
111 Wis.2d 287 (1983)
330 N.W.2d 611
STATE of Wisconsin, Plaintiff-Respondent,
v.
James DAHLK, Defendant-Appellant.
No. 81-1681-CR.
Court of Appeals of Wisconsin.
Submitted on briefs May 17, 1982.
Decided January 10, 1983.
*289 For the defendant-appellant the cause was submitted on the briefs of Gerald C. Nichol and Lee, Johnson, Kilkelly & Nichol of Madison.
For the plaintiff-respondent the cause was submitted on the brief of James E. Doyle, Jr., district attorney, and C. William Foust, assistant district attorney.
Before Gartzke, P.J., Bablitch, J. and Dykman, J.
GARTZKE, P.J.
Defendant was convicted in a jury trial of violating sec. 945.04(1), Stats., permitting real estate under his control to be used as a gambling place. *290 He appeals from the judgment of conviction and the order denying his motion to dismiss the amended complaint. We affirm.
Defendant raises the following issues:
1. Should the state have been allowed to amend its complaint?
2. Were the allegations of the amended complaint sufficient?
3. Is sec. 945.04(1), Stats., unconstitutionally vague and overbroad?
4. Was the evidence sufficient for a guilty verdict?
5. Did the trial court err when instructing the jury and responding to its request for clarification?
The facts are largely undisputed. February 1, 1980 Linda Pigorsch, a special agent of the Dane County District Attorney's Office, accompanied by her husband, a police sergeant, went to a Verona warehouse owned by Dahlk and May, Inc. About thirty or forty people were present. Defendant conducted a "pyramid club" meeting.
Sergeant Pigorsch testified that defendant explained how the club operated. An "investor" purchases a membership in the club for $1,000 in cash. The investor is then given three manila envelopes. One envelope contained a "tracking sheet" to start a new pyramid. The investor then attempts to sell two memberships. If he sells a membership he keeps $500 and puts the other $500 into one of the other two envelopes and passes it to the person whose name appears on the inside of the envelope. Each of the two buyers also receives three envelopes and sells memberships to two more people. The process continues to the last thirty-two positions on the pyramid. When each of those thirty-two persons sells memberships to two persons, $500 from each of their sixty-four buyers comes back to the investor. Defendant explained that the possible profit to the investor depended on the people below the investor continuing to maintain *291 the chain. The investor might not receive the whole $32,000 if "legs" of the pyramid reached a dead end before reaching the bottom level. Defendant encouraged investors to keep track of the sales below them and to help push new sales.
The Pigorschs testified that defendant said that all transactions were to take place at the warehouse, where he had secretaries to record the transactions. All transactions were to be made personally by passing money in envelopes. One person handed defendant an envelope from which he flashed five $100 bills. The Pigorschs said defendant said he had made $18,000, a statement defendant denied.
Sergeant Pigorsch testified that defendant answered questions pertaining to the club's legality. Defendant said he had checked with his attorneys, who had checked with the Attorney General's Office. He said that the Dodgeville police chief was on the chain and that a district attorney had said it was legal. Defendant gave the Pigorschs a tracking sheet and documents explaining the club rules and how it operated. He told them not to make copies and not to give them to law enforcement people. He introduced them to a person who was interested in selling them memberships.
The Pigorschs attended another club meeting at the warehouse February 4, 1980. Sergeant Pigorsch testified that fifty to sixty other people attended. Defendant said that Bob Kaehr was going to take a leg of the club and start his own operation because the warehouse was getting crowded. The secretaries were present. People were exchanging envelopes. The next day the district attorney's office issued a release published by a local newspaper which stated that an illegal pyramid club existed in Dane County. February 6 the Pigorschs attended another meeting at the warehouse. Kaehr made a presentation to twenty to twenty-five people. In response *292 to a question about the newspaper article, defendant said his attorney told him that the club was an illegal lottery and if you joined "you'd be taking your chances." Defendant testified that Kaehr made that statement. Defendant said the club was getting large and would split up and meet at various locations.
Defendant testified that five pyramid club meetings had been held at the warehouse, including the meetings of February 4 and 6. He ended the February 6 meeting when someone told him officers were present to make an arrest. February 8 a meeting was held at another location. It was then decided to have no further meetings until the legality of the club was established.

1. Amended Complaint

The original complaint limited its factual allegations to the February 1 meeting. Defendant contends that the trial court erred in permitting the state to amend the complaint to include allegations of meetings held February 4 and 6. The original complaint was filed March 10, 1980. The amended complaint was submitted June 4, 1980 and accepted by the trial court August 13, 1980. Trial was held May 14, 1981. He contends that his extensive and costly research for three months on the original complaint was rendered substantially useless by the amendment.
[1]
The purpose of an information is to inform the defendant of the charges against him. Whitaker v. State, 83 Wis. 2d 368, 373, 265 N.W.2d 575, 578 (1978). The same is true of a complaint. The complaint informed defendant that the charge was violating sec. 945.04(1), Stats., permitting real estate under his control to be used as a gambling place. Defendant had notice of the charge against him and the factual basis for it. The amendment expanded the factual basis to include club activities conducted on other dates but did not change *293 the charge. The inconvenience defendant suffered from expansion of the factual basis for the charge could not seriously interfere with preparation for a trial held nine months later. The trial court did not err in permitting the amended complaint.

2. Sufficiency Of Amended Complaint

Defendant contends that the amended complaint should have been dismissed for failure to state facts constituting a probable violation of sec. 945.04(1), Stats. He contends that the amended complaint was deficient because it failed to allege he violated the commercial gambling statute, sec. 945.03. He contends that the statutory definition of lottery does not cover the club's activities as described in the amended complaint and that the meetings alleged in the amended complaint were too few to constitute a principal use of the warehouse.
Section 945.04(1), Stats., provides in relevant part: "Whoever intentionally does any of the following is guilty of a Class A misdemeanor: (1) Permits any real estate owned or occupied by him or under his control to be used as a gambling place...."
So far as is material, sec. 945.01(4), Stats., defines a "gambling place" as: "[A]ny building or tent ... or any room within any of them, one of whose principal uses is any of the following: ... conducting lotteries ...."
A lottery is "an enterprise wherein for a consideration the participants are given an opportunity to win a prize, the award of which is determined by chance, even though accompanied by some skill." Sec. 945.01(2)(a), Stats.

A. Commercial Gambling

[2]
Defendant argues that sec. 945.04(1), Stats., the statute he is charged with violating, relates only to "[p]ermitting *294 premises to be used for commercial gambling." The statute is so entitled. The title, however, is not a part of the statute. Sec. 990.001(6), Stats. A title may be used only to resolve existing doubts or ambiguities as to statutory meanings and not to create ambiguity where none exists. Wisconsin Valley Imp. Co. v. Public Serv. Comm., 9 Wis. 2d 606, 618, 101 N.W.2d 798, 804 (1960).
[3]
The plain language of sec. 945.04(1), Stats., pertains to permitting real estate to be used as a "gambling place." "Gambling place" is defined by sec. 945.01(4) without reference to "commercial gambling." Because sec. 945.04 (1) is unambiguous in this respect, we ignore its title. A violation of sec. 945.03, the commercial gambling statute, is not a prerequisite to a violation of sec. 945.04, permitting real estate to be used as a gambling place. The amended complaint was not deficient for failing to allege a violation of sec. 945.03.

B. Lottery

Defendant contends that the club's operations do not fall within the statutory definition of a lottery and that the amended complaint, which described those operations, therefore failed to state sufficient facts constituting the offense charged, that he permitted a lottery to be conducted on his premises.[1] He asserts that the definition *295 of a lottery in sec. 945.01(2)(a), Stats., is ambiguous and must be strictly construed in his favor. State v. Wilson, 77 Wis. 2d 15, 28, 252 N.W.2d 64, 70 (1977).
Defendant finds an ambiguity in sec. 945.01(2)(a), Stats., because sec. 945.12 provides that to set up or promote an endless sale chain of motor vehicles is to set up and promote a lottery.[2] He cites State v. Kenyon, 85 Wis.2d 36, 49, 270 N.W.2d 160, 166 (1978), for the proposition that ambiguity can be created by the interaction of separate statutes as well as by the interaction of the words and structures of a single statute.
We find no ambiguity. The interaction referred to in Kenyon was a conflict between statutes. The Kenyon court was called on to apply a statute, which appeared unambiguous on its face, but which was irreconcilable with another. 85 Wis. 2d at 50, 270 N.W.2d at 167. No conflict exists between the general definition of a lottery in sec. 945.01(2)(a), Stats., and the crime of setting up or promoting endless chain sales of motor vehicles under sec. 945.12. We need not reconcile one statute with another.
*296 [4]
Short of conflict, ambiguity can be created by the interaction of separate statutes, in the sense that one statute affects the operation of another and reasonable persons can disagree regarding that operation. See In Matter of Estate of Walker, 75 Wis. 2d 93, 102, 248 N.W.2d 410, 414 (1977) (statute imposing inheritance tax on the "balance" "over the exemption" provided in another statute rendered ambiguous by the latter statute). Ambiguity in that sense is absent. The general lottery statute, sec. 945.01(2), Stats., and the endless chain statute, sec. 945.12, may be applied independently without affecting the operation of each other.
Defendant argues that the elements of "prize" and "chance" in sec. 945.01(2)(a), Stats., are absent from his club's operations. "Prize" is not defined by the statute, but we may look to a recognized dictionary for the common and ordinary meaning of words. In re Estate of Haese, 80 Wis. 2d 285, 291, 259 N.W.2d 54, 56 (1977). Webster's Third New International Dictionary (unabr. 1976) defines "prize" in this context as "something that may be won by chance."
Defendant contends that, because skill rather than chance determines whether an investor ultimately receives $32,000, no lottery was conducted at his warehouse. We disagree. A lottery offers the opportunity to win a prize, "the award of which is determined by chance, even though accompanied by some skill." Sec. 945.01(2)(a), Stats. Chance rather than skill must therefore be the dominant factor controlling the award in a lottery. Most jurisdictions apply the "dominant factor" test, by which a scheme is a lottery if chance dominates even though some degree of skill or judgment is present.[3]Roberts v. Communications Inv. Club, 431 A.2d 1206, 1211 (R.I. 1981).
*297 Roberts, supra, involved the same scheme as defendant's. The Roberts court said that although the scheme "may have involved some degree of skill or judgment, it is clear that the element of chance permeated it."[4] 431 A.3d at 1211. Other jurisdictions have concluded that similar pyramid or chain schemes are dominated by chance because obtaining the prize depends on factors beyond the investor's control and are lotteries. See, e.g., State v. Bull Investment Group, Inc., 351 A.2d 879, 885 (Conn. Super. 1974) (pyramid sales of discount coupons); Wesware, Inc. v. State, 488 S.W.2d 844, 848 (Tex. Civ. App. 1972) (pyramid sales of cookware); People ex rel. Kelley v. Koscot Interplanetary, Inc., 195 N.W.2d 43, 54 (Mich. App. 1972) (pyramid sales of cosmetics); State by Lefkowitz v. ITM, Inc., 275 N.Y.S. 2d 303, 324-28 (Sup. Ct. 1966) (referral sales of household appliances); Commonwealth v. Allen, 404 S.W.2d 464, 467 (Ky. App. 1966) (referral sales of goods); Sherwood & Roberts-Yakima, Inc. v. Leach, 409 P.2d 160, 163 (Wash. 1965) (referral sales of fire alarm and radio intercom systems).
Defendant contends that skill dominates over chance because the chain process depends on the efforts of individuals and because each investor will try to recruit new members. We disagree.
[5]
Whether an investor in the club receives a profit depends on when he enters the chain, the number of persons he induces to pay $1,000 to get in, the number of persons *298 his buyers and their buyers induce to pay $1,000, and whether the market is saturated. The earliest club members, those who enter at or near the top of the pyramid, have a greater chance of profiting than do latecomers. Viewing the scheme as a whole, an investor's profit depends on occurrences he cannot control: whether other people induce still others to pay $1,000 to join the scheme.
Defendant contends that if the pyramid club is a lottery, every speculative investment is a lottery. Whatever similarities exist between pyramid clubs and speculative ventures, defendant's argument is unsound. The legislature has specifically excepted the latter from the gambling statutes. Section 945.01(1), Stats., provides in relevant part:
A bet is a bargain in which the parties agree that, dependent upon chance even though accompanied by some skill, one stands to win or lose something of value specified in the agreement. But a bet does not include:
(a) Bona fide business transactions which are valid under the law of contracts including without limitation:
1. Contracts for the purchase or sale at a future date of securities or other commodities....
. . . .
The pyramid club has no element of a "bona fide business transaction." It simply involves money exchanges. No contracts are entered for the purchase or sale of securities or commodities. A pyramid club does not fall within the exception under sec. 945.01(1)(a)1.
The analogy of a pyramid club to a speculative investment is unpersuasive, even in the absence of a statute comparable to sec. 945.01(1)(a)1, Stats. Unlike a speculative venture, defendant's club has a classic gambling trait: shuffling a given number of dollars between participants with no effect on the total wealth of the group. A speculative investment may increase or decrease the wealth of all investors in proportion to their investments. *299 The skill involved in locating a sound speculative investment is far different from the skill of shrewd operators who start a money pyramid and locate investors before the pool of potential members is exhausted.[5]
*300 Defendant contends that construing sec. 945.01(2)(a), Stats., to include his pyramid club violates the rule that penal statutes are strictly construed in favor of the accused. The rule he relies on is not violated. It is inapplicable. The statute has not been shown to be ambiguous. The rules of statutory construction are inapplicable to unambiguous statutes. State v. Rabe, 96 Wis. 2d 48, 70, 291 N.W.2d 809, 819 (1980).
We conclude that the amended complaint alleged facts which, if proven, showed that defendant's pyramid club redistributes money among individuals by a process which, although accompanied by some salesmanship, is predominantly controlled by chance. It therefore stated sufficient facts to constitute the offense charged, that defendant permitted the operation of a lottery on his premises, within the meaning and intent of sec. 945.04 (1), Stats.

C. Principal Use of Premises

[6]
Defendant contends that the amended complaint alleged insufficient use of the warehouse for pyramid club meetings to constitute a "principal use" of the premises. A complaint is sufficient if a fair-minded magistrate could reasonably conclude that the facts alleged justify further criminal proceedings and that the charges are not merely capricious. State ex rel. Cullen v. Ceci, 45 Wis. 2d 432, 442, 173 N.W.2d 175, 179 (1970).
*301 State v. Morrissy, 25 Wis. 2d 638, 642-43, 131 N.W.2d 366, 369 (1964) (emphasis added), discussed the meaning of "principal uses" in sec. 945.01(4), Stats:
The term . . . contemplates a comparison of the degree of use between a class of principal uses and incidental uses. No mathematical definition can be given, and admittedly the line of demarcation is difficult to draw. . . .
The use of a place or room at any given time may determine its principal use at that time but for the purpose of sec. 945.01(4), Stats., such use must be considered in light of the overall or other uses of the place or room. A sufficient period of time must be considered to fairly ascertain the character of the alleged gambling place in terms of principal uses. . . .
The Morrissy court rejected the contention that a Monday night poker game in defendant's tavern could not constitute a principal use of the tavern because the game occurred only twenty-five or twenty-six times a year.
The amended complaint alleged that three club meetings occurred at the warehouse, that all club transactions were to take place at the warehouse, and that such meetings had been taking place for about three weeks previously. It alleged that at the February 4 meeting Kaehr said he was starting a new group because the existing one had been meeting at the warehouse for about three weeks and was getting too large.
[7]
We conclude that under Morrissy, supra, the amended complaint contains sufficient factual allegations showing that conducting pyramid club meetings was one of the principal uses of the warehouse. Consequently, the trial court did not err in denying defendant's motion to dismiss the amended complaint.

3. Vagueness And Overbreadth

Defendant contends that sec. 945.04(1), Stats., is unconstitutionally vague and overbroad. He asserts that the *302 statute does not give fair notice that the activities of a pyramid club constitute a lottery. He argues that because the prize and chance elements in his club are so similar to those in a lawful speculative investment, a reasonable person could believe the two types of ventures are the same. Because sec. 945.12 specifically outlaws automobile chain sales, he contends that a reasonable person could believe that other chain schemes are lawful. We reject each contention.
Vagueness and overbreadth are different concepts. State v. Starks, 51 Wis.2d 256, 263, 186 N.W.2d 245, 249 (1971). Overbreadth pertains to the possibility that sanctions may be applied against constitutionally protected conduct. Id.; State v. Zwicker, 41 Wis. 2d 497, 507, 164 N.W.2d 512, 517 (1969). Defendant does not contend that constitutionally protected conduct is involved. Accordingly, overbreadth is not an issue. We turn to the vagueness issue.
As applied to statutory definitions of crimes, "The concept of vagueness rests on the constitutional principle that procedural due process requires fair notice and proper standards for adjudication." State v. Courtney, 74 Wis. 2d 705, 709, 247 N.W.2d 714, 718 (1976) (footnote omitted). If a person of ordinary intelligence could not reasonably be expected to understand that his conduct was unlawful, he cannot be prosecuted. State ex rel. Gutbrod v. Wolke, 49 Wis. 2d 736, 750, 183 N.W.2d 161, 168 (1971). The Gutbrod court said:
Fairness requires fair warning of the existence of a crime and the fact of a penalty, but it does not require exact knowledge of all relevant criminal provisions governing the particular act he contemplates doing. . . . The fairness test of due process requires only that the statute convey "sufficiently definite warning as to the proscribed conduct when measured by common understanding and practices." *303 49 Wis. 2d at 750-51, 183 N.W.2d at 168 (quoting United States v. Petrillo, 332 U.S. 1, 8 [1947]) (footnotes omitted).
A reasonable person should realize that a pyramid scheme differs significantly from a speculative investment. A pyramid scheme merely transfers money from those on the bottom to those on top, with no possible net change in wealth for all participants. All participants in a speculative investment share the profits and losses in proportion to their investments. The "chance" element differs significantly because the skill in selecting between speculative investments is far different from gulling persons into a pyramid.
The existence of sec. 945.12, Stats., the motor vehicle sale chain statute, should not lead a reasonable person to conclude that all other chain schemes are lawful. Section 945.12 merely declares one type of chain transaction unlawful. A thoughtful person desiring to obey the law ought also determine whether another chain scheme falls within the general prohibition against lotteries in sec. 945.01.
Defendant argues that because the authors of opinions on which he relied believed the club was lawful or were confused about its legality, the statute's vagueness is established. When deciding to join the club, he relied on an opinion which is not of record by an unidentified attorney and on a newspaper article. The article is headlined, "Attorney General Says Pyramid `Game' Illegal," but reports that a district attorney told several club members it was not illegal. A town constable said the club was legal. Defendant saw another opinion by unidentified attorneys, the substance of which is epitomized by the following excerpt: "In summary, an argument can be made that the money pyramid game is a lottery under the Wisconsin definition. Arguments to the contrary can also be made. The Wisconsin law is certainly *304 not as clear as it could be." Defendant's brother testified that a person in the Attorney General's Office would not say whether the club was legal or illegal.
[8]
In State v. Evjue, 253 Wis. 146, 159, 33 N.W.2d 305, 311 (1948) (citations omitted), the court said:
It is not violative of due process of law for a legislature in framing its criminal law to cast upon the public the duty of care and even of caution, provided that there is sufficient warning to one bent on obedience, that he comes near the proscribed area.
Defendant admitted he suspected the legality of the pyramid club. He therefore knew he was sailing close to the rocks and shoals of the criminal law. That he miscalculated the risk does not render the statute unconstitutionally vague.
We reject defendant's last constitutional contention that a "principal use" of the premises is an insufficient standard for determining whether premises are being used as a gambling place under sec. 945.04(1), Stats. The statute distinguishes between "principal" and "incidental" uses of premises. Morrissy, supra. A person of ordinary intelligence can be expected to understand the distinction.
We conclude that defendant has failed to show that the statute is unconstitutionally vague.

4. Sufficiency Of Evidence

Defendant moved to dismiss when the state rested, claiming it had failed to meet its burden of proof. He challenges the sufficiency of the evidence to satisfy the "principal use" requirement in sec. 945.01(4), Stats. He asserts that a reasonable juror could not have concluded that he intentionally permitted the warehouse to be used for a lottery.
Our review of the sufficiency of the evidence on a motion to dismiss at the close of the state's case is limited *305 to whether, "considering the state's evidence in the most favorable light, the evidence adduced, believed and rationally considered, is sufficient to prove the defendant's guilt beyond a reasonable doubt." State v. Duda, 60 Wis. 2d 431, 439, 210 N.W.2d 763, 767 (1973) (citations omitted).
[9]
Sufficient credible evidence existed for the jury to conclude that the use of the warehouse for pyramid club meetings constituted a principal rather than an incidental use of the premises. We need not reiterate that evidence. The testimony of the Pigorschs as to the club's operation was sufficient for the jury to conclude that it was a lottery within the meaning of sec. 945.01(2), Stats.
We turn to the sufficiency of the evidence to prove intent. Defendant contends that because he did not know his pyramid club was an illegal lottery, the jury could not find he permitted the warehouse to be used as a gambling place. The contention has no merit.
Defendant's mistake as to the legality of the pyramid club under the criminal laws of this state does not negate the existence of intent. State v. Collova, 79 Wis. 2d 473, 488, 255 N.W.2d 581, 588 (1977); State v. Britzke, 108 Wis. 2d 675, 683, 324 N.W.2d 289, 292 (Ct. App. 1982). "An honest error, whether of fact or of law other than criminal law, is a defense if it negatives the existence of a state of mind essential to the crime." Sec. 939.43(1), Stats. (emphasis added). It is undisputed that defendant allowed the warehouse to be used for the pyramid club's operations. The jury possessed sufficient evidence to find he had the requisite criminal intent, notwithstanding an error as to the lawfulness of those operations.

5. Jury Instructions

Defendant contends that the trial court erroneously instructed the jury on the meaning of "principal use," erred when it responded to the jury's request for clarification, *306 and erred when instructing the jury on mistake of law.
The trial court instructed the jury:
One of whose principal uses means one of the most important or chief functions of the real estate. A principal use need not be the only use or even 50 percent of the total usage of the real estate. The use of any place or room at any given time may determine its principal use at that time, but that use must be considered in light of the overall or other uses of the place or room. In order to constitute one of the principal uses, the usage must be more than incidental. You must view the character of the alleged gambling place over a sufficient period of time to determine whether the conducting of a lottery constituted one of the principal uses. You are not restricted to the dates set forth in the complaint in determining the sufficiency of usage.
The jury asked the court:
Can you quantify for us the period of time involved "at that time" as a week, two weeks, year, et cetera? . . .
Can you define "incidental?" . . .
Can you define "principal?" . . .
The court responded:
The term "at that time" . . . correlates to the use of the term "at any given time" earlier in the same sentence. You have to refer to the sentence as a whole when you get back to the jury room.
. . . [T]he term "incidental" is used in its common and ordinary meaning.
. . . [T]he third paragraph from the bottom on the third page when taken as a whole is an attempt to define the term "one of the principal uses" as part of the definition of what constitutes a gambling place.
The trial court's instructions properly paraphrased Morrissy, 25 Wis. 2d at 642-43, 131 N.W.2d at 369. The clarification in no sense changed those instructions. No *307 error occurred in the instructions or clarification as to "principal use."
Defendant claims error in the following instruction: "It is for the jury to determine whether the Pyramid Club constitutes an illegal lottery. The defendant's honest mistake as to the criminal law in this area does not, by itself, constitute a defense to this charge." He claims that reasonable jurors could believe they were being instructed that he had violated the law. The contention has no merit. Immediately before the challenged instruction, the court instructed the jury on the law of lotteries, and that to find him guilty, the jury must be satisfied beyond a reasonable doubt that he permitted real estate owned by him to be used as a gambling place. The first sentence in the challenged instruction reemphasized the jury's duty to make a determination as to the club's legality. A reasonable juror could not have been misled as defendant claims.
By the Court.  Judgment and order affirmed.
NOTES
[1]  Defendant does not dispute that the amended complaint describes the club's operation with substantial accuracy. The amended complaint alleged:

The defendant explained that a person could "buy into" this "club" for $1,000, and be placed at the bottom step, or step 6, of the pyramid with 31 others; that person should then sell two "memberships" for $1,000 each, keep $1,000 and pass $1,000 to the person above him on the pyramid; by selling those "memberships", the person would move from step 6 to step 5 on the pyramid; if each of the two new "members" sold two memberships, the person would move to step 4; this process would continue until the person reached step 1, if all the other people had sold their memberships, the 32 new people entering at step 6 would pay him or her $1,000 each; the person, therefore, could receive $32,000 and also recover the cost of his $1,000 "membership"....
[2]  Section 945.12, Stats., provides:

Whoever sets up, promotes or aids in the promotion of a plan by which motor vehicles are sold to a person for a consideration and upon the further consideration that the purchaser agrees to secure one or more persons to participate in the plan by respectively making a similar purchase and in turn agreeing to secure one or more persons likewise to join in said plan, each purchaser being given the right to secure money, credits, goods or something of value, depending upon the number of persons joining in the plan, shall be held to have set up and promoted a lottery and shall be punished as provided in s. 945.02. The further prosecution of any such plan may be enjoined.
[3]  Contra, Braddock v. Family Finance Corp., 506 P.2d 824, 826-27 (Idaho 1973) (if skill plays any part in determining the distribution there is no lottery). This "pure chance" doctrine is incompatible with sec. 945.01(2)(a), Stats.
[4]  Commenting on the element of chance, the Roberts court quoted from Note, Pyramid Schemes: Dare To Be Regulated, 61 Geo. L. J. 1257, 1269 (1973) (footnote omitted), which stated: "The element of chance is present because the financial gain of any participant is the result of factors outside his control: the action of prior participants, the degree of market saturation, and the prospects of an individual continuing the recruiting chain."
[5]  The inevitability of market saturation is easily illustrated. Assuming that every club participant recruits two new members, the following table shows the number of persons necessary to fill out that level of the club (column A) and the total number of persons who have participated in the club through that level (column B):



                 COLUMN A                COLUMN B
CLUB LEVEL    (Number at Level)    (Total Participants)
__________    __________________   _____________________
     1                1                       1
     2                2                       3
     3                4                       7
     4                8                      15
     5               16                      31
     6               32                      63
     7               64                     127
     8              128                     255
     9              256                     511
    10              512                   1,023
    11            1,024                   2,047
    12            2,048                   4,095
    13            4,096                   8,191
    14            8,192                  16,383
    15           16,384                  32,767
    16           32,768                  65,535
    17           65,536                 131,071
    18          131,072                 262,143
    19          262,144                 524,287
    20          524,288               1,048,575

Of the 1,048,575 participants through level 20, the 524,288 at level 20 will have lost $1,000 because they have not sold memberships. The 507,904 participants at levels 15-19 will have broken even because they have sold two memberships but have received no $500 payments, there being no members six levels below them. The 16,382 participants at levels 2-14 will have profited by $32,000 each because they received payments from members six levels below them. One person, the originator, will have profited by $64,000 (assuming the originator keeps the $1,000 from his two buyers at level two and collects $500 from the 124 members at levels three through seven because his name would be at the top). The 1980 population of Dane County, in which defendant's club operated, was 323,545. Wisconsin Blue Book at 718 (1981). To complete the pyramid through level 20 would require the participation of about one of every four persons in the state. The 1980 Wisconsin population was 4,705,335. Id. at 748.
