According to the evidence presented at trial, the defendants participated in and encouraged others to join a classic “pyramid scheme.” A Superior Court jury convicted them of violating G. L. c. 271, § 7 (setting up or promoting a lottery). On appeal, the defendants argue that their motions for required findings of not guilty should have been granted for two distinct *593reasons. First, they argue that the scheme at issue was not a “lottery” subject to the statute. Second, they argue that their role in the scheme did not rise to the level of “promoting” it. They also argue error in the jury instructions. We affirm.
Background. Applying the familiar standard set forth in Commonwealth v. Latimore, 378 Mass. 671, 676-678 (1979), we conclude that the jury could have found the following facts.2 During 2006, a money-making venture circulated through the Cape Verdean community in the Dorchester section of Boston. This venture was sometimes referred to as the “table game,” because the participants were said to be sitting at imaginary “tables.” There were fifteen players at each “table,” with the players divided into four levels denominated as courses of a meal. There were eight players in the “appetizer” course, four at “soup and salad,” two at “entree,” and one at “dessert.” New participants joined at the “appetizer” level. In order to join, each player had to pay an entrance fee of between $1,000 and $5,000 (depending on the table).3 That money was paid to the person who was enjoying dessert. This would conclude the round, and the person who had completed his meal would retire fully sated. The remaining players would be split into two new tables, with each player advancing to the next course at the new *594table. Each of the four “soup and salad” players at each new table was then to recruit two new appetizer participants to complete the table. The tables would replicate in this fashion, with players looking to advance through the four courses to the payoff at the end. Assuming all went according to plan, the person who had finished the meal would leave the table with eight times what he or she had initially paid to join the game.
The defendants each participated in the pyramid scheme and actively recruited others to join. Their soliciting of others took many forms, including personal conversations, electronic mail messages, and conference calls.
Discussion. 1. Whether the table game is a “lottery.” As noted, the defendants argue that — as matter of law — the table game is not a “lottery” within the meaning of G. L. c. 271, § 7.4 That term has been the subject of a good deal of case law. As the Supreme Judicial Court has long recognized, “lottery” encompasses a large variety of activities, which include three elements: “(1) the payment of a price for (2) the possibility of winning a prize, depending upon (3) hazard or chance.” Commonwealth v. Lake, 317 Mass. 264, 267 (1944), citing Commonwealth v. Wall, 295 Mass. 70, 72 (1936), and Commonwealth v. Plissner, 295 Mass. 457, 463 (1936).5 There is no question that the first two elements are satisfied here: players paid a *595“price” (the entry fee) for the possibility of winning a “prize” (the payoff they obtained if and when they reached the dessert course). The debate is over the third element. The defendants argue that whether one “wins” the game cannot fairly be said to depend on “hazard or chance.” They point out that players were required to recruit others to join, and they suggest that winning depended largely on the “skill” of the players in completing that task. On this basis, they argue that, as matter of law, the game could not be considered a “lottery.” See Commonwealth v. Lake, 317 Mass. at 267 (holding that “a game is . . . considered a lottery if the element of chance predominates and not a lottery if the element of skill predominates”).
We reject the defendants’ argument. As in other classic pyramid schemes, players in the table game stood to turn the expected profit so long as participation in the game kept growing. However, as is self-evident from the mathematics on which such schemes are based, it is inevitable that at some point the pool of potential participants would become saturated. At that point, there would no longer be the supply of new players necessary to feed the ever-growing appetite of the system. As a result, the large group of participants who had not yet completed their dessert would remain unsated and lose the funds they had paid to join. As the United States Supreme Court recognized over a century ago, pyramid schemes “must ultimately and inevitably result in failure.” Public Clearing House v. Coyne, 194 U.S. 497, 515 (1904).
Given that pyramid schemes necessarily follow an ill-fated trajectory, whether someone succeeds or fails by joining one effectively turns on the happenstance of precisely where along that trajectory he joins. Even to the extent that a given player in *596the game in question here might marginally have been able to improve the chances of winning by employing “skill” in recruiting others, we believe that success or failure remained largely outside a player’s control and was therefore predominantly determined by “chance.”
The large majority of other courts that have examined similar statutes have come to the same conclusion. For example, in determining that a pyramid scheme fell within the language of a Federal statute that prohibited a “lottery or scheme for the distribution of money ... by lot, chance, or drawing,” the United States Supreme Court concluded that “the amount of such return [achieved by members of the scheme who successfully recruited others] depends so largely, and indeed almost wholly, upon conditions which the member is unable to control, that we think it fulfills all the conditions of a distribution of money by chance.” Public Clearing House v. Coyne, 194 U.S. at 512-513.6 See Lashbrook v. State, 550 N.E.2d 772, 775-776 (Ind. Ct. App. 1990); Solon v. Meuer, 141 Misc. 2d 993 (N.Y. Civ. Ct. 1987); Roberts v. Communications Inv. Club of Woon-socket, 431 A.2d 1206, 1207-1208, 1211-1212 (R.I. 1981); Burnom v. State, 55 S.W.3d 752, 754 (Tex. App. 2001); State v. Dahlk, 111 Wis. 2d 287, 294 & n.1, 296-300 (Ct. App. 1983).7 Those jurisdictions that have come to the opposite conclusion have done so based on specific statutory wording or interpretative principles not applicable here.8
To be sure, the fact that money invested in an enterprise may *597be subject to risk, with the potential return largely dependent on the actions of others, does not by itself render the enterprise an illegal lottery. Indeed, if this were the case, then most business enterprises could be considered “lotteries.” As courts have recognized, however, pyramid schemes exhibit distinctive elements that distinguish them from legitimate business ventures. For one thing, pyramid schemes merely shuffle money among the participants without affecting their collective wealth.9 This is a “classic gambling trait” that differentiates such schemes from legitimate speculative investments. State v. Dahlk, supra, 111 Wis. 2d at 298-300 (“pyramid club” found to constitute an illegal “lottery”). Additionally, the very fact that pyramid schemes are doomed to fail prevents them from being considered “a legitimate business enterprise.” Public Clearing House v. Coyne, 194 U.S. at 515.
Further support for our interpretation of G. L. c. 271, § 7, can be found by examining the Legislature’s use of the term “lottery” in a neighboring section of the same chapter. General Laws c. 271, § 6A, inserted by St. 1938, § 144,10 outlaws a certain type of practice known as a “chain referral” sales scheme, a practice or plan by which
“goods or anything of value is 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 or purchases 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 . . . .”
G. L. c. 271, § 6A. That section provides that anyone who *598engages in such a practice “shall be held to have set up and promoted a lottery and shall be punished as provided in [G. L. c. 271, § 7].” Ibid. A chain referral sales scheme shares many characteristics of a pyramid scheme, although it pushes at the boundaries of the ordinary usage of the term “lottery.” The fact that the Legislature nevertheless has stated that such a scheme is a “lottery” punishable under § 7 confirms that the Legislature intended the term “lottery” to encompass a broad array of practices that distribute rewards based on chance, including pyramid schemes. See generally Boswell v. Zephyr Lines, Inc., 414 Mass. 241, 247 (1993) (noting that courts should look to related statutes for interpretive guidance).
2. Jury instruction. In a related argument, the defendants contend that the judge provided the jury inadequate instruction on the meaning of the term “lottery.” The Supreme Judicial Court has held that “[wjhether [a] game was predominantly one of chance or of skill [is] a question for the jury.” Commonwealth v. Lake, 317 Mass. at 268. In order for the jury to play its role in deciding that question, the defendants sought to have the jury instructed on the skill versus chance distinction. The trial judge declined that request, and she instead instructed the jury that a “lottery” had to include “some element of chance or luck,” without mentioning the potential role that “skill” might play.11 Despite the judge’s rejection of their position, the defendants declared themselves “content” with the instructions.
Because the defendants did not preserve their challenge to the jury instruction on what constitutes a “lottery,” our review of any such claim is limited to whether the instruction was erroneous and, if so, whether it created a substantial risk of a miscarriage of justice. Commonwealth v. Alphas, 430 Mass. 8, 13 (1999). Commonwealth v. Ortega, 441 Mass. 170, 180 (2004). We conclude that the instruction was erroneous in that the jury were informed that there needed merely to be “some element” of chance, not that chance had to “predominate[].” See Com*599monwealth v. Lake, 317 Mass. at 267.12 However, we also conclude that this error did not create a substantial risk of a miscarriage of justice. As discussed above, there is no merit to the defendants’ argument that “chance” played a limited role in the table game. The error in the jury instruction was therefore not material.
3. The defendants’ role. There was overwhelming evidence upon which the jury could have concluded that the defendants actively touted the pyramid scheme and recruited others to join it. The defendants nevertheless argue that the evidence was insufficient to establish that they “promoted” the scheme.13 They contend that they were mere participants who were simply following rules that had long before been established by others, and that their role was not materially different from other participants (some of whom the Commonwealth had promised not to prosecute in order to secure their testimony). The defendants argue that one cannot be convicted of “promoting” a lottery without playing a more significant role than they played, and they suggest that one needs to have initiated, managed, controlled, or personally profited from the scheme.
*600“A statute is to be interpreted according to the plain and ordinary meaning of its words.” Commonwealth v. Conaghan, 433 Mass. 105, 110 (2000), citing Rambert v. Commonwealth, 389 Mass. 771, 773 (1983), and Commonwealth v. Colon-Cruz, 393 Mass. 150, 167 (1984). The plain and ordinary meaning of “promote” is the same as the definition the judge provided to the jury: “[t]o promote something means to assist or help move along a particular cause, to move it forward to advance a cause. To promote also means to try to sell a particular cause. So, promote has the ordinary meaning that we all understand.”14 See, e.g., The American Heritage Dictionary of the English Language 1403 (4th ed. 2006) (defining “promote” as “to contribute to the progress or growth of; further” and “to attempt to sell or popularize by advertising or publicity”). The defendants have provided no compelling argument that the Legislature intended a different meaning here.
There was abundant evidence on which the jury could have found that the defendants “promoted” the table game under the definition that the judge correctly provided. Proof that the defendants played some sort of overarching role in promoting the game was unnecessary.15 See Commonwealth v. Boyle, 346 Mass. 1, 4 (1963) (“The possession of any recorded memorandum intended to be a minute of a bet is sufficient to demonstrate a violation of either G. L. c. 271, § 7, or § 17, or both of these sections, depending upon the contents of the memorandum”). *601Therefore, the judge properly denied the defendants’ motions for required findings of not guilty.16
Judgments affirmed.
The defendants were tried jointly over their opposition (together with a third defendant, who was acquitted). On appeal, they do not challenge the judge’s allowance of the Commonwealth’s motion for joinder or the denial of defendant S tewart-Johnson’s motion to sever. However, they do argue that the Commonwealth failed to “differentiate” among certain documents or items found at their home or to link such documents or items to one or the other of them. On this basis they suggest that it would be improper to take such items into account in analyzing whether the evidence was sufficient. Without crediting any such arguments or suggestions, we note that there is no need to rely upon the items in conducting our sufficiency analysis, and we have not done so.
The payments were characterized as “gifts,” with players encouraged to complete form “gifting statements” that referenced Federal tax law. It is not clear whether such statements were employed in a clumsy (and misguided) attempt to comport with the tax laws, or whether they served instead merely as a means of convincing new recruits that the scheme was legal. Instructions to the game also included a list of “magic words” to be used in the recruiting process, as well as words to be avoided. The recruiting efforts relied heavily on allusions to spirituality and social communion. For example, instructions for the marketing of the game encouraged the regular use of prayer at recruiting sessions, and they described the game (when played by women) as a “women’s gifting circle” that “created a powerful way to access the spiritual and physical energies.”
General Laws c. 271, § 7, as appearing in St. 1968, § 115, reads in whole as follows:
“Whoever sets up or promotes a lottery for money or other property of value, or by way of lottery disposes of any property of value, or under the pretext of a sale, gift or delivery of other property or of any right, privilege or thing whatever disposes of or offers or attempts to dispose of any property, with intent to make the disposal thereof dependent upon or connected with chance by lot, dice, numbers, game, hazard or other gambling device, whereby such chance or device is made an additional inducement to the disposal or sale of said property, and whoever aids either by printing or writing, or is in any way concerned, in the setting up, managing or drawing of such lottery, or in such disposal or offer or attempt to dispose of property by such chance or device, shall be punished by a fine of not more than three thousand dollars or by imprisonment in the state prison for not more than three years, or in jail or the house of correction for not more than two and one half years.”
The statute dates to 1719, and it has been amended many times over the centuries. Its language in fact criminalizes a wide range of conduct in addition to “settling] up or promoting] a lottery.” For example, it broadly prohibits *595“disposing] of or offering] or attempting] to dispose of any property, with intent to make the disposal thereof dependent upon or connected with chance by lot, dice, numbers, game, hazard or other gambling device.” See note 4, supra. Despite the presence of such catchall language, courts examining the statute have focused on the term “lottery.” Over time, “lottery” has become used as a shorthand for a wide variety of gambling practices deemed to be prohibited by the statute. Such practices extend significantly beyond the narrowest sense of the term (the sale of chances that a number selected by a player will match one chosen in a random drawing). Thus, for example, a pinball game with a cash prize has been viewed as a “lottery” within the meaning of the statute. Commonwealth v. Macomber, 333 Mass. 298 (1955).
The Supreme Court cited to a dictionary definition of “chance” as “something that befalls, as the result of unknown or unconsidered forces; the issue of uncertain conditions; an event not calculated upon; an unexpected occurrence; a happening; accident, fortuity, casualty.” Public Clearing House v. Coyne, 194 U.S. at 512. As this definition signifies, the concept of “chance” is broader than that of “randomness” (under which specific potential outcomes have an equal probability of occurring).
The pyramid schemes at issue in both Lashbrook v. State, supra, and Solon v. Meuer, supra, were identical to the one at issue here, except that people were said to be sitting in airplanes instead of at tables. See Lashbrook v. State, supra at 774-775; Solon v. Meuer, supra at 993.
See Braddock v. Family Fin. Corp., 95 Idaho 256, 258 (1973) (holding that pyramid scheme not lottery because State follows pure chance doctrine under which “[i]f skill plays any part in determining the distribution [of a prize] there is no lottery” [citation omitted]); State v. DeLuzio, 247 N.J. Super. 101, 109 (App. Div. 1993) (holding that pyramid scheme was not lottery *597under statute requiring that “chance” be “represented by and differentiated by numbers or by combinations of numbers or by some other media”), aff’d per curiam, 136 N.J. 363 (1994).
No exchange of goods, services, or other marketplace values occurs among the participants. There is instead a process of financial musical chairs leaving the late participants without their entry fee and without anything in return.
Neither party cited § 6A in their briefs. We issued an order directing the parties to be prepared to discuss that statute at oral argument, and we questioned both sides about the import of the statute at that time.
The trial judge explained her rejection of the defendants’ request as follows: “If [the jurors] come back with something, I’ll have to instruct at that point but I think to begin rather than talk about skill versus chance at this point in time it’s, I think, based upon the evidence that’s been established in this case.”
In fairness to the trial judge, we note that the “some element of chance” formulation comes verbatim from Mobil Oil Corp. v. Attorney Gen., 361 Mass. 401, 406 (1972). However, the extent of the role played by chance (versus skill) was not at issue in that case, and we do not interpret it as sub silentio overruling Commonwealth v. Lake, 317 Mass. at 267, which it favorably cites.
We also note that the trial judge separately instructed the jury that the Commonwealth additionally needed to prove that the defendants “intended to make the disposal of something of value depend upon or connected with chance by lot, numbers or gain” (an element the Commonwealth itself maintained it had to prove in addition to the defendants’ having promoted a lottery, even though a parsing of the unwieldy language of the statute makes this less than clear). In any event, that additional instruction does not itself cure the problem with the judge’s charge regarding the meaning of “lottery” because the “connected with chance” language is similar to the “some element of chance” formulation.
General Laws c. 271, § 7, subjects to punishment not only one who “sets up or promotes a lottery,” but also one who “aids either by printing or writing, or is in any way concerned, in the setting up, managing or drawing of such lottery.” See note 4, supra. Although the indictments alleged that each defendant “set up and/or promoted or aided in the set up and/or promotion of a lottery,” the trial judge presented the case to the jury based solely on a “promoting” theory.
The defendants apparently did not request an alternative definition, and in any event, they did not object to the instruction but instead declared themselves “content” with it. Nor do they actually argue on appeal that the judge erred in defining “promote” as she did.
Through a great deal of evidence, the Commonwealth sought to prove at trial that the defendants did in fact play a far larger role in promoting the scheme than did the average participant (for example, through taking the lead in organizing conference calls and the like). We need not resolve the relative extent of their roles in comparison to other participants, because in the case before us that ultimately goes at most to the wisdom of the Commonwealth’s decision to target them, and not other participants, for prosecution, rather than to the sufficiency of the Commonwealth’s evidence to prove the crime charged. For the same reason, we need not resolve whether there is any merit to the defendants’ suggestions that, in conducting our sufficiency analysis, we should not rely on some of the evidence through which the Commonwealth had sought to demonstrate the leadership role each defendant played. See note 2, supra.
In passing, the defendants complain that the Commonwealth based its case on “many separate and discrete acts,” and they suggest that the judge erred by not providing a specific unanimity instruction (even though none was requested). We see no merit in this argument. “Generally, a defendant is entitled to a specific unanimity instruction only ‘when the Commonwealth has proceeded on “alternate theories” ’ of guilt, defined as ‘separate, distinct, and essentially unrelated ways in which the same crime can be committed.’ ” Commonwealth v. Lonardo, 74 Mass. App. Ct. 566, 571 (2009), quoting from Commonwealth v. Santos, 440 Mass. 281, 287-288 (2003). “The law does not require that ‘the jury must be unanimous in their parsing of the details as to how a crime was committed.’ ” Commonwealth v. Lonardo, supra, quoting from Commonwealth v. Santos, 440 Mass. at 289.