Cozzo's falsification of that bingo license application as a sign of Cozzo's willingness to participate in the illegal enterprise.
The jury also had before it further evidence of Cozzo's active participation in the enterprise once the gambling commenced. After the Grand Palace opened its doors, Cozzo played a leading role; he was no bit player. Acting as a de facto manager of the hall, Cozzo had access to the back room, the control center of the gambling operation. He determined which games would be played, participated in the operation of the games, handled the gambling proceeds, and paid the veterans for their work  all in violation of Illinois law as well as § 1955. See Cyprian, 23 F.3d at 1199 n. 14 (to establish a violation of § 1955, the government must show that the defendant conducted, financed, managed, supervised, directed, or owned a gambling business that: (1) violated state law; (2) involved five or more persons; and (3) was either in substantial continuous operation for more than 30 days or had gross revenue of $2,000 or more in a single day).
And Cozzo remained a prominent figure in the enterprise even after the ownership of the Grand Palace was transferred to Useni. After the sale, Useni and Cozzo told Mariani, Levitansky, and Marotta that they would take orders from Cozzo and Useni. Additionally, Useni's girlfriend Johnson testified that Cozzo and Useni were in charge of the hall. A rational jury easily could conclude from all this that Cozzo agreed to facilitate the illegal enterprise.
But even if that were not enough, the jury had further evidence of Cozzo's guilty intent in the form of the shredding of the winning and losing pull-tab tickets prior to the, sale of the hall to Bingo Partners and the placing of the shredded remains in opaque bags. Furthermore, Marotta testified that Cozzo had attempted to get unregistered pull-tabs from him. Finally, the jury had before it Cozzo's threats to Marotta as well. Cozzo told Marotta he was a "dead man" if he talked to the FBI, and reiterated that threat to Marotta after Marotta had been in contact with the FBI. Those threats were made more than a year after Cozzo had ceased active involvement in the Grand Palace. When viewed in conjunction with the other evidence, they allowed the jury to find that Cozzo was aware of the scope of the enterprise and intended to participate in it.
The evidence supporting the jury's finding that Useni agreed to participate in the illegal gambling enterprise is similar to the evidence presented against Cozzo. While Useni's participation in the preparations for the opening of the Grand Palace was not as extensive as Cozzo's, there was evidence before the jury that Useni was also in on the illegal plan from the start. Shlifka introduced Useni to Mariani shortly after the plan for the Grand Palace was presented to Mariani. Useni also attended the two planning meetings in 1994 and therefore was present when Shlifka discussed concealing the fact that the veterans were getting paid. Moreover, like Cozzo, Useni was heavily involved in the illegal gambling occurring at the Grand Palace. Useni had access to the back *648 room. By assisting in the operation of the games and the paying of the veterans, he directly participated in the systematic violation of the Illinois gambling laws occurring at the Grand Palace.
While Useni's claim of ignorance of the criminal enterprise he was supporting is very weak, after he purchased the Grand Palace the claim is totally without merit. The undisputed testimony at trial was that Useni, along with Cozzo, was in charge of the hall after the sale. Despite Useni's certification on his provider application that he had read the charitable gambling rules and that none of his employees would manage or operate the games, the games continued to be run illegally. The evidence clearly showed that Useni both knew and intended to further the illegal gambling occurring at the Grand Palace on his watch.
Other substantial evidence of Useni's guilty knowledge buttresses that conclusion. Useni, like Cozzo, participated in shredding the used pull-tabs and placing them in opaque bags. Useni told Johnson that the money from the games was going into a "slush fund" that would allow him to retire early. Right before he sold the Grand Palace, Useni also told Johnson that he thought the Grand Palace was bugged and that she should not talk to anyone who appeared to be an FBI agent. From this evidence (that Useni was trying to cover his tracks), a rational jury could conclude that Useni knew he was implicated in the illegality underpinning the whole Grand Palace operation.
Given the volume of evidence against Useni and Cozzo on the racketeering conspiracy count, it is not surprising that Useni and Cozzo try to shift the focus away from the evidence on the record and concentrate their argument on what evidence was not presented at trial. They point to the absence of evidence that they ever skimmed any of the proceeds from the gambling and argue that the government has therefore failed in its evidentiary burden. That argument is a red herring. The government did not have to show that Cozzo and Useni purloined even one penny to convict them on the racketeering count. Instead, all the government needed to show was that they were aware of an enterprise involved in, among other things, gambling that was purposely and continuously in violation of the Illinois gambling laws, and that they intended to participate in it. As the preceding discussion shows, the government met that burden.
2. Mail Fraud Counts
Next, both Cozzo and Useni challenge their convictions on the seven mail-fraud counts. The mail-fraud counts involve bingo and pull-tab license applications that Bingo Partners submitted via the mails to the state of Illinois in 1997. Cozzo and Useni argue that they cannot be held liable for any mail fraud based on actions taken by Bingo Partners in 1997 because their involvement with the Grand Palace ceased in May 1996 when Useni sold the hall to Bingo Partners: Furthermore, they argue that there was no evidence that they knew of the mailing of any of the applications in 1997.
A conviction for mail fraud must be supported by evidence that a defendant participated in a scheme to defraud and caused the mails to be used in furtherance of that scheme. United States v. Barger, 178 F.3d 844, 847 (7th Cir.1999). A defendant need not actually have used the mails himself to be liable for mail fraud. Instead, the evidence is sufficient to support a conviction for mail fraud if the defendant acted "with the knowledge that [the use of the mails] would `follow in the ordinary course of business, or where such use [could] reasonably [have been] foreseen.'" *649 Am. Auto. Accessories, Inc. v. Fishman, 175 F.3d 534, 542 (7th Cir.1999) (quoting United States v. Alexander, 135 F.3d 470, 474-75 (7th Cir.1998)) (second alteration in original).
The jury in this case had sufficient evidence before it to convict Useni and Cozzo on the mail-fraud counts. As was outlined in the discussion of the racketeering conspiracy count, the jury could have reasonably found that Useni and Cozzo were willing participants in the scheme to defraud both the IAWV posts of gambling proceeds raised in their name and the state of Illinois of tax revenue. There was also evidence from which a reasonable jury could, conclude that the mailing of the license applications by Bingo Partners was in furtherance of the same fraudulent scheme, and that Useni's and Cozzo's participation in the scheme continued on into the time period in which Bingo Partners mailed the applications. The Grand Palace continued to be operated in the same manner after it was sold to Bingo Partners as when Useni and Cozzo were in charge. Indeed, Useni and Cozzo ensured that Bingo Partners would be able to continue operation of the hall. They left the money to operate the games for Bingo Partners to use until Bingo Partners got on its feet. Useni agreed to lend Bingo Partners the use of his provider's license in, exchange for $1000 a week. And Bingham, a stalwart in the previous regime, helped explain to the veterans comprising Bingo Partners how to run the Grand Palace.
Moreover, Useni and Cozzo had a financial incentive to make sure the Grand Palace did not fold under Bingo Partners's watch. The terms of the sale of the Grand Palace to Bingo Partners required Bingo Partners to make monthly payments to both, Cozzo and Useni. Those monthly payments were made from the proceeds of the gambling; they were taken directly from the pull-tab machine. Both Cozzo and Useni demonstrated their interest in those payments, as they called Bingo Partners on different occasions inquiring about the money owed them. In short, because of the aid they provided to Bingo Partners and the money they continued to receive from the gambling, both Cozzo and Useni continued to participate in the illegal scheme even after the Grand Palace was sold to Bingo Partners.
Finally, the jury had sufficient evidence to conclude that Useni and Cozzo reasonably could have foreseen the mailing of the bingo and pull-tab applications by Bingo Partners. The jury could reasonably have concluded that Cozzo was well aware that the continuing viability of the gambling at the Grand Palace depended on the annual renewal of the licenses, since he had attempted to have a bingo license application submitted using the names of his sisters and girlfriend. Similarly, Useni had submitted a provider application when he was owner of the Grand Palace and could therefore have anticipated that the bingo and pull-tab licenses had to be renewed annually as well. Accordingly, the jury's convictions on the mail fraud counts were supported by the evidence.
3. Tax Conspiracy
Useni and Cozzo also challenge their conviction for conspiring to commit tax fraud in violation of 18 U.S.C. § 371 by concealing income from the gambling at the Grand Palace.[10] They argue that the *650 evidence was not sufficient to show that they participated in the tax conspiracy.
To prove a violation of § 371, the government must establish: (1) an agreement to commit an offense against the United States, in this case to defraud the United States by wilfully concealing assets resulting in a failure to, report income in violation of 26 U.S.C. § 7206(4); (2) an overt act in furtherance of the conspiracy; and (3) knowledge of the conspiratorial purpose. United States v. Soy, 454 F.3d 766, 768 (7th Cir.2006). The evidence presented at trial, viewed in the light most favorable to the government, was sufficient to allow a reasonable jury to conclude that each of those three elements was met. Specifically, the government satisfied its burden with respect to two overt acts alleged in the indictment: the filing of a fraudulent Employer's Quarterly Federal Tax Return ("Form 941")[11] for the Grand Palace on October 31, 1995, and the filing of a false Corporation Income Tax Return ("Form 1120") on behalf of the Grand Palace on July 12, 1995.
Cozzo and Useni were in charge of the Grand Palace during the time period in which those two documents were filed. The Grand Palace's accountant, Levitansky, testified that Cozzo and Useni told him that he was to direct any questions to them. Cozzo and Useni knew that the veterans were being paid, since they attended the planning meeting where the payment of the veterans was discussed and even paid the veterans themselves on occasion. It is also undisputed that while Useni and Cozzo were in charge of the hall, the number of pull-tab games being played  and thus the revenue generated from the games  was massively under-reported on the quarterly pull-tab returns for the IAWV. Given that non-veterans like Bingham controlled the reporting on the bingo and pull-tab returns submitted on behalf of the IAWV posts, a reasonable jury could conclude that anything not reported as revenue for the. IAWV posts was going into the Grand Palace's coffers. And, as outlined in the first section, the jury could have reasonably concluded from the ample evidence of guilty intent that Cozzo and Useni were aware of the unreported proceeds, even if they did not personally profit from the purloined proceeds themselves. Finally, it is undisputed that neither Cozzo nor Useni reported to Levitansky the money being paid to the veterans or the unreported revenue from the pull-tab games. A reasonable jury could therefore conclude that Useni and Cozzo were participants in the conspiracy to defraud the United. States of tax revenue by under-reporting both the amount of wages paid to employees of the Grand Palace, as well as the earnings of the Grand Palace from unreported pull-tab games.
B. Useni's Trial Challenges
Besides his challenges to the sufficiency of the evidence, Useni makes several objections to the manner in which the trial was conducted. First, Useni argues that he should have been granted a new trial because statements made by the prosecutor at closing improperly shifted the burden of proof. A district court's decision not to grant a new trial is reviewed for an abuse of discretion. United States v. Emerson, 501 F.3d 804, 812 (7th Cir.2007). When Useni's lawyer raised this issue at trial, he did not direct the *651 trial court to any specific comment by the prosecutor. In his brief on appeal, Useni directs this court to a span of five pages of the trial transcript, although he still does not specify the exact comments that he finds prejudicial.
After reviewing those pages of the trial transcript, we do not find anything. improper. Some of the comments made by the prosecutor were about the defense's failure to ask questions of government witnesses.[12] In United States v. Kelly, 991 F.2d 1308, 1314 (7th Cir.1993), we held that a prosecutor may comment on a defendant's failure to call or ask particular questions of a witness so long as he does not tax the defendant's right not to, testify. Useni did not testify at trial. However, the prosecutor's comments, like the comments by the government lawyer in Kelly, were confined to responding to specific arguments defense lawyers had made about the credibility of two of the government's witnesses. Cf id. at 1313-14. The comments did not come close to "invit[ing] the jury to infer guilt from the defendant's decision not to testify," and therefore did not tax Useni's right not to testify. United States v. Sblendorio, 830 F.2d 1382, 1391 (7th Cir.1987). Useni's challenge to those comments is without merit.
Useni's second objection suffers a similar fate. Useni argues that he was deprived of a fair trial by a statement Cozzo's attorney made at closing about Cozzo's decision to testify. Unlike Useni, Cozzo testified during trial, and Cozzo's attorney sought to highlight that fact during closing. The statement by Cozzo's attorney to which Useni objects is the following: "Now, a defendant has a right not to testify. If Phil [Cozzo] didn't testify, you couldn't hold it against him. But he took the stand. He opened himself up to any of their questions and any of their rebuttal witnesses."
There is nothing improper about that statement. See United States v. Petullo, 709 F.2d 1178, 1182 (7th Cir.1983). In Petullo, we held that a similar statement by counsel, asking the jury only to draw favorable inferences from his client's willingness to testify, was not unfairly prejudicial to a nontestifying codefendant because the statement was limited and counsel concurrently stressed the right not to testify. Id. Petullo controls here, and Useni is not entitled to a new trial because of the comments by Cozzo's lawyer.
Next, Useni argues that the district court improperly prevented his counsel from impeaching Mariani, a high-ranking IAWV member and the organizer of Bingo Partners, by omission[13] the court excluded the testimony of Agent Michael Cole of the FBI and Agent Mark Lischka of the IRS. The district court's evidentiary decisions are reviewed for an abuse of discretion. United States v. Cunningham, 462 F.3d 708, 712 (7th Cir.2006). Furthermore, "when reviewing evidentiary errors, we will only reverse and order a new trial provided that the improper admission *652 was not harmless, which is to say `only if the error had a substantial influence over the jury, and the result reached was inconsistent with substantial justice.'" United States v. Owens, 424 F.3d 649, 653 (7th Cir.2005) (quoting United States v. Hernandez, 330 F.3d 964, 969 (7th Cir. 2003)).
Mariani testified that Useni at first demanded Bingo Partners pay cash for the Grand Palace. On cross-examination, Useni's lawyer asked Mariani if he told Agent Cole of the FBI about the cash demand at their June 9, 2003, proffer meeting, to which Mariani responded, "I probably was never asked." Useni's lawyer also asked Mariani if he told Agent Lischka about the cash demand at their March 10, 2004, proffer meeting. This time Mariani responded, "I would have to say `yes.'" After the conclusion of the government's case, Useni's lawyer made an offer of proof outside the presence of the jury and elicited testimony from Cole and Lischka in an attempt to impeach Mariani by omission. Cole testified, consistent with Mariani, that Mariani did not mention the cash demand when they discussed the purchase of the Grand Palace at their June 9, 2003, meeting. Lischka, on the other hand, contradicted Mariani's testimony and testified that the subject of the cash demand did not come up at their March 20, 2004, meeting. The district court excluded the testimony of both agents; Useni challenges that decision.
The district court acted well within its discretion when it excluded Cole's proffered testimony. That testimony just reiterated what Mariani had already implicitly admitted  that he did not mention the cash demand at his June 9, 2003, meeting with Cole. It did not aid in establishing the point, crucial for impeachment by omission, that the cash demand ought to have come up at that meeting and therefore its omission was suspect. In fact, Cole's testimony suggested just the opposite: that it would not have been natural for the cash demand to have come up during the proffer meeting.[14] Thus, while Useni was free to argue to the jury that the cash demand was the type of information that should naturally have come up during the proffer meeting with Cole, and thereby impeach Mariani by omission, Cole's testimony was not helpful for establishing impeachment by omission and the district court did not abuse its discretion by excluding it.
The exclusion of Lischka's testimony is more problematic. Mariani's testimony that he told Lischka of the cash demand was directly contradicted by Lischka himself, who said that the cash demand was not mentioned. The government argues that Lischka's testimony was not necessary because the district court perfected Mariani's impeachment by permitting Useni's lawyer to argue at closing, without contradiction from the government, *653 that Mariani did not tell Lischka about the cash demand. But Lischka's impeaching evidence was not before the jury, and  as the court instructed the jury  lawyer's arguments are not evidence. Mariani's testimony that he thought he did tell Lischka thus stood unrebutted on the record. Nevertheless, any error that occurred from the exclusion' of Lischka's testimony was harmless. That Useni wanted to be paid in cash for the bingo hall, though relevant to show Useni's guilty intent, was hardly the centerpiece of the government's evidence on that point. As was outlined in the discussion of the sufficiency of the evidence on the racketeering conspiracy count, the government had overwhelming evidence to prove Useni's guilty intent without the evidence of the cash demand even being considered.
Besides his challenge to the exclusion of Lischka's and Cole's testimony, Useni also challenges the admission of certain testimony from several other witnesses. Those challenges do not merit extended discussion. Rather, it suffices to say that those objections relate to arguments we have already rejected, such as Useni's contention that he did not participate in either the racketeering or tax-fraud conspiracies, or his contention that he had no part in the illegal scheme after Bingo Partners bought the Grand Palace.[15] Because the evidence supported the contrary of what Useni is contending, the district court did not abuse its discretion in admitting the evidence to which Useni now objects.
Moving, on, Useni argues that the district court erred by failing to give his, proffered theory of defense instruction.[16] We review de novo a district court's refusal to give a theory of defense instruction.[17]United States v. Eberhart, 467 F.3d 659, 666 (7th Cir.2006).

*654 A defendant is entitled to a jury instruction as to his or her particular theory of defense provided: (1) the instruction represents an accurate statement of the law; (2) the instruction reflects a theory that is supported by the evidence; (3) the instruction reflects a theory which is not already part of the charge; and (4) the failure to include the instruction would deny the appellant a fair trial.
United States v. Prude, 489 F.3d 873, 882 (7th Cir.2007). The district court refused to give the proffered instruction "as drafted" because it believed that the instruction was "basically the defendant testifying without being subject to cross-examination." In addition, the district court believed that the proffered instruction was more akin to argument than to a presentation of the defense's theory.
We find no error in the exclusion of Useni's proffered instruction. The proffered instruction was not a typical theory of defense instruction. Cf. United States v. Paters, 16 F.3d 188, 190 (7th Cir.1994); see also United States v. Josleyn, 99 F.3d 1182, 1194 (1st Cir.1996). The district court was correct when it observed that a good portion of Useni's proposed instruction was better suited for closing argument than a theory of defense instruction. Argument is not the purpose of a theory of defense instruction, see United States v. Scott, 19 F.3d 1238, 1245 (7th Cir.1994), yet Useni's proposed instruction contained a string of arguments, couched as factual statements about Useni's state of mind. The statements were argumentative because they were more about the evidence the government had failed to produce than what evidence was actually before the jury. Furthermore, one of those statements  that Useni was not aware that helping run the games violated state law &was completely unsupported by the evidence.
To the extent that Useni's proposed instruction did convey his theory of defense, that theory was already adequately covered in the charge to the jury. United States v. Irorere, 228 F.3d 816, 826 (7th Cir.2000) ("[A] defendant is only entitled to such an instruction when his theory of defense is not already adequately captured by the proffered instructions."). Useni's theory at trial was that he was just a grunt worker at the Grand Palace, a janitor and kitchen manager who had no idea what was really going on there. The instructions read to the jury emphasized in several places that the jury had to find that Useni knew about the illegal activity occurring at the Grand Palace and willingly participated in it before the jury could convict him. The jury was instructed that Useni had to "knowingly" join the racketeering conspiracy, as well as "knowingly" participate in the scheme to defraud. The jury was also instructed that "knowingly" meant "the defendant realized what he was doing and was aware of the nature of his conduct, and did not act through ignorance, mistake or accident." The jury was further instructed that "the Government must prove beyond a reasonable doubt that the defendant was aware of the common purpose and was a willing participant in the charged conspiracy." Finally, the jury was instructed that
[a] defendant's presence at the scene of a crime and knowledge that a crime is being committed [are] not alone sufficient to establish the defendant's guilt.
A defendant's association with conspirators or persons involved in a criminal enterprise or a scheme to defraud is not by itself sufficient to prove his participation or membership in a conspiracy, mdash; *655 scheme to defraud and/or a criminal enterprise.
If a defendant performed acts that advanced a criminal activity, but had no knowledge that a crime was being committed or was about to be committed, those acts alone are not sufficient to establish the defendant's guilt.
Those instructions, along with the closing argument of Useni's counsel, clearly conveyed Useni's theory of defense to the jury. Cf. United States v. Hendricks, 319 F.3d 993, 1006 (7th Cir.2003) (finding that the charge given, which included an instruction that the jury had to find that the defendant knowingly and intentionally possessed the firearm in order to convict, coupled with the defendant's ability to argue his theory in front of the jury, fully presented the defense's theory in a prosecution for illegal possession of a firearm). Consequently, Useni was not deprived of a fair trial by the exclusion of his theory of defense instruction.
Finally, Useni asserts that the cumulative effect of all the errors he alleges occurred at trial amounts to reversible error. Although an error by itself may be harmless and insufficient to taint a jury, the combined effect of multiple erroneous rulings may result in significant harm necessitating another trial. United States v. Smith, 502 F.3d 680, 690 (7th Cir.2007). However, in this case we have discerned, at most, one trial error  and that error was harmless. See Alvarez v. Boyd, 225 F.3d 820, 824 (7th Cir.2000). Useni's cumulative effect argument therefore fails.
C. Dismissal of the Indictment
In addition to his challenges to the sufficiency of the evidence, Cozzo also asserts that the district court erred in refusing to dismiss the indictment.[18] On appeal, Cozzo focuses on three grounds upon which he believes the district court ought to have dismissed the indictment. First, Cozzo claims that the district court erred in denying his motion to dismiss the indictment on the ground that the five-year statute of limitations, prescribed, in 18 U.S.C. § 3282(a), had run when Cozzo was indicted on April 25, 2002. "We review de novo whether the limitations period has run, giving deference to necessary factual determinations by the district court." United States v. Are, 498 F.3d 460, 464 (7th Cir.2007).
At the outset, we note that Cozzo's argument that, the statute of limitations had run when he was indicted requires this court to conclude that Cozzo's involvement in the illegal activity occurring at the Grand Palace ceased when Bingo Partners took over the hall. The indictment charged Cozzo with multiple conspiracies, as well as conducting an illegal gambling business. Although the indictment alleged that the conspiracies and the operation of the illegal gambling business began in 1994, well outside of the statute of limitations period, it also alleged that they continued on until 1999, well inside the statute of limitations period. To stay within the statute of limitations period, Cozzo would have to have continued his involvement in the conspiracies and the illegal gambling business after Useni sold the hall to Bingo Partners, or at least the government would have to show that Cozzo did not withdraw from participating in any of them after' the sale of the Grand Palace. United States v. Curry, 977 F.2d 1042, 1058 (7th Cir.1992). If either of those were the case, the statute of limitations *656 posed no barrier to Cozzo's prosecution since Bingo Partners continued to engage in illegal activity  including operating the illegal gambling business and committing the conduct underlying the substantive mail-fraud counts  into the statute of limitations period. See United States v. Yashar, 166 F.3d 873, 875 (7th Cir.1999) (noting that conspiracies, such as the RICO and tax conspiracy charged here, are "continuing offenses" that continue for purposes of the statute of limitations so long as any action is taken in furtherance of the conspiracy); see also United States v. Jeffers, 532 F.2d 1101, 1108-09 (7th Cir.1976), vacated in part on other grounds, 432 U.S. 137, 97 S.Ct. 2207, 53 L.Ed.2d 168 (1977) (noting that the offense of conducting an illegal gambling business under 18 U.S.C. § 1955 necessarily entails conspiring to conduct an illegal gambling enterprise, thus making a § 1955 violation a continuing offense). Because we have already found in the context of discussing Useni's and Cozzo's liability for the substantive mail-fraud counts that there was sufficient evidence from which a jury could conclude that Useni and Cozzo continued to participate in the illegal activity occurring at the Grand Palace even after it was sold to Bingo Partners, Cozzo's statute of limitations argument fails. Thus, the district court properly ruled that § 3282(a) was not an obstacle to Cozzo's prosecution.
Next, Cozzo takes issue with the district court's denial of his motion to dismiss the indictment based on prosecutorial misconduct in front of the grand jury. Cozzo argues that the government improperly elicited testimony from witnesses who testified that Cozzo was an owner of the Grand Palace. Cozzo asserts that those references to him as the owner of the Grand Palace were untrue and improperly influenced the grand jury's decision to indict him. We review a district court's denial of a motion to dismiss an indictment based on prosecutorial misconduct for abuse of discretion. United States v. Burke, 425 F.3d 400, 412 (7th Cir.2005).
The government's knowing use of false testimony violates due process. Id. at 412. For an indictment to be dismissed on account of false testimony presented to the grand jury, the defendant must show prejudice amounting to either "proof that the grand jury's decision to indict was substantially influenced, or that there is `grave doubt' that the decision to indict was substantially influenced, by testimony which was inappropriately before it." United States v. Feurtado, 191 F.3d 420, 424 (4th Cir.1999) (citing Bank of Nova Scotia v. United States, 487 U.S. 250, 256, 108 S.Ct. 2369, 101 L.Ed.2d 228 (1988)). Cozzo has failed to make that showing. He offers no evidence or argument that counters the district court's finding that whether or not Cozzo owned the Grand Palace was irrelevant to the grand jury's decision to indict him because ownership was not an element of any of the' charged offenses. Thus, the district court did not abuse its discretion by denying Cozzo's motion.
Lastly, Cozzo argues that the district court erred in denying his motion to dismiss count two of the indictment. Count two charged the defendants with operating an illegal gambling business in violation of 18 U.S.C. § 1955. Cozzo argues that § 1955 was meant to combat large-scale illegal gambling used to fund organized crime, not the type of "technical" violations of Illinois gambling law involved in this case. Cozzo cites United States v. Zizzo, 120 F.3d 1338 (7th Cir. 1997), as an example of the factual scenario to which § 1955 was meant to apply. Zizzo involved an illegal sports-betting organization, the proceeds from which were used to fund the Chicago Outfit, a notorious *657 crime syndicate. 120 F.3d at 1343-44. In contrast to the gambling operation in Zizzo, Cozzo argues that, by applying § 1955 to this case, the government is allowed to bring racketeering charges against people whom Congress never intended the racketeering laws to prosecute.
Cozzo's argument is without merit. Nothing in the text of § 1955 prevents its application to misdemeanor violations of state gambling law. Section 1955 makes it a crime to "conduct[ ], finance[ ], manage[ ], supervise[ ], direct[ or own[ all or part of an illegal gambling business." 18 U.S.C. § 1955(a). To prove the existence of an illegal gambling business, the government must demonstrate that the business violated "the law of [the] State or political subdivision in which it is conducted." 18 U.S.C. § 1955(b)(1)(i). The text of § 1955 does not distinguish between state misdemeanor and felony law. Rather, all it requires is that the gambling violate state law, regardless of whether the violation amounted to a felony or simply a misdemeanor.
Cozzo fails to point to any case law that undermines our reading of § 1955. Indeed, case law appears contrary to his position. The Eighth Circuit rejected a similar challenge to § 1955 in United States v. Matya, 541 F.2d 741 (1976). The defendants in Matya argued that Congress did not intend for § 1955 to be used to elevate a state law misdemeanor into a federal felony. In rejecting that argument, the Eighth Circuit noted that violation of state law is not the sole element of a § 1955 offense, which also requires the involvement of five or more persons in a gambling business either in substantial continuous operation for a period of thirty or more days, or involving gross revenues of $2,000 in any single day. Id. at 748. Thus, it was inaccurate to characterize § 1955 as simply "elevating" a state misdemeanor into a federal felony.[19]Id. Furthermore, the Eighth Circuit found it significant that the House Report which accompanied the Organized Crime Control Act of 1970, of which § 1955 is a part, made no mention of any distinction between state felonies and state misdemeanors in the application of § 1955. Id. Finally, because "[m]ajor gambling activities were a principal focus of congressional concern," the Eighth Circuit found that it could not conclude that Congress had ruled out the use of state misdemeanors as a predicate to a § 1955 violation. Id. (quoting Iannelli v. United States, 420 U.S. 770, 787, 95 S.Ct. 1284, 43 L.Ed.2d 616 (1975)) (alteration in original).
We agree with the Eighth Circuit. This case, in fact, offers a perfect example of why Congress did not distinguish between misdemeanor and felony violations of state gambling laws for purposes of § 1955. To operate the Grand Palace in the manner that Cozzo and his cohorts did, the Illinois gambling laws had to be systematically flouted. Though each violation of the Illinois gambling laws in this case, considered individually, may have been a mere "technical" or "minor" violation, in the aggregate they allowed the operators of the Grand Palace to divert from the games almost $3 million in illegal proceeds, a figure which represented the government's *658 conservative estimate of the illegal proceeds.
Cozzo has presented nothing to persuade us, in contravention of the case law and clear text of § 1955, that § 1955 was meant to apply only to felony violations of state gambling law with an organized crime nexus. We therefore do not find any error in the district court's failure to dismiss the § 1955 count because it was predicated on misdemeanor violations of the Illinois gambling laws.
D. Sentencing
While both Useni and Cozzo mention their sentencing in their briefs, neither provides argument substantial enough to warrant appellate review. "We have repeatedly warned that perfunctory and undeveloped arguments, and arguments that are unsupported by pertinent authority, are waived. . . ." United States v. Holm, 326 F.3d 872, 877 (7th Cir.2003) (internal quotation omitted); see also 330 W. Hubbard Restaurant Corp. v. United States, 203 F.3d 990, 997 (7th Cir. 2000) ("In order to develop a legal argument effectively, the facts at issue must be bolstered by relevant legal authority; a perfunctory and undeveloped assertion is inadequate to raise a separate basis for appeal."). Cozzo's opening brief does not contain any argument concerning his sentencing. It simply states, "Cozzo seeks leave to supplement the record with the sentencing transcript and to supplement this brief with an argument concerning sentencing should it be appropriate." Consequently, he has waived any appellate review of his sentence. United States v. Hook, 195 F.3d 299, 310 (7th Cir.1999) ("A party's failure to address or develop a claim in its opening brief constitutes a waiver of that claim. . . . ").
Useni's discussion is hardly better. Useni only devotes a page and a half to his sentence in his opening brief. In that space, Useni does no more than provide the standard of review for sentencing decisions, list three unsupported factual assertions, and claim that his sentence was per se unreasonable. Cf. Hook, 195 F.3d at 310 (broad language and unsupported assertions insufficient to merit review). Useni does not cite to relevant authority to support his argument. See Sanchez v. Miller, 792 F.2d 694, 703 (7th Cir.1986) (failure to cite relevant authority constitutes a waiver). Because Useni has failed to develop his reasonableness argument in any meaningful way, he has waived appellate review of his sentence. See Sere v. Bd. of Trs. of Univ. of Ill., 852 F.2d 285, 287 (7th Cir.1988) ("It is not the obligation of this court to research and construct the legal arguments open to parties, especially when they are represented by counsel.") (quoting Sanchez, 792 F.2d at 703).

III.
The evidence was sufficient to support Useni's and Cozzo's convictions for racketeering conspiracy, mail fraud, and tax fraud. The district court did not commit any error that deprived Useni of a fair trial, nor did it err in refusing to dismiss the indictment. Finally, because both Useni and Cozzo failed to develop any arguments as to why their sentences were unreasonable, they have waived any appellate review of the same. We AFFIRM.
NOTES
[1]  A pull-tab is a card with a pattern of symbols on the front and perforated tabs on the back. The tabs, when pulled back, reveal colored play symbols. If the symbols on the back match the pattern of symbols on the front of the card, then the player wins the prize indicated on the card.
[2]  Bingo and pull-tab licensees are required to pay 5% of the gross proceeds of the games to the Illinois Department of Revenue. 230 ILCS 20/5; 230 ILCS 25/3.
[3]  Shlifka died after the indictment in this case was handed down but before trial began.
[4]  The record does not disclose whether Useni or Cozzo had actual knowledge of an FBI investigation of the Grand Palace in 1996. Coincidentally, however, the FBI obtained an order authorizing the interception of oral communications in May 1996, the same month that Useni sold the Grand Palace to Bingo Partners.
[5]  Bingham died before the grand jury handed down the indictment.
[6]  Sarno, Lenoci, and Prebis all entered guilty pleas but did not testify at Cozzo's and Useni's trial. As for Riccio, the record does not indicate whether he ever pleaded guilty or went to trial after his counsel filed an unopposed motion to sever his trial from the other defendants on account of his deteriorating medical condition.
[7]  At trial, Johnson testified that she has been married for over thirty years and that she was married at the time she was having a relationship with Useni.
[8]  Lexby arrived at that figure by adding up his estimate of the unreported pull-tab profits and bingo proceeds. Lexby based the figure for the bingo proceeds on the taped backroom conversations obtained while Bingo Partners operated the Grand Palace. On the other hand, Lexby based the figure for the unreported pull-tab profits on what went unreported during Cozzo's and Useni's tenure at the Grand Palace, since the last time there was a discrepancy between the actual number of pull-tab boxes sold and the number of pull-tab boxes reported was the first quarter of 1996, the last quarter Useni and Cozzo were actively involved in the operation of the Grand Palace before its sale to Bingo Partners. To calculate the unreported pull-tab profits from 1994 to 1996, Lexby multiplied $5745 times the number of sessions to get a figure representing total pull-tab revenue. Lexby used the $5745 amount because that represented 10 boxes of pull-tabs sold, which, based on the evidence, was the average number of boxes that were sold each session. Lexby then subtracted the pull-tab proceeds reported to the state from his calculation of the total pull-tab revenue to arrive at the total amount of unreported proceeds. From there, Lexby multiplied the unreported proceeds by .30, a profit multiplier that Lexby had calculated by dividing the reported pull-tab proceeds by the reported pull-tab profits, and obtained $959,426, a number representing the estimated unreported pull-tab profits; in other words, the amount that the operators of the Grand Palace kept and did not give to the IAWV posts from the sale of pull-tabs between 1994 and 1996.
[9]  To the extent that Useni and Cozzo also challenge their convictions for engaging in an illegal gambling operation under 18 U.S.C. § 1955 on the same grounds, such an argument is foreclosed by this court's opinion in United States v. Cyprian, 23 F.3d 1189, 1199 (7th Cir.1994). In Cyprian, we stated that knowledge that an activity is illegal is not a necessary element of a § 1955 offense. Furthermore, even if knowledge were necessary, our analysis of their challenges to the sufficiency of the evidence to support their convictions under § 1955 would be essentially the same as the analysis we employ for their challenges to their convictions for conspiring to commit racketeering offenses; thus, there is no need to address those challenges separately.
[10]  Useni also challenges his two convictions under 26 U.S.C. § 7206(1) for wilfully understating the Grand Palace's corporate income on the July 12, 1995, return and the May 20, 1998, amended return for the Grand Palace. (Useni was charged with those offenses because he signed those returns.) Because the analysis is essentially the same for those two counts as for the § 371 offense, Useni's sufficiency challenge to his convictions on those counts does not merit separate discussion,
[11]  A Form 941 is the document on which an employer reports to the Internal Revenue Service the wages it has paid to employees. See 26 C.F.R. § 31.6011(a)-1.
[12]  For example, Useni's lawyer at closing had suggested that Carole Johnson, Useni's ex-girlfriend, was biased against him because they had broken up. In response, the prosecutor pointed out that Johnson had never been asked about her current feelings for Useni while she was on the stand.
[13]  "The theory of impeachment by omission is that `if [a] former statement fails to mention a material circumstance presently testified to, which it would have been natural to mention in the prior statement, [then] the prior statement is [considered] sufficiently inconsistent' to be admitted to impeach the present testimony." Moylan v. Meadow Club, Inc., 979 F.2d 1246, 1249 (7th Cir.1992) (quoting 1 John W. Strong, McCormick on Evidence § 34 at 114-15 (4th ed. 1992)) (first alteration in original).
[14]  As to why he did not ask Mariani about the form of payment for the Grand Palace, Cole testified:

We had the contracts and everything and we saw that they were paid by check. didn't  I guess at the time none of us really thought to ask him. You know, if you are drawing up a legal contract it is probably going to be fairly difficult to be paid, in cash and not have that.
The district judge appeared to reach the same conclusion:
Now, I don't want to leap to anybody's defense here, but if Useni is, in fact, paid by check, there is a contract which looks like it is payment by check, why would somebody ask the question  why would it necessarily be, or even likely to be the question asked[?] . . . Why would anybody say  did he ask" for another form of payment[?] Somebody might ask that question, but why is it so incredible that no one would?
[15]  Useni also argues that evidence as to whether a particular witness was a veteran was not relevant and should not have been elicited by the government's attorney. But that evidence was very relevant, considering that the jury had to know who was or was not a veteran in order to determine if the Illinois gambling laws were being violated. Consequently, we see no error in the district court having admitted such testimony.
[16]  Useni proposed the following instruction:

It is defendant Frank Useni's theory of defense that he began working at the Grand Palace Bingo Hall in May 1994 as the kitchen manger [sic] and the janitor in effect, which were his main and almost exclusive duties continually during the entire time he was there; that he was later offered the opportunity to buy the. Hall which appeared to offer a purchaser the opportunity to earn additional money by selling bingo supplies, which were then being sold to the veterans at the Grand Palace and by keeping the profits generated by the kitchen;
That, while present at the Grand Palace Bingo Hall, he never knowingly directly or indirectly joined any conspiracy, scheme to defraud or criminal enterprise to commit any illegal acts of any kind;
In that regard, at no time was he aware that volunteering to help veterans in any way with the Bingo or related games on occasion violated any federal or state laws or that the mere existence of any of these games at the Hall violated any such laws;
Further, that, he neither was involved in nor aware of the preparation and/or filing of any of the Bingo Applications and/or Tax returns and Pull-tab Returns that were filed on behalf, of the Grand Palace, Inc. were materially false.
Finally, that the only payments he received from his employment with the Grand Palace Bingo Hall  his wages and his payments for the sale of the Hall  were lawful under state, and thus, federal law, and that he never knowingly participated in any scheme, conspiracy or criminal enterprise to receive or allow others to receive any unlawful monies.
[17]  Although the government argues that this issue should be reviewed for plain error due to Useni's failure to object, we find that Useni did properly preserve the issue for the same reasons given in United States v. James, 464 F.3d 699, 707 n. 1 (7th Cir.2006).
[18]  In his brief, Useni adopts all of Cozzo's arguments concerning the dismissal of the indictment.
[19]  The Eighth Circuit agreed with the Ninth Circuit's conclusion that it was constitutionally permissible for Congress to define a federal felony partially in terms of a state misdemeanor. See id. at 749 n. 16 ("Congress's power to proscribe conduct carries with it the power to impose appropriate penalties without attempting to match them to varying state punishments for similar conduct." (quoting United States v. Kerrigan, 514 F.2d 35, 37 n. 1 (9th Cir.1975))).
