PHILLIPS, District Judge, sitting by designation.
This gambling prosecution stems from a thirty-five (35) count indictment returned by a federal grand jury sitting in Colorado on February 5, 1986. The indictment charged fourteen defendants, including the seven appellants here, with violating several federal criminal statutes. The pertinent statutes on appeal are 18 U.S.C. § 1955 (operating an illegal gambling business in violation of the laws of Colorado, involving five or more persons, with gross wagers in excess of $2,000 on any single day), 18 U.S.C. § 1952 (interstate use of a telephone to facilitate the gambling business); 26 U.S.C. § 7201 (income tax evasion), 26 U.S.C. § 7262 (failure to pay gambling occupation tax), and 26 U.S.C. § 7203 (failure to file requisite tax forms).
Four defendants entered pleas of guilty prior to trial. Three defendants were acquitted on all charges by the jury. The remaining seven defendants, appellants here, suffered convictions on the counts depicted in the chart below:
CHARGES AND COUNTS OF CONVICTION
18 U.S.C. § 1955 18 U.S.C. § 1952 26 U.S.C. § 7201 26 U.S.C. § 7262 26 U.S.C. § 72031
Aaron Mosko Ct. 1 Cts. 2,3 Cts. 8,9 Ct. 10
Phil Pinelli Ct. 1 Cts. 6,7 Cts. 11,12 Ct. 13
David Pinelli Ct. 1 Ct. 15 Ct. 14
William Burbidge Ct. 1 Ct. 18 Cts. 16,17
Martin Mosko Ct. 28
Thomas Gottone Ct. 1 Ct. 27
Robert Sheehan Ct. 1
Appellants have raised numerous issues on appeal. The principal issues involve: (1) challenges to the sufficiency of the evidence by various appellants; (2) constitutional challenges to 18 U.S.C. § 1955 and the applicable Colorado gambling statutes; (3) the trial court’s denial of a mistrial motion arising out of the inadvertent submission of non-evidentiary materials to the jury during deliberations; (4) the admission of expert gambling testimony offered by the government; (5) the trial court’s denial of appellants’ motions to suppress all evidence obtained as a result of a court-authorized wiretap; and (6) the trial court’s denial of severance motions made by two defen[1465]*1465dants at the close of the government’s case. We find that there was abundant evidence from which a reasonable jury could find the defendants guilty of the offenses for which they were convicted, and further find no reversible error in the record of this case. Accordingly, we affirm the convictions of all seven appellants.
I. SUFFICIENCY OF THE EVIDENCE
In a challenge based upon the sufficiency of the evidence, we must affirm the judgment of conviction if there is record evidence which would allow a rational trier-of-fact to find the appellants guilty of the crimes charged in the indictment. Jackson v. Virginia, 443 U.S. 307, 324, 99 S.Ct. 2781, 2791, 61 L.Ed.2d 560 (1979). Moreover, this Court must view the evidence in the light most favorable to the government. Glasser v. United States, 315 U.S. 60, 80, 62 S.Ct. 457, 469, 86 L.Ed. 680 (1942); United States v. Hooks, 780 F.2d 1526, 1529-31 (10th Cir.), cert. denied, 475 U.S. 1128, 106 S.Ct. 1657, 90 L.Ed.2d 199 (1986). Viewed in that light, we conclude that the evidence, both direct and circumstantial, satisfies the test.
The government’s evidence at trial focused on appellants’ gambling activities from September through December, 1984. The evidence consisted of the testimony of thirty-six (36) witnesses, including numerous bettor witnesses, the introduction of several hundred tape recordings of telephone conversations intercepted pursuant to court-authorized electronic surveillance, documentary evidence seized pursuant to search warrants executed on December 9, 1984 after the termination of the wiretap, and expert testimony by an FBI agent on the roles played by the various defendants in the gambling operation.
The electronic surveillance in this case was active for approximately twenty-four days in November and December, 1984. The government’s wiretap evidence and seized records in this case indicated the gambling business in question accepted wagers in excess of $2,300,000 in November and December, 1984. [Exs. 608-611].
Special Agent William Holmes of the Federal Bureau of Investigation testified as an expert witness for the government as to the roles of each of the participants m the gambling activity in question. His opinions were based on review of the electronic surveillance and search evidence. [Supp. Vol. 1, p. 36]. He did not rely on and was not privy to the testimony of the bettor witnesses. [Id.]. At the outset of his testimony, Holmes explained some basic gambling terminology which will be helpful in explaining the roles of each of the appellants.
Holmes described the “point spread” or “line” as having the purpose of attracting equal amounts of betting on each side of a contest. Bookmakers change the line on a particular game to attract betting on the other team. A line of “Denver minus six” means Denver is favored by six points and to win a bet on Denver, Denver must win by seven or more points. The term “vig” or “vigorish” represents a ten percent commission charged to losing bets, which compensates the bookmaker for the privilege of placing bets. In other words, a $100 losing bet would require payment of $110, which payment includes a $10 “vig”. According to Holmes, a bookmaker theoretically strives to accept the same amount of bets on each side of a contest, or balance his books, and take the “vig” as profit.
Agent Holmes explained the concept of “lay-off wagering” as that which allows a bookmaker “to get rid of wagers that he feels he is not financially able to handle and reduce the risk of great financial loss by having to pay off on large sums of money.” [Supp. Vol. 1, pp. 16-25]. The following example of lay-off wagering was provided by Holmes during his testimony: Suppose Bookmaker X has wagers of $1,500 on team A and $1,000 on team B. Bookmaker X would lay-off the $500 excess on team A with Bookmaker Y. If team A wins, Bookmaker X would collect $1,000 from those who bet on team B, plus the 10% vig for a total of $1,100. Bookmaker X would collect his $500 lay-off wager from Bookmaker Y, which would make the total amount collected $1,600. From this amount, he would have to pay his bettors who had bet $1,500 on team A. Bookmaker X would thus make a profit of $100 without risking any of his own money. If [1466]*1466Bookmaker X had not laid-off his excess wagers and team A had won, then he would have collected $1,100 from the losers ($1,000 + 10% vig) and had to pay out $1,500 to the winners for a net loss of $400. [Supp. Vol. 1, pp. 16-25]. As will be shown, the concept of lay-off wagering played a central role in the successful prosecution of appellants.
Viewing the evidence in the light most favorable to the government, as we must, a brief summary of the evidence pertaining to each appellant is set forth below:2
A. Aaron Mosko
The evidence in this case demonstrated that defendant Aaron Mosko was in the business of accepting wagers on sporting events. The government’s analysis of the evidence used in reconstructing the gambling activity demonstrated that Aaron Mosko accepted over $1,000,000 in wagers in November and December, 1984. [Ex. 609]. The government also introduced evidence, including numerous wiretap conversations, which demonstrated that defendant Aaron Mosko exchanged line information with various defendants and placed lay-off wagers with other bookmakers. The evidence further established that certain defendants placed lay-off wagers with other bookmakers on behalf of Aaron Mos-ko. [Ex. 384-A, Vol. 14, p. 20; Ex. 172-A, Vol. 9, p. 115; Ex. 180-A, Vol. 9, p. 116; Ex. 616, Vol. 18, p. 12-56; Ex. 617, Vol. 18, p. 12-61; Ex. 368-A, Vol. 14, p. 36; Ex. 609].
Taped conversations between Aaron Mos-ko and Phil Pinelli were played at trial in which Pinelli gave Mosko the line on numerous games. [Ex. 384-A, Vol. 14, p. 20; Ex. 172-A, Vol. 9, p. 115]. The jury also heard a conversation between Phil Pinelli and Aaron Mosko where Mosko and Pinelli agreed to line movements on the SMU-Arkansas game. [Ex. 180-A, Vol. 9, p. 116]. The government also introduced a taped conversation between Mosko and Thomas Gottone in which Mosko advised Gottone of the lines on various games. [Ex. 396-A, Vol. 14, p. 23],
Also introduced at trial was a series of taped conversations between Mosko and Robert Sheehan in which Sheehan asked Mosko if he was “alright”, to which Mosko responded by asking Sheehan to see what he could “get Miami and Seattle at.” [Ex. 368-A, Vol. 14, p. 26]. Sheehan later called back reporting the lines on the Miami and Seattle games to Mosko who then appeared to request Sheehan to place wagers on the two games for him. [M]. Additional taped conversations introduced by the government consisted of Aaron Mosko discussing with bettors the mechanics of “laying-off” and alluding to the fact that he made lay-off bets. [Ex. 530-A, Vol. 11, pp. 5-33 to -34; Ex. 616, Vol. 18, p. 12-56; Ex. 617, Vol. 18, p. 12-61].
FBI Agent Holmes, the government’s expert, testified that Mosko was in the business of accepting sports wagering activity and that Martin Mosko was at least a “phoneman” for Aaron Mosko who accepted wagers from bettors and relayed them to Aaron Mosko.3 He described individuals identified as Robert Sheehan and “Denny” as “beards” for Aaron Mosko who placed wagers with other bookmakers on Mosko’s behalf.4 He further described Thomas Got-tone as a lay-off source who exchanged wagering activity with Aaron Mosko. He further opined that Aaron Mosko and Phil Pinelli were engaged in a business relationship; that Pinelli advised Mosko as to what to lay-off, and furnished Mosko line [1467]*1467changes that Pinelli would get from William Burbidge. [Yol. 15, pp. 9-31 to -32],
B. Phil Pinelli
The evidence introduced by the government established that defendant Phil Pinelli was in the business of accepting wagers on sporting events. Specifically, the evidence indicated that Phil Pinelli accepted over $800,000 in wagers during November and December, 1984. [Ex. 608, Vol. 15, p. 9-88].
Evidence consisting of taped conversations between Phil Pinelli and his brother David Pinelli demonstrated a mutuality of risk between the two brothers in their wagering activities, [Ex. 341-A, Vol. 12, p. 114], and indicated the brothers had mutual financial interests. [Ex. 259-A, Vol. 12, p. 88]. Further, wiretapped telephone conversations demonstrated that Phil Pinelli accepted wagers from, and placed wagers with, other bookmakers.
For instance, from taped conversations introduced by the government it was evident that Phil Pinelli accepted wagers from another bookmaker, Aaron Mosko, and placed bets by telephone with Ralph Lackey. [Ex. 192-A, Vol. 10, p. 4-87; Ex. 194, Vol. 10, p. 4-87]. In particular, the government introduced a taped conversation between Aaron Mosko and Phil Pinelli in which Mosko told Pinelli that he “needed” certain amounts on various games. [Ex. 192-A, Vol. 10, p. 4-87]. In another telephone conversation introduced by the government between Pinelli and a person identified as “Doc”, Pinelli told Doc that he had “about five or six bookmakers and they unload their, like Aaron and them guys, they load all their shit on me.” [Ex. 320-A, Vol. 12, p. 112].
The evidence introduced by the government also indicated that Phil Pinelli kept his gambling records in such a way as to obfuscate their true meaning. For instance, a review of seized records indicates that none of his accounts were identified by recognizable names, but rather by entries such as “K” and “PB”. [Ex. 10], Moreover, the government introduced a taped conversation between Pinelli and Aaron Mosko in which Pinelli explained to Mosko that he kept his books in a certain manner so ever up my say twenty to twenty, you know, they can’t say what they are.” [Ex. 345-A, Vol. 12, p. 115]. Phil Pinelli received line information for his gambling activities by placing telephone calls to Las Vegas. [Ex. 154-A; Vol. 9, p. 92; Ex. 278-A],
FBI Agent Holmes testified that in his opinion Phil Pinelli was in the business of accepting sports wagering activity and David Pinelli was his partner and assisted Phil in accepting wagers, setting line, and deciding lay-off policy. [Vol. 15, p. 9-7]. Holmes further opined that Pinelli was engaged in a business relationship with William Burbidge where they shared line information. [Vol. 15, p. 9-24].
C. William Burbidge
The evidence introduced against defendant William Burbidge established that he was in the business of accepting sports wagering activity. This evidence included the testimony of various bettor witnesses who testified that they placed wagers with Burbidge, or placed wagers with Ralph Lackey and later settled the outcome of those wagers with Burbidge. [Vol. 9, pp. 43-46; Vol. 9, pp. 69-72], Additionally, an FBI handwriting analyst, Joseph Bowers, testified that there was a high probability that documents identified as gambling records seized from the residence of Ralph Lackey contained the handwriting of Bur-bidge and Lackey. [Vol. 14, pp. 100, 107]. Evidence in the form of wiretap telephone conversations demonstrated that on several occasions Burbidge discussed line information with Phil Pinelli and particularly discussed what points they would use on certain games. [Ex. 318-A, Vol. 12, p. 111]. An additional wiretap conversation had Phil Pinelli placing wagers with Ralph Lackey. [Ex. 103-A, Vol. 9, p. 13].
FBI gambling expert Holmes testified that in his opinion: (1) Burbidge was in the business of accepting sports wagering activity; (2) Lackey was a phoneman who accepted wagers and disseminated line information on behalf of Burbidge; (3) Bur-bidge and Phil Pinelli had a business relationship where they shared line informa[1468]*1468tion; (4) Burbidge sometimes acted as a beard for Pinelli; and (5) Burbidge sometimes provided line information for Aaron Mosko. [Vol. 15, pp. 9-24 to -25],
D. Thomas Gottone
The government’s evidence against Thomas Gottone included numerous taped conversations between Gottone and Aaron Mosko. In several of these conversations Mosko and Gottone exchanged line information, agreed on the line to be used on certain games, and exchanged wagers. [Ex. 527-A, Vol. 12, p. 82; Ex. 307-A, Vol. 12, p. 109; Ex. 196-A, Vol. 10, p. 4-88], In one taped conversation Gottone and Mosko went through a number of games with Mosko giving Gottone various amounts. The conversation concluded with Mosko stating, “If you get loaded on Denver by seven thirty or something, call me.” Got-tone responded “Okay” and Mosko said, “You know, I mean I’m loaded on Denver but that doesn’t matter.” [Ex. 219-A, Vol. 10, p. 4-113],
Agent Holmes described Tom Gottone as a lay-off source who exchanged wagering activity with Aaron Mosko. [Vol. 15, p. 9-32],
E. Robert Sheehan
The government’s theory at trial was that defendant Robert Sheehan was a beard, or lay-off conduit, for Aaron Mosko. The main evidence introduced by the government against Robert Sheehan consisted of taped conversations between Sheehan and Aaron Mosko. These conversations demonstrated that Sheehan was placing bets with third parties on behalf of Aaron Mosko. [Exs. 249-A, 253-A, 254-A, Vol. 12, p. 81; Ex. 339-A, Vol. 12, p. 114]. For instance, in one series of three conversations between Sheehan and Mosko, Shee-han called Mosko and inquired if Mosko was “heavy”. Mosko responded that it was too early to have accepted a large amount of wagers. He added that his “bettors all wait until the last minute.” Mosko asked Sheehan to call back later. Later Sheehan called Aaron Mosko back and Mosko asked Sheehan to “[g]et me about three thousand on Miami minus fourteen....” Sheehan responded, “Let me call him right now.” A few minutes later Sheehan called Mosko again and informed Mosko that “[y]ou got it.” [Ex. 249-A, 253-A, 254-A], In another taped conversation between the two, Mosko informed Sheehan that all the bets he was receiving on a particular game were on Chicago. The conversation continued:
Sheehan: Well, if you need to lay anything off, you know.
Mosko: I’ll call you if I do.
[Ex. 339-A, Vol. 12, p. 114].
Agent Holmes described Robert Sheehan as a beard for Aaron Mosko who placed wagers with other bookmakers on Mosko’s behalf. [Vol. 15, p. 9-32],
F. David Pinelli
The evidence introduced by the government demonstrated that David Pinelli and his brother Phil Pinelli were partners in a gambling partnership.
Tape recorded conversations between the two brothers demonstrated the mutuality of financial interests between' the two. [Ex. 230-A, Vol. 11, p. 5-97; Ex. 221, Vol. 10, p. 113]. For instance, in one conversation the Pinellis discussed what they collectively had on Denver and how much they wanted to “lay-off”. [Ex. 230-A, Vol. 11, p. 5-97]. In another conversation David and Phil Pinelli went over the day’s wagering activity. [Ex. 221-A, Vol. 10, p. 113].
Agent Holmes described David Pinelli as a partner of Phil Pinelli in his gambling business who assisted Phil in accepting wagers, setting line, and deciding lay-off policy. [Vol. 15, p. 9-7].
G. Martin Mosko
The evidence demonstrated that Martin Mosko accepted wagers on behalf of his father Aaron Mosko. [Ex. 338, Vol. 14, p. 24; Ex. 273, Vol. 12, p. 90]. In addition the government offered evidence from which a mutuality of financial interest between Martin Mosko and his father Aaron could be inferred. [Ex. 326-A].
In one taped conversation, Martin and Aaron Mosko discussed what they “needed” on the afternoon games. [Id.] In an[1469]*1469other taped conversation between Martin and Aaron Mosko, Martin reported all wagers he accepted in Aaron’s absence. [Ex. 273-A, Vol. 12, p. 90]. Later, in this same conversation Martin stated “I laid off, a, a, a dime with Minnesota plus twelve.” [Id.].
Agent Holmes described Martin Mosko’s role as at least a phoneman who accepted wagers from bettors and relayed them to Aaron Mosko. [Vol. 15, pp. 9-31 to -32].
H. Conclusions Regarding Sufficiency of the Evidence
Central to appellants’ challenge to the sufficiency of the evidence is their claim that the government did not prove the jurisdictional elements of 18 U.S.C. § 1955. Section 1955 makes it a crime to operate an illegal gambling business in violation of the laws of the State of Colorado involving five or more persons which was in substantially continuous operation in excess of thirty days, or which had gross wagers in excess of $2,000 on any single day. Here, the multiple telephone calls on particular days, as well as the coordination among appellants which was evident in many conversations, together with the generated revenues, which were substantially in excess of $2,000 per day, amply provide a basis for the jury’s findings.
The remaining charges may be briefly summarized. Title 18 U.S.C. § 1952 prohibits interstate telephone calls which facilitate a gambling business. Title 26 U.S.C. § 7201 declares unlawful all willful attempts to evade the 2% excise tax on wagers accepted. Title 26 U.S.C. § 7203 makes it a misdemeanor for willful failure to file a tax return, while 26 U.S.C. § 7262 is a misdemeanor offense arising out of the failure to pay the gambling occupation tax.
We are convinced that the evidence collectively, both direct and circumstantial, when viewed in the light most favorable to the government, satisfies each of the essential elements of Section 1955 and the other counts of conviction, and demonstrates appellants’ participation in a substantial and continuous bookmaking business conducted by multiple bookmakers and others linked through lay-off wagering, exchange and use of line information, and ancillary activities.
II. CONSTITUTIONALITY OF 18 U.S.C. § 1955 AND RELATED STATUTES
Appellants Phil and David Pinelli, Robert Sheehan, Thomas Gottone, William Bur-bridge and Aaron Mosko assert 18 U.S.C. § 1955 is unconstitutionally vague. Three of the appellants, Phil Pinelli, David Pinelli and Robert Sheehan, argue 18 U.S.C. § 1955 is unconstitutional as applied to them. Finally, appellants Phil Pinelli, David Pinelli and William Burbridge urge the unconstitutionality of Colorado’s gambling statutes, Colo.Rev.Stat. §§ 18-10-101 to 18-10-107, particularly Colo.Rev.Stat. § 18-10-106(1), because they are allegedly vague and overbroad in violation of the first, fifth, and fourteenth amendments and article II, section 10 of the Colorado Constitution. We reject each of these arguments.
This Court has previously upheld the constitutionality of 18 U.S.C. § 1955 on three grounds: (1) that the statute is a valid and constitutional exercise of congressional power under the Commerce Clause of the United States Constitution; (2) it is not repugnant to the Due Process Clause of the fifth amendment; and (3) the statute does not invite double jeopardy. See United States v. Smaldone, 485 F.2d 1333, 1342-43 (10th Cir.1973).
Today, we join five other circuits in ruling that Section 1955 is not void for vagueness. See United States v. McCoy, 539 F.2d 1050, 1058 (5th Cir.1976), cert. denied, 431 U.S. 919, 97 S.Ct. 2185, 53 L.Ed.2d 230 (1977); United States v. Thomas, 508 F.2d 1200, 1203 (8th Cir.), cert. denied, 421 U.S. 947, 95 S.Ct. 1677, 44 L.Ed.2d 100 (1975); United States v. Mattucci, 502 F.2d 883, 890 (6th Cir.1974) (by implication); United States v. Sacco, 491 F.2d 995, 1003 (9th Cir.1974) (en banc); and United States v. Riehl, 460 F.2d 454, 459 (3rd Cir.1972); see also United States v. Avarello, 592 F.2d 1339, 1345 (5th Cir.1979).
Here, appellants argue 18 U.S.C. § 1955 is rendered unconstitutionally vague by the use in the statute of the word “conduct”, which is undefined. In addition, the appellants urge that unconstitutional vagueness in Section 1955 is demonstrated by the con[1470]*1470flicting interpretations given by lower courts to the word “conduct”.
The void-for-vagueness doctrine requires that a penal statute define a criminal offense with sufficient specificity that ordinary people can understand what conduct is prohibited and in a manner that does not encourage arbitrary and discriminatory enforcement. Kolender v. Lawson, 461 U.S. 352, 357, 103 S.Ct. 1855, 1858, 75 L.Ed.2d 903 (1983). Although the doctrine focuses both on actual notice to citizens and arbitrary enforcement, the Supreme Court has recognized that the most important aspect of the vagueness doctrine "is not the actual notice, but the other princi-pa~ elements of the doctrine-the requirement that a legislature establish minimal guidelines to govern law enforcement." Smith v. Goguen, 415 U.S. 566, 574, 94 S.Ct. 1242, 1247, 39 L.Ed.2d 605 (1974).
Title 18 U.S.C. § 1955 was enacted as Part C of Title VIII of the Organized Crime Control Act of 1970, 84 Stat. 937.5 The legislation was aimed toward curtailing syndicated gambling.6 The statute requires that three elements be established to constitute an offense: there must be a gambling operation which: (1) violates the law of a State or political subdivision in which it is conducted; (2) involves five or more persons who conduct, finance, manage, supervise, direct or own all or part of such business; and (3) 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 a single day. 18 U.S.C. § 1955.
We find that the terminology used in the statute, the discernible legislative intent, and the construction given Section 1955 by other circuits establish minimal enforcement standards and refute the vagueness challenge. The intent of Congress as to the precise meaning of the word “conduct” is neither defined by the statute nor in the history of Section 1955. However, 18 U.S.C. §§ 1955 & 15117 were enacted to[1471]*1471gether as sections 802 and 803 of the Organized Crime Control Act of 1970. The same language is used in both statutes to define an “illegal gambling business.” Words of a statute which otherwise might be considered unduly vague may be considered sufficiently definite because of their use in other legislation. Omaechevarria v. Idaho, 246 U.S. 343, 349, 38 S.Ct. 323, 326, 62 L.Ed. 763 (1918). Sections 1955 and 1511 should be construed together. United States v. Becker, 461 F.2d 230, 232 (2nd Cir.1972). When referring to the “illegal gambling business” in Section 1511, Congress stated:
The section applies generally to persons who participate in the ownership, management, or conduct of an illegal gambling business. The term “conduct” refers both to high level bosses and street level employees. It does not include the player in an illegal game of chance, nor the person who participates in an illegal gambling activity by placing a bet.
1970 U.S.Code Cong. & Admin.News at 4029.
In Sanabria v. United States, the Supreme Court noted: “[n]umerous cases have recognized that 18 U.S.C. § 1955 (1976 ed.) proscribes any degree of participation in an illegal gambling business, except participation as a mere bettor.” 437 U.S. 54, 70-71 n. 26, 98 S.Ct. 2170, 2182 n. 26, 57 L.Ed.2d 43 (1978) (emphasis supplied).
Appellants urge that the unconstitutional vagueness and ambiguity in 18 U.S.C. § 1955 are demonstrated by conflicting interpretations given by lower courts. The Supreme Court has stated:
[t]he strong presumptive validity that attaches to an Act of Congress has led this Court to hold many times that statutes are not automatically invalidated as vague simply because difficulty is found in determining whether certain marginal offenses fall within their language.
United States v. National Prod. Corp., 372 U.S. 29, 32, 83 S.Ct. 594, 597, 9 L.Ed.2d 561 (1963) (cites omitted). The interpretations placed by various lower courts on the word “conduct” merely demonstrate the difficulty in determining the marginal offenses, not that the statute is void for vagueness. See, e.g., United States v. Thomas, 508 F.2d at 1206 (“[I]solated and casual lay off bets and an occasional exchange of line information may not be sufficient to establish that one bookmaker is conducting or financing the business of a second bookmaker.”); United States v. Campion, 560 F.2d 751, 754 (6th Cir.1977) (“Nothing in the record suggests that Cam-pion’s involvement had a significant or substantial impact upon the gambling enterprise.”); United States v. Jenkins, 649 F.2d 273, 275 (4th Cir.1981) (“[T]he lay-off man need not be present every day.... He must only be available on the critical day when the bookmaker is overbet and needs to reduce his financial risk. One contact is enough for a lay-off man to become a bookmaker_”).
Appellants Phil and David Pinelli and Robert Sheehan argue 18 U.S.C. § 1955 is unconstitutional as applied to them. Only Robert Sheehan, however, presents factual arguments based on the record to support this constitutional challenge. He illustrates that he had minimal involvement in this gambling enterprise inasmuch as the only evidence presented relating to him consisted of wiretap conversations, on three different days, in which he discussed four bets with Aaron Mosko. Additionally, he urges the ratio of the dollar value of his bets to the overall dollars wagered and the ratio of the number of his bets to the overall number show his minor role in the operation. Sheehan further argues 18 U.S.C. § 1955 failed to give him fair warning that his conduct would be a violation. We think the statute, and the case law interpreting it, gave appellants adequate warning that their conduct constituted a criminal offense.
Appellants Phil Pinelli, David Pi-nelli, and William Burbridge assert the Colorado gambling statutes, Colo.Rev.Stat. §§ 18-10-101 to -107, particularly Section 18-10-106(1), are unconstitutionally over-broad in violation of the first, fifth, and fourteenth amendments and article II, section 10 of the Colorado Constitution.
[1472]*1472A brief reading of Count I of the Indictment under which appellants were charged shows it alleges violations of four of the Colorado gambling statutes, Colo.Rev.Stat. §§ 18-10-103, -105, -106, & -107. Appellants, however, attack the constitutionality of only Section 18-10-106(1). Portions of the statutes should not be viewed in isolation. Street v. Lincoln Nat’l Deposit Co., 254 U.S. 88, 41 S.Ct. 31, 65 L.Ed. 151 (1920).
When the Colorado Legislature adopted its gambling statutes in 1963, it noted the close relationship between professional gambling and other organized crime, and declared that its policy was “to restrain all persons from seeking profit from gambling activities.” Colo.Rev.Stat. § 18-10-101. The Colorado Legislature declared an array of gambling activities illegal: engaging in gambling, Section 18-10-103; possession of gambling devices, Section 18-10-105; maintaining gambling premises, Section 18-10-107. Section 18-10-101(2) declared that the provisions of the gambling statutes were to be liberally construed, administered and enforced with a view to carrying out these declared policies.
Appellants urge that Section 18-10-106(1) unconstitutionally infringes upon their first amendment rights of freedom of speech and expression. The over breadth doctrine prohibits a statute from making criminal otherwise innocent and constitutionally protected conduct. Broadrick v. Oklahoma, 413 U.S. 601, 613, 93 S.Ct. 2908, 2916, 37 L.Ed.2d 830 (1973). The crucial question then is whether the statute sweeps within its prohibitions conduct that may not be punished because of the protection of the first and fourteenth amendments. Grayned v. City of Rockford, 408 U.S. 104, 115, 92 S.Ct. 2294, 2302, 33 L.Ed.2d 222 (1972). Specifically, appellants contend that Section 18-10-106(1), unduly interferes with the first amendment rights of freedom of speech and expression. We disagree.
The Colorado Supreme Court has upheld the constitutionality of certain portions of the Colorado gambling statutes against both vagueness and overbreadth challenges based upon infringement of free expression. People v. Wheatridge Poker Club, 194 Colo. 15, 569 P.2d 324 (1977). The Colorado Supreme Court specifically found the statute “conveyed sufficient warning as to proscribed conduct.” Id. at 328. In addition, the Colorado Supreme Court stated: “[w]e are unable to conclude that any of the activity arguably reached by the statute could be characterized as free expression or involving any right to privacy as that right has been previously defined.” Id. We believe these holdings of the Colorado Supreme Court to be sound and provide support for upholding the constitutionality of Colo.Rev.Stat. § 18-10-106(1).
It has never been deemed an abridgment of the freedom of speech or expression to make a course of conduct illegal “merely because the conduct was in part initiated, evidenced, or carried out by means of language, either spoken, written or printed.” Giboney v. Empire Storage & Ice Co., 336 U.S. 490, 502, 69 S.Ct. 684, 690, 93 L.Ed. 834 (1949).
The Supreme Court has repeatedly expressed its reluctance to strike down a statute on its face where there are many situations to which it might be validly applied. “Thus, even if there are marginal applications in which the statute would infringe on First Amendment values, facial invalidation is inappropriate if the ‘remainder of the statute ... covers a whole range of easily identifiable and constitutionally proscribable ... conduct ... Parker v. Levy, 417 U.S. 733, 760, 94 S.Ct. 2547, 2563, 41 L.Ed.2d 439 (1974).
The Supreme Court has also recognized that where conduct and not merely speech is involved, the overbreadth must “not only be real, but substantial as well, judged in relationship to the statutes plainly legitimate sweep.” Broadrick v. Oklahoma, 413 U.S. at 615, 93 S.Ct. at 2917. Here, the Colorado gambling statutes clearly prohibit a whole range of easily identifiable and constitutionally proscribable conduct.
Speech and expression are regulated by the Colorado gambling statutes only to the extent that they involve gambling activities. See McKenzie v. Municipality of Anchorage, 631 P.2d 514 (Alaska Ct.App. 1981). We hold that the Colorado gam[1473]*1473bling statutes, specifically Colo.Rev.Stat. § 18-10-106(1), are neither vague nor over-broad.
III. MISTRIAL MOTIONS
Five appellants assert that the trial court committed reversible error by denying a mistrial upon the discovery that a non-evidentiary “post-it” tab had been inadvertently sent to the jury.8 We disagree.
During the trial, the government utilized a number of reference tabs on exhibits to assist in the preparation and presentation of the case. These colored tabs could be seen by the jury. At the conclusion of the case, the trial court provided the parties an opportunity to inspect all of the evidence to be submitted to the jury. Despite the trial court’s stated desire that all exhibits be examined to assure that only items received in evidence be sent to the jury room, and despite at least one defense counsel’s assurance that the exhibits had been checked, one yellow “post-it” tab was not removed from Government Exhibit 66. That exhibit, with the yellow tab, was sent to the jury’s deliberation room. The notation on the yellow tab read “Phil Pinelli lay-off 11/26/84.”
During deliberations, the jury sent a note to the trial court indicating that the tab was folded under the page and asked: “Is the yellow posted part of the evidence?” The district judge, after consultation with counsel, responded as follows:
The yellow “post-it” tab on Exhibit 66 was not received as a part of the evidence. That tab was mistakenly left on the exhibit when it was received in evidence. It was a note made by government lawyers and refers only to the government’s contention. I have removed the tab and you will completely disregard it in considering the evidence in this case.
It would be a violation of your oath to give it any consideration.
[Yol. 24, p. 5].
Based on this unfortunate incident, several defendants moved for a mistrial on a variety of grounds. [Id. at 7-9]. The primary grounds were the alleged undue emphasis placed on Exhibit 66 as a result of the tab, and the government’s characterization of the document as one which evidenced a “lay-off” bet between Phil Pinelli and William Burbidge. The trial court then denied the mistrial motions, stating:
Also, it is my view that the jury has shown its conscientiousness in its efforts to consider only the evidence presented in the course of the trial by the very fact that they recognize that that was probably not a part of that exhibit and was probably there inadvertently and it gives me great confidence in the jury to have a note of this type received from them.
[Yol. 14, p. 11].
Contrary to appellants’ assertion that we must reverse if there is even the “slightest possibility of harm” which could result from the jury viewing unadmitted evidence, we instead examine the record to determine if the district court abused its discretion in denying the mistrial motions. See United States v. Hueftle, 687 F.2d 1305, 1310 (10th Cir.1982). We also examine the record to determine whether appellants’ right to a fair and impartial trial was impaired. Id.
In Hueftle, a card stating “They’re Guilty, Nuke’M” was discovered to have been included with the evidence submitted to the jury. The trial court in Hueftle, in addition to giving a cautionary instruction, polled the jury to determine the prejudicial effect of the card on the deliberations, a step not taken here. On appeal, we held that the inclusion of the card in the jury exhibits was not so blatantly prejudicial that the verdict must be overturned. Hueftle, 687 F.2d at 1310-11. After reviewing the record, we make similar findings here.
The extraneous matter in this case was not additional evidence, but rather a “post-it” tab which was inadvertently sent to the jury, and which was merely cumulative of the government’s contentions. While the trial court did not poll the jury [1474]*1474concerning the prejudicial effect of the incident, no poll was requested by any appellant prior to the return of the verdict.9 The conscientiousness displayed by the jury and the cautionary instruction given by the trial court convince us that the matter was properly handled, and the alleged error, if any, in failing to poll the jury was harmless. See United States v. Treadwell, 760 F.2d 327, 340-41 (D.C.Cir.1985).
IV. EXPERT GAMBLING TESTIMONY
Two appellants, Aaron Mosko and Robert Sheehan, challenge the trial court’s admission of expert testimony rendered by FBI Agent Holmes. We review this evidentiary ruling under an abuse of discretion standard. United States v. Buchanan, 787 F.2d 477, 483 (10th Cir.1986); United States v. Fleishman, 684 F.2d 1329, 1335 (9th Cir.), cert. denied, 459 U.S. 1044, 103 S.Ct. 464, 74 L.Ed.2d 614 (1982).
Holmes, after reviewing the intercepted telephone conversations and seized documentation, testified as an expert witness as to his opinion of the roles of each of the participants in the gambling operation. He also provided the jury with an extensive glossary of professional gambling terminology. He did not attempt to offer opinions on the credibility of witnesses who appeared at trial.
The admission of Holmes’ testimony is governed by Rules 702 and 704 of the Federal Rules of Evidence.
Rule 702 provides:
If scientific, technical, or other specialized knowledge will assist the trier of fact to understand the evidence or to determine a fact in issue, a witness qualified as an expert by knowledge, skill, experience, training, or education, may testify thereto in the form of an opinion or otherwise.
Rule 704 provides, in pertinent part:
(a) Except as provided in subdivision (b) [mental state or condition], testimony in the form of an opinion or inference otherwise admissible is not objectionable because it embraces an ultimate issue to be decided by the trier of fact.
Holmes testified that he was a supervisory special agent assigned to the Gambling Unit of the FBI Laboratory in Washington, D.C. During his nineteen years with the FBI, he has been qualified as an expert witness in gambling cases on more than 200 occasions. His responsibilities include the detection, interpretation and identification of gambling records and gambling paraphernalia. He holds a Bachelor’s Degree in Economics and a Master’s Degree in Forensic Science, and regularly serves as an instructor to local law enforcement officers in the area of gambling. After a brief recitation of his qualifications at trial, counsel for appellant Aaron Mosko stipulated to Holmes’ expertise. [Supp. Vol. Aug. 12, 1987 at 5-10].
Much of Holmes’ testimony was admitted without objection. The only pertinent objections occurred when Holmes began to provide his opinions on the roles played by the various defendants in the gambling operation. [Vol. 15, pp. 9-6, -67, -74, -82], Given the complexity of the case, the volume of tape recordings and documentary exhibits, as well as the average person’s unfamiliarity with the professional gambling business, it was well within the discretion of the trial judge to permit such testimony on the theory that Holmes’ specialized knowledge would assist the trier-of-fact in understanding the evidence. Fed.R.Evid. 702. Moreover, the testimony of Holmes did not offend Rule 704, which allows opinion testimony embracing an ultimate issue. Fed.R.Evid. 704.
Aside from the fact that the plain language of Rule 704 is the short and complete answer to most of appellants’ objections, we note that other courts have permitted law enforcement witnesses to provide both lay and expert opinions concerning the roles played by participants in a variety of illegal activities, including gambling operations. See, e.g., United States v. Fleishman, 684 F.2d at 1335, and cases [1475]*1475cited therein; and United States v. Mas-son, 582 F.2d 961, 964 (5th Cir.1978). Under the circumstances of this case, we find that the district court did not abuse its discretion in admitting the testimony of Holmes.
V. ADMISSION OF WIRETAP EVIDENCE
All appellants, with the exception of Martin Mosko, challenge the admissibility of evidence obtained as a result of court-authorized electronic surveillance on two grounds. First, appellants assert that the trial court erred in refusing to suppress the contents of the wire interceptions based on the government’s failure to comply with 18 U.S.C. § 2518(l)(e). Second, appellants argue that the four-day delay between the termination of the wiretap and the sealing of the original tapes required suppression. Neither ground has merit.
Each application for court-authorized interception of wire communications requires the following information:
a full and complete statement of the facts concerning all previous applications known to the individual authorizing and making the applications, made to any judge for authorization to intercept, or for approval of interceptions of, wire, oral, or electronic communications involving any of the same persons, facilities or places specified in the application, and the action taken by the judge on each such application.
18 U.S.C. § 2518(l)(e).
It is undisputed that appellant Phil Pinel-li had been previously named as an inter-ceptee in a state wiretap affidavit at the time the application to intercept wire communication was submitted to the district court. The Colorado state wiretap affidavit, in turn, led to the initiation of a federal criminal prosecution, United States v. McNulty, 729 F.2d 1243 (10th Cir.1983).10 It is also undisputed that the government in this case failed to list Phil Pinelli as a prior interceptee pursuant to Section 2518(l)(e) when it applied to the federal district court for authorization to intercept wire communications in the instant case.
Based on these allegations and others, the district court held a pretrial evidentiary hearing on appellants’ motions to suppress. Robert Mydans was the government attorney who signed the affidavit requesting the court-authorized wiretap. He testified that had he known of Phil Pinelli’s status in the state wiretap case, he would have listed Phil Pinelli as a prior interceptee in the affidavit he submitted to the district court.
From a review of the record in this case, it is clear that the government’s failure to list Phil Pinelli as a prior interceptee was unintentional, and that none of the suppressed McNulty wiretap evidence was included in the application or affidavit submitted by the government in this case. As conceded by counsel for Phil Pinelli at oral argument, had the government listed Phil Pinelli as a prior interceptee, inclusion of that information would have served to support the government’s application for an interception order in this case. United States v. Mosko, 654 F.Supp. 402, 408 (D.Colo.1987). In short, the failure to comply with Section 2518(l)(e) under the circumstances of this case does not require suppression. See United States v. Donovan, 429 U.S. 413, 425 n. 14, 97 S.Ct. 658, 667 n. 14, 50 L.Ed.2d 652 (1977); United States v. Abramson, 553 F.2d 1164, 1169 (8th Cir.1977).
Similarly, the district court fully considered the four-day delay between the termination of the wiretap and the sealing of the original tapes. The district court found that the government amply explained the reasons for the delay at the evidentiary hearing held prior to trial and further found that suppression was unwarranted. These findings are not clearly erroneous. United States v. Diana, 605 F.2d 1307, 1314 (4th Cir.1979) (thirty-nine (39) day sealing delay did not require suppression), cert, denied, 444 U.S. 1102, 100 S.Ct. 1067, 62 L.Ed.2d 787 (1980).
[1476]*1476We note that the district court held a lengthy evidentiary hearing on the admissibility of the wiretap evidence and heard arguments on the multiple challenges to this evidence advanced by appellants. The district court subsequently issued a detailed opinion denying the various suppression motions. United States v. Mosko, 654 F.Supp. 402. We affirm the district court’s denial of the suppression motions for substantially the same reasons set forth in the district court’s well-reasoned opinion.
VI. MID-TRIAL SEVERANCE MOTIONS
At the conclusion of the government’s case, counsel for appellant Phil Pinelli made a series of requests. He sought a severance of the two tax evasion counts (Counts 11 and 12) from the remaining counts, or alternatively, a court-imposed restriction on the scope of cross examination if Phil Pinelli chose to testify as to the tax evasion counts. He also made a related request to waive jury trial on the two tax evasion counts. [Vol. 19, pp. 13-17]. The requests were grounded on Phil Pinelli’s assertion that he desired to testify regarding the tax evasion counts, but retain his fifth amendment privilege with respect to the gambling charges. His brother, David Pinelli, who also faced two tax charges (Counts 14 and 15), made the same request with respect to Count 14 only. [Vol. 19, p. 19]. The government declined the defendants’ offers to waive jury,11 and the district court denied the defendants’ requests. We find that the requests were neither timely nor meritorious.
The decision on whether to grant a severance lies within the sound discretion of the trial court and its decision will not be reversed on appeal in the absence of a strong showing of prejudice. United States v. Hayes, 861 F.2d 1225, 1231 (10th Cir.1988); United States v. Heath, 580 F.2d 1011, 1022 (10th Cir.1978), cert. denied sub nom., 439 U.S. 1075, 99 S.Ct. 850, 59 L.Ed.2d 42 (1979).
The defendants’ burden to show an abuse of discretion is a difficult one. United States v. Van Scoy, 482 F.2d 347, 349 (10th Cir.1973). Here, both defendants requested for the first time at the conclusion of the government’s case-in-chief a severance of counts and a proposed waiver of jury. Furthermore, none of the pretrial motions filed by the defendants suggested any fifth amendment concerns associated with the joint trial of the gambling charges and the tax counts. Given the fact that the tax and gambling charges in this case were inextricably intertwined, even a timely motion for severance would have posed a formidable obstacle for the defendants in this ease. Here, however, the severance motions were not timely made and therefore were appropriately denied. United States v. Sanders, 463 F.2d 1086, 1089 (8th Cir. 1972).
VII. REMAINING GROUNDS
The remaining grounds for reversal have been carefully examined and none is meritorious. They are (1) allegedly prejudicial verdict forms; (2) post-trial denial of a defense motion to interview jurors; (3) failure to grant a defense motion for a bill of particulars; (4) allegedly improper jury instructions; and (5) failure of the trial court to grant a defense motion for a new trial on the grounds of cumulative prejudice.
JUDGMENT AFFIRMED.
Before HOLLOWAY, Chief Judge, McWilliams, mckay, logan, SEYMOUR, ANDERSON, TACHA, BALDOCK, BRORBY, EBEL, Circuit Judges, and PHILLIPS **, District Judge.
ORDER
The appeals in the captioned cases were disposed of by the court’s opinion filed on June 9, 1989. The court now has for consideration appellants’ petitions for rehearing in 87-2511, U.S.A. v. Phil Pinelli and 87-2513, U.S.A. v. David Pinelli. The court [1477]*1477also has for consideration appellants’ petitions for rehearing, with suggestions for rehearing en banc, in 87-2565, U.S.A. v. Robert Sheehan, 87-2616, U.S.A. v. William Burbidge, and 87-2678, U.S.A. v. Aaron Mosko.
Upon consideration whereof, the panel judges who filed the opinion sought to be reheard grant rehearing for the limited purpose of discussing issues raised in the petitions for rehearing. A separate opinion on rehearing is filed coincident with the filing of this order.
In accordance with Rule 35, Federal Rules of Appellate Procedure, the petitions for rehearing en banc were transmitted to all judges of the court who are in regular active service. No member of the panel and no judge in regular active service on the court having requested that the court be polled on rehearing en banc, Rule 35, Federal Rules of Appellate Procedure, the suggestions for rehearing en banc are denied.
Circuit Judge JOHN P. MOORE did not participate.
Before BALDOCK, McWILLIAMS, and PHILLIPS, District Judge.