The District of Columbia Lottery Board licensed Soo Young Bae, then a Washington merchant, to operate a terminal that prints and dispenses lottery tickets for sale. Bae used the terminal to generate tickets with a face value of $525,586, for which he did not pay. The winning tickets among these had a total redemption value of $296,153, of which Bae successfully obtained all but $72,000. Bae pleaded guilty to computer fraud, 18 U.S.C. 1030(a)(4), and the district court sentenced him to 18 months in prison. Bae challenges his sentence, in calculating which the district court valued the "loss" due to the fraud at $503,650--the market value of the tickets less the commission Bae would have received from the Lottery Board had he sold those tickets. We affirm.

In sentencing a defendant for fraud the district court must make a "reasonable estimate" of the victim's "loss." U.S.S.G. 2F1.1(b) & application n.9. Although Bae challenges the method by which the district court arrived at its estimate, he does not contest any of the data potentially relevant to the loss calculation, that is, the face value of the tickets, the commission he would have earned for selling the tickets he generated, and the value of the winning tickets. "The appropriate method for calculating loss amounts under the Guidelines is a prototypical question of legal interpretation, and we review de novo." United States v. Walker, 234 F.3d 780, 783 (1st Cir. 2000) (emphasis omitted).

The general rule in a case involving property obtained by fraud is that the measure of loss is "the fair market value of the particular property at issue." U.S.S.G. 2B1.1 application n.2 (incorporated by reference in U.S.S.G. 2F1.1 application n.8). Bae argues that "[a]t the instant any lottery ticket is printed," it is worth whatever value the lottery drawing later assigns to it; losing tickets, that is, have no value. Bae thus calculates the loss at $296,153, the value of his winning tickets. His approach misconceives the probabilistic nature of the lottery ticket, however; as the Government notes, "the value of the ticket is the value of a chance to win." Tickets are indistinguishable--and each has an equal probability of winning--until the drawing determines the winner(s). Prior to that time, all tickets have the same market value because they all have the same chance of winning a prize, which is why they all sell at the same price. A ticket's market value, moreover, always exceeds its expected payoff, because the ticket is priced at a level that also reflects some of the value consumers derive from playing the odds.

A ticket's value changes with the drawing, of course: once the lucky numbers are announced, the value of the winning tickets rises to the value of the prize money while the value of the losing tickets goes to zero. Numerous goods, however-from automobiles to common stocks--may change in value soon after they are purchased. Nonetheless, for the purpose of sentencing, the loss associated with their fraudulent procurement is equal to the value of the goods at the time of the offense. See, e.g., Walker, 234 F.3d at 783 (partial return of funds subsequent to embezzlement does not reduce valuation of loss); accord United States v. Baker, 200 F.3d 558, 561 (8th Cir. 2000); United States v. Burridge, 191 F.3d 1297, 1301 (10th Cir. 1999).

Bae also argues that in this case market price is an inappropriate measure of loss because "[t]he act of printing those tickets cost the D.C. Lottery nothing." There is no basis, however, for Bae's implicit suggestion that market price is an inadequate measure of loss merely because the fraudulently obtained good has a low marginal cost of production. See United States v. Watson, 189 F.3d 496, 501 (7th Cir. 1999) (value of stolen cigarette tax stamps is "fair market value of the stamps, not their replacement cost"); United States v. Jenkins, 901 F.2d 1075, 1083-84 (11th Cir. 1990) (loss due to theft of nonnegotiable stock certificates is face value, not cost of reprinting certificates). The Guidelines adopt fair market value rather than replacement cost as the measure of loss for good reason. See U.S.S.G. 2B1.1 application n.2. As the Government points out, measuring loss in terms of replacement costs rather than at fair market value would result in anomalous and capricious sentences. For example, if loss were measured by reference to replacement cost, then fraudulently obtaining a good from a consumer would be punished more severely than fraudulently obtaining the same good from the manufacturer, which can replace it at a lower cost. Similarly, defrauding a more efficient producer would carry a lower sentence than defrauding a less efficient producer of the same good. Nor does Bae offer any reason to think that the instanced anomalies are somehow ameliorated in cases where the fraudulently obtained item can be replaced cheaply; on the contrary, using replacement cost as the measure of loss only when replacement cost is low would increase the arbitrariness of the sentencing regime.

Bae offers a variant upon this argument when he contends that the fair market value of the tickets is an inappropriate measure of the loss that he caused because generating his tickets did not reduce the number of tickets that could be and were sold to others. This suggests that loss is poorly measured by the fair market value of a good the replacement cost of which is close to zero. For the reasons explicated above, abandoning fair market value as a measure of loss in favor of replacement cost only when replacement cost is low is a perverse policy and we reject it.

We also reject Bae's alternative argument that the proper measure of loss in this case is the Lottery Board's lost profit ($207,496), calculated as the market value of the fraudulently obtained tickets less both (1) the commission the Board would have paid Bae for selling those tickets and (2) the amount it would have had to pay to redeem the winning tickets among them had they been purchased lawfully. The Government suggests that the Guidelines should lead courts to "hesitate[ ] to engage in net loss calculations," and we agree. Lost profit is an undesirable measure of loss for roughly the same reasons that replacement cost is: Both measures would penalize frauds differently depending upon whether the victim is a consumer or a producer; create disparities in sentencing for the fraudulent procurement of identical items from different producers; and require the courts to inquire into the costs of production, rather than looking to the generally more accessible market value, in order to calculate a sentence. Estimating loss based upon lost profits rather than fair market value is also inconsistent with the principle that the full value of a stolen item is the measure of loss even if the item is later returned. See U.S.S.G. 2B1.1 application n.2; Walker, 234 F.3d at 783. (Because it is limited by the plea agreement it entered into in this case, the Government does not contest the district court's decision to deduct from its estimate of the loss the commission that Bae would have received had he legitimately sold the tickets that he printed, although this deduction is in principle indistinguishable from the deduction of payoffs foregone that Bae proposes here and we reject.)

Contrary to Bae's suggestion, our present conclusion is not inconsistent with our statement in United States v. Gottfried that estimates of loss under the Sentencing Guidelines seek "to measure the economic harm ... caused" to the victim. 58 F.3d 648, 651 (1995). In Gottfried, an attorney in the Department of Veterans Affairs destroyed documents in order to reduce his workload, and we held that the resulting loss to the Government could be estimated as the costs of "undoing the full extent of the damage." Id. at 652. There was no market by which to value the destroyed records, so "market value ... did not reflect the harm to the government," id.; when fair market value does provide "a reasonable estimate of the loss," U.S.S.G. 2F1.1 application n.9, however, it is to be preferred. See U.S.S.G. 2B1.1 application n.2.

Finally, Bae suggests that using market value as the measure of loss will "produce disparate sentences for similar crimes" because defendants who generate the same number of tickets but whose winnings differ will be sentenced similarly. As the Government properly points out, that is not a disparity because "the fortuity of 'winning' the lottery" is irrelevant. A lottery ticket is a chance to win a prize, and two defendants, one of whom gets a losing and one a winning ticket by fraud, commit the same act and therefore merit the same treatment. There would be a disparity, however, under Bae's approach: The unlucky malefactor who prints out only losing tickets presumably would get no sentence at all. Bae asks whether an offender who fraudulently obtains a single ticket that proves to be worth millions should be subject only to the minimal sentence associated with the face value of one ticket. Should such an offender attempt to redeem his winnings, as did Bae, the actual or the intended loss associated with that attempt, see U.S.S.G. 2F1.1 application n.8, would be the full amount of the jackpot. (We need not decide how to apply the Guidelines to a winner who, unlike Bae, was apprehended before trying to claim his prize.)

In conclusion, a "reasonable estimate" of the loss caused by Bae's fraud is the fair market value of the lottery tickets at the time that Bae printed them. The sentence imposed by the district court is therefore

Affirmed.*