KILKENNY, Circuit Judge:
NATURE OF THE CASE
Appellant was indicted, tried by a jury, and convicted of filing a false and fraudulent income tax return, understating his income for the year 1975, in violation of 26 U.S.C. § 7201.
From January, 1975, through May, 1976, appellant was the manager of slot machine operations for the Fremont Hotel and Casino in Las Vegas, Nevada. Briefly stated, the evidence showed that appellant acquired substantial holdings in real estate, stocks, and savings accounts while his liabilities increased by less than $13,000.00 in 1975. The government showed that appellant experienced an increase in net worth of $64,664.00 in twelve months on a reported taxable income of less than $26,000.00, and ultimately demonstrated that appellant had a true taxable income for the year 1975 of $68,000.00, and that he had evaded $12,-878.00 in taxes. Substantial evidence was presented from which it could be inferred that the likely source of the increase in net worth was a slot machine “skim.”
METHOD OF PROOF
Appellee employed what is commonly known as the “net worth and expenditures”
method of proof. This procedure was approved by the Supreme Court in Holland v. United States, 348 U.S. 121, 75 S.Ct. 127, 99 L.Ed. 150 (1954), and was recognized and approved by this court as recently as United States v. Gardner, 611 F.2d 770 (CA9 1980).
In framing the law on the subject, the Supreme Court has said that the government, to sustain a conviction, must prove the three elements of the offense: (1) the existence of a tax deficiency, (2) willfulness in evading taxes, and (3) an affirmative act constituting an evasion or attempted evasion of the income tax. Sansone v. United States, 380 U.S. 343, 351, 85 S.Ct. 1004, 1010, 13 L.Ed.2d 882 (1965). In proving the elements, the government is required to: (1) accurately establish the defendant’s opening net worth, (2) identify a likely source of taxable income from which it may be inferred that the defendant’s increase in net worth arose, and (3) conduct a reasonable investigation of any leads that suggest that defendant properly reported his income. Holland, supra; Gardner, supra. The latter three requirements are imposed because of the nature of the net worth and expenditures method of proof. As Holland and Gardner caution, the evidence in this kind of case should be carefully reviewed “bearing constantly in mind the difficulties that arise when circumstantial evidence as to guilt is the chief weapon of a method that is itself only an approximation.” Holland, supra at 129, 75 S.Ct. at 132.
PRINCIPAL ISSUES ON APPEAL
I. Whether the government proved the existence of a tax deficiency.
II. Whether the government proved the element of willfulness of appellant in attempting to evade income taxes.
III. Whether the government proved an affirmative act constituting an evasion of income taxes.
I.
The establishment of an accurate opening net worth is crucial under the net worth and expenditures method of proof for “the correctness of the result depends entirely upon the inclusion in this sum of all assets on hand at the outset.” Holland, supra 348 U.S. at 132, 75 S.Ct. at 134. Our review of the record convinces us that the government has supplied evidence to meet this requirement. Appellant’s chief argument is that he must have had a cash hoard on hand at the end of 1974 and that this would mean that his opening net worth was substantially greater than the amount the government established. In this regard, he argues that the government failed to investigate and “purify” assets and sources of income allegedly revealed by a “150 M” notation on a 1974 new account form with a brokerage firm, by large bank deposits in 1972, 1973, and 1975, and by a 1967 loan application.
The government is not required “to embark on a Magellan-like expedition in order to prove that the unreported income was taxable.” United States v. Heitt, 581 F.2d 1199, 1201 (CA5 1978). It is only required to pursue any reasonable leads as to possible sources of nontaxable income, United States v. Hom Ming Dong, 436 F.2d 1237, 1242 (CA9 1971). It need not “negate every possible source of nontaxable income, a matter peculiarly within the knowledge of the defendant.” Holland, supra 348 U.S. at 138, 75 S.Ct. at 137. The principle remains that once the government has established its case, the defendant remains silent at his peril. Holland, supra at 138-139, 75 S.Ct. at 136-37; United States v. Costello, 221 F.2d 668, 671 (CA2 1955), aff’d. 350 U.S. 354, 76 S.Ct. 406, 100 L.Ed. 397 (1956).
Appellant provided no reasonable leads, but now argues that the documents and deposits mentioned above put the government on notice of possible sources of income. We disagree. The loan application made only vague references to some assets allegedly held by appellant in 1967. Only a fraction of those assets were even valued on the application; and that at only $2,500.00. There was no indication that these assets were sold to produce a cash hoard or that they were the source of nontaxable income. At trial, it became apparent that the “150 M” notation on the brokerage house new account form meant nothing. Testimony revealed that it was put on the form by a salesman and that there was no evidence in the record to substantiate the figure. Finally, there was no reasonable suggestion that the bank deposits camo from nontaxable sources. It would be entirely unreasonable to require the government to pursue these phantom clues as to some mysterious sources and assets.
We, of course, recognize that the burden is always on the government to prove each element of the offense beyond a reasonable doubt. The record reveals that the government thoroughly investigated appellant’s financial status at the beginning of 1975. It established appellant’s opening net worth figure by considering the information contained in appellant’s income tax returns over the previous six years, nine bank accounts and their records, the acquisition and sale of ten securities, and six real estate transactions. Viewing the evidence in the light most favorable to the government, as this court must, Gardner, supra at 775; Horn Ming Dong, supra at 1242, there is sufficient evidence to support the jury’s verdict on this question.
As part and parcel of this issue of the sufficiency of the evidence of a tax deficiency, it is appellant’s contention that the government failed to meet its burden of proving the likely source for the unreported income, Holland, supra 348 U.S. at 138, 75 S.Ct. at 136; Gardner, supra at 775, and that the district court improperly admitted figures from standard budgets prepared by the Bureau of Labor to show appellant’s living expenses.
We have no difficulty in holding that the jury could well have found that the likely source of taxable funds was the illegal diversion of money from slot machine revenues at the Fremont Hotel, where appellant was the slot machine manager. Fremont employees testified to the unusual system of dealing with slot machine revenues. The comptroller of the Fremont testified that during 1975 his representative was barred from the counting and wrapping of coins taken from the slot machines. Other witnesses testified regarding the operation of an unusual auxiliary bank which was very susceptible to being used to divert funds. The corporate head of the Fremont testified that he had filed an insurance claim to recover money lost by the Fremont through employee dishonesty. Most convincingly, a statistical expert examined the Fremont’s slot machines, reviewed their reported performance, and compared them with similar machines at other casinos and with the manufacturer’s built in performance specifications. He concluded that the odds against such machines performing as poorly as the Fremont’s records indicated were greater than two billion to one. We disagree with appellant’s contention that this statistical analysis should not have been admitted because it was speculative, confusing to the jury, and introduced without proper foundation. There is no question that it was highly relevant to whether moneys were being diverted from the slot machines and that it would likely assist the trier of fact in reaching its decision as to whether the government showed a likely source of income. The admission of the testimony was well within the trial court’s discretion under FRE 702 and 703.
We observe that those involved in gambling and its related activities are engaged in enterprises having indeterminate possibilities and capable of bringing in large sums of money in cash. Costello, supra at 672. Appellant was manager of the slot machine operation at the Fremont and was present at the counting and wrapping of the coins. He also told an acquaintance that he had been making $1,000.00 a day during his tenure at the Fremont. Taken in its totality, the evidence, both circumstantial and direct, established the likely source of appellant’s unreported income.
As noted above, the proof of the nondeductible expenditures is one factor in the net worth and expenditures method of proof. The taxpayer’s nondeductible expenditures are added to the adjusted net values of the defendant’s assets at the end of the subject year and, consequently, increase the figure to be compared with the opening net worth. In this case, the government found that during 1975 there was little activity in appellant’s checking account and that the microfilming from two of appellant’s banks was illegible. Consequently, it was impossible to reconstruct appellant’s living expenses in the typical manner of producing checking account records. Instead, the government was forced to rely on independent estimates from the Bureau of Labor on what a person with appellant’s reported income and family and financial obligations would be expected to spend on nondeductible items. Certainly, appellant must have expended some funds to maintain himself. At all times the government relied on the figures most favorable to appellant. Under these circumstances, we see no reason why these statistics should not have been admitted.
II.
Relying principally on a set of guidelines set forth in Spies v. United States, 317 U.S. 492, 63 S.Ct. 364, 87 L.Ed. 418 (1943), appellant argues that there is absolutely no evidence, circumstantial or otherwise, to support the finding of willfulness. However, the Spies decision does not support appellant’s position. For that matter, the decision recognizes that willfulness may be shown by a variety of circumstances:
“Congress did not define or limit the methods by which a willful attempt to defeat and evade might be accomplished and perhaps did not define lest its effort to do so result in some unexpected limitation. Nor would we by definition constrict the scope of the Congressional provision that it may be accomplished ‘in any manner.’ By way of illustration, and not by way of limitation, we would think affirmative willful attempt may be inferred from conduct such as keeping a double set of books, making false entries or alterations, or« false invoices or documents, destruction of books or records, concealment of assets or covering up sources of income, handling of one’s affairs to avoid making the records usual in transactions of the kind, and any conduct, the likely effect of which would be to mislead or conceal. If the tax-evasion motive plays any part in such conduct the offense may be made out even though the conduct may also serve other purposes such as concealment of other crime.” Spies, supra at 499, 63 S.Ct. at 368. [Emphasis supplied.]
It is clear that the acceptable indicia of willfulness are not set in concrete.
It has been said that the crime of attempted tax evasion has its roots in nondisclosure. United States v. Ramsdell, 450 F.2d 130, 133 (CA10 1971). Every indication is that appellant was involved in a slot machine “skim.” Certainly, one engaged in such conduct would not be expected to fore-go his prior secretive design of concealment and tell all on his tax return. We consider it significant that the underlying activity producing the unreported income is itself illegal. We also note that the amount of the understatement alone is sizeable and we think that that is not altogether irrelevant on the issue of willfulness. However, mere understatement of income, without more, is not sufficient evidence on this element. Holland, supra 348 U.S. at 139, 75 S.Ct. at 137; United States v. House, 524 F.2d 1035, 1044-45 (CA3 1975).
Here, we have much more than a mere understatement. One of the important indicia of willfulness mentioned in Spies is handling one’s affairs to avoid making a record of transactions, and any other conduct, the likely effect of which is to mislead or to conceal. See also, United States v. Mansfield, 381 F.2d 961 (CA7 1967), cert. denied 389 U.S. 1015, 88 S.Ct. 593, 19 L.Ed.2d 661. Appellant made large cash deposits and withdrawals from his several accounts during the indictment period and he acquired large holdings in corporate stock by paying $6,000.00 in cash in one instance and $20,000.00 in cash in another. Certainly, such large acquisitions are normally accomplished by a check or with some other record of the transaction.
The record shows that for the six years from 1969 through 1974, the six years preceding the indictment, appellant was employed as a slot machine mechanic, making a taxable income of something less than $10,000.00 per annum on up to a high of just over $16,000.00. In 1975, he became the manager of all slot machine operations of his employer, the Fremont Hotel. He was paid at the beginning at the rate of $732.00 twice each month, up to $780.00 prior to the termination of his employment in May, 1976. Not only did he work full time at this job, but there is testimony in the record which would show that he occasionally worked seven days a week. Almost half of the salary checks went directly into a savings account. In addition to all of the unusual cash transactions and the substantial increase in his wealth on a reported income which could not account for the increase, appellant remarked to an associate that he was earning $1,000.00 a day. While each of these factors standing alone might not be sufficient to support a finding of willfulness, we have no difficulty in holding that the entire record provided substantial evidence from which a jury could properly infer that appellant knowingly underreport-ed his income for the purposes of attempting to evade income taxes.
III.
Appellant’s filing a false and fraudulent return understating his income is sufficient to satisfy the affirmative act requirement. Sansone, supra 380 U.S. at 352, 85 S.Ct. at 1010; United States v. Schafer, 580 F.2d 774 (CA5 1978), cert. denied 439 U.S. 970, 99 S.Ct. 463, 58 L.Ed.2d 430; Swallow v. United States, 307 F.2d 81, 83 (CA10 1962), cert. denied 371 U.S. 950, 83 S.Ct. 504, 9 L.Ed.2d 499 (1963).
INCIDENTAL ISSUES
Appellant’s contention that the district court abused its discretion in refusing to conduct an investigation into the allegation that the jury relied on sources outside the record is meritless. For that matter, counsel’s conduct in calling the jurors after the verdict and secretly tape recording the conversations was improper. To hold a hearing on whether the jury relied on sources outside the record, with counsel’s investigation as the basis for such a hearing, might well establish a precedent which would encourage the harassment of jurors and encourage jury tampering. See United States v. Weiner, 578 F.2d 757 (CA9 1978), cert. denied 439 U.S. 981, 99 S.Ct. 568, 58 L.Ed.2d 651.
We have examined appellant’s claim under Brady v. Maryland, 373 U.S. 83, 83 S.Ct. 1194, 10 L.Ed.2d 215 (1963), and find it but a figment of his imagination.
CONCLUSION
Viewing the entire evidence in the light most favorable to the government, as we must, we find there was sufficient evidence to find appellant guilty beyond a reasonable doubt. Furthermore, the other assignments of error are groundless. The judgment of conviction must be affirmed.
IT IS SO ORDERED.
. To prove the existence of a tax deficiency under the net worth and expenditures method of proof, the government must first establish an “opening net worth” or total net assets of the taxpayer at the beginning of a given year. The government then proves the increase in the taxpayer’s net worth for the year by calculating the difference between the net worth of the taxpayer’s assets at the beginning and at the end of the year. To that figure is added the taxpayer’s nondeductible expenses, including living expenses, yielding the putative income. If that figure is substantially greater than that reported by the taxpayer, the government claims the difference is unreported income.
. We note that had they in fact been sold between 1969 and 1975, appellant failed to report any gain on his tax returns.
. See also, United States v. Hom Ming Dong, 436 F.2d 1237, 1240 (CA9 1977) (absence of business record sufficient to establish willfulness); Feichtmeir v. United States, 389 F.2d 498, 503 (CA9 1968) (buying of several large cashier’s checks on different days, irregularities in personal books, large volume of currency transactions during indictment period sufficient to support a finding of willfulness); United States v. Swallow, 511 F.2d 514 (CA10 1975), cert. denied 423 U.S. 845, 96 S.Ct. 82, 46 L.Ed.2d 66; United States v. House, 524 F.2d 1035 (CA3 1975).