{¶ 1} This case is before us pursuant to a remand from the Supreme Court of Ohio in which we were directed to consider appellants’ argument that R.C. 2915.01(AAA)(1) is unconstitutionally void due to vagueness. That argument had been rendered moot by our original decision in the case.

{¶ 2} Appellants, Pickaway County Skilled Gaming, L.L.C., and Stephen S. Cline, filed this action seeking a declaratory judgment regarding the constitutionality of R.C. 2915.01(AAA) and 2915.06 as amended by Am.Sub.H.B. 177 of the 127th General Assembly. Appellants asserted a number of constitutional grounds for their claim, including violation of the Due Process Clauses of the United States and Ohio Constitutions, violation of the Equal Protection Clauses of the United States and Ohio Constitutions, violation of the single-subject provision of the Ohio Constitution, and violation of the referendum provision of the Ohio Constitution.

{¶ 3} The trial court granted judgment in favor of appellees, the Ohio Attorney General, the Ohio Department of Public Safety, the Pickaway County Sheriff, and the Pickaway County Prosecuting Attorney (collectively “the state”) on all of the *684constitutional grounds asserted. We affirmed in part and reversed in part, finding that the Am.Sub.H.B. 177 amendment to R.C. 2915.01(AAA)(1), which changed the definition of “skill-based amusement machines” to require that such machines not award as a prize merchandise with a wholesale value exceeding $10, violated the Equal Protection Clauses of the United States and Ohio Constitutions because we concluded that the $10 limitation on prizes awarded by skill-based amusement machines is not rationally related to the state’s interest in regulating gambling machines. Pickaway Cty. Skilled Gaming, L.L.C. v. Cordray, 183 Ohio App.3d 390, 2009-Ohio-3483, 917 N.E.2d 305, ¶ 50. We found moot appellants’ argument, raised as part of their first assignment of error, that the amendment to R.C. 2915.01(AAA)(1) is unconstitutionally vague. Id. at ¶ 54. We rejected the remainder of the constitutional challenges appellants set forth, including appellants’ vagueness challenge to the Am.Sub.H.B. 177 amendment to R.C. 2915.01(AAA)(2). Id. at ¶ 69.

{¶ 4} The Supreme Court of Ohio reversed our conclusion regarding appellants’ equal-protection violation, finding that the $10 limitation on the value of prizes awarded by skill-based amusement machines is rationally related to legitimate government interests. Pickaway Cty. Skilled Gaming, L.L.C. v. Cordray, 127 Ohio St.3d 104, 2010-Ohio-4908, 936 N.E.2d 944. The court remanded the case to us for consideration of appellants’ claim that the amendment to R.C. 2915.01(AAA)(1) is unconstitutionally vague. Id. at ¶ 49.

{¶ 5} The Am.Sub.H.B. 177 amendment to R.C. 2915.01(AAA)(1) provides:

“Skill-based amusement machine” means a mechanical, video, digital, or electronic device that rewards the player or players, if at all, only with merchandise prizes or with redeemable vouchers redeemable only for merchandise prizes, provided that with respect to rewards for playing the game all of the following apply:

(a) The wholesale value of a merchandise prize awarded as a result of the single play of a machine does not exceed ten dollars;

(b) Redeemable vouchers awarded for any single play of a machine are not redeemable for a merchandise prize with a wholesale value of more than ten dollars;

(c) Redeemable vouchers are not redeemable for a merchandise prize that has a wholesale value of more than ten dollars times the fewest number of single plays necessary to accrue the redeemable vouchers required to obtain that prize; and

(d) Any redeemable vouchers or merchandise prizes are distributed at the site of the skill-based amusement machine at the time of play.

*685{¶ 6} A plaintiff may succeed in a facial challenge to the constitutionality of a statute only by “ ‘establish[ing] that no set of circumstances exists under which the Act would be valid.’ ” Washington State Grange v. Washington State Republican Party (2008), 552 U.S. 442, 449, 128 S.Ct. 1184, 170 L.Ed.2d 151, quoting United States v. Salerno (1987), 481 U.S. 739, 745, 107 S.Ct. 2095, 95 L.Ed.2d 697. “The Supreme Court of Ohio has stated that ‘[w]hen a statute is challenged under the due-process doctrine prohibiting vagueness, the court must determine whether the enactment (1) provides sufficient notice of its proscriptions to facilitate compliance by persons of ordinary intelligence and (2) is specific enough to prevent official arbitrariness or discrimination in its enforcement.’ ” Ohio Democratic Party v. Ohio Elections Comm., 10th Dist. No. 07AP-876, 2008-Ohio-4256, 2008 WL 3878364, ¶ 22, quoting Norwood v. Horney, 110 Ohio St.3d 353, 2006-Ohio-3799, 853 N.E.2d 1115, ¶ 84.

{¶ 7} Appellants argue that the $10 limitation on the wholesale value of a prize awarded as the result of a single play of a skill-based amusement machine is unconstitutionally vague because (1) the statute does not include any means by which to determine the “wholesale value” of a particular item of merchandise and (2) fluctuations in the wholesale value of a particular item of merchandise would make it impossible to determine with any certainty the wholesale value of that item at the time the prize is awarded. The state argues that neither of these factors render the $10 prize limitation unconstitutionally void, because the wholesale value can be determined by looking at the relevant market, i.e., the market from which the operator of the skill-based amusement machine purchased the prize to be awarded; and the value of the prize should be determined at the time the operator of the skill-based amusement machine purchases the item of merchandise, not at the time the prize is awarded.

{¶ 8} We agree with the state. There are multiple examples of statutes in which the value of an item must be determined, e.g., theft statutes in which the level of the offense depends upon the value of the property involved, and the courts have been able to determine such values by considering the relevant market. See State v. Cunningham (1990), 67 Ohio App.3d 366, 587 N.E.2d 310 (value of clothing stolen from a department store was not based on price-tag total, where evidence showed that items stolen were being offered at a discount). The fact that there may be an issue regarding the type of proof that would be necessary to support a claim by the state that the $10 prize limitation had been exceeded does not render the statute unconstitutionally vague. We also agree with the state’s assertion that the value of the prize awarded for playing a skill-based amusement machine would be more appropriately determined at the time the prize was obtained by the operator, not at the time the item is awarded as a prize.

*686{¶ 9} Consequently, the $10 limitation on the value of prizes awarded for playing skill-based amusement machines does provide sufficient notice of its proscriptions to facilitate compliance by persons of ordinary intelligence and is specific enough to prevent official arbitrariness or discrimination in its enforcement.

{¶ 10} Accordingly, we overrule that portion of appellants’ assignment of error asserting that the $10 prize limitation set forth in R.C. 2915.01(AAA)(1) is unconstitutionally void for vagueness, and affirm the judgment of the Franklin County Court of Common Pleas.

Judgment affirmed.