POSNER, Circuit Judge.

After pleading guilty to wire fraud, 18 U.S.C. § 1343, the defendant was sentenced to 48 months in prison and ordered to pay restitution of $718,000 to the victims of his fraud. Given the scale and sophistication of the fraud, which involved Lopinski’s looting millions of dollars from a multi-hundred-milhon-dollar corporation that he controlled, the only ground of his appeal — -that the district judge violated Fed. R.Crim.P. 11(c)(1) by failing to inform him at the guilty-plea hearing that the government would have to prove that the fraud was intentional — borders on the comic. Although there was no written plea agreement, an “Acknowledgment of Rights and Voluntary Plea” that Lopinski helped prepare in collaboration with his lawyers not only states that he understands the elements of the offenses with which he was charged, but recites fact's that demonstrate the intentional character of the fraud beyond any doubt. In moving to withdraw his plea, he argued that his lawyers had failed to dispel a misconception created in his mind by the fact that the words “intent to defraud” do not appear in the Acknowledgment. The judge held a hearing at which the lawyers testified that they had made clear to Lopinski that if he had not intended the fraud, he should not plead guilty. The judge believed the lawyers and denied the motion to withdraw the guilty plea.

Though Lopinski by his motion to withdraw his plea and by his false testimony in support of it (and his further false denials of intent to defraud made at his sentencing hearing) had shown himself unrepentant, the judge granted him a sentencing discount for acceptance of responsibility. U.S.S.G. § 3E1.1. The government, cross-appealing the sentence, argues that the judge committed a clear error in finding that Lopinski had accepted responsibility for his misconduct.

Lopinski did plead guilty, and that normally is a necessary condition for the acceptance of responsibility discount; but it is not sufficient. § 3E1.1 Application Note 3; United States v. Ewing, 129 F.3d 430, 435-36 (7th Cir.1997). The purpose of the discount is not merely to induce guilty pleas, sparing the government the expense of a trial and the risk of acquittal, valid benefits that can justify the quid pro quo of a reduced sentence, United States v. Bonanno, 146 F.3d 502, 512-13 (7th Cir.1998); United States v. Beserra, 967 F.2d 254, 256 (7th Cir.1992); it is also to reflect the reduced risk of recidivism of a defendant who by facing up to the wrongfulness of his conduct takes the first step to better behavior in the future. United States v. Stewart, 198 F.3d 984, 987 (7th Cir.1999); United States v. Bomski, 125 F.3d 1115, 1119 (7th Cir.1997); United States v. Mogel, 956 F.2d 1555, 1560 (11th Cir.1992). The cases indicate that both purposes must be present for the discount to be proper. United States v. Grimm, 170 F.3d 760, 766 (7th Cir.1999); United States v. Pryor, 32 F.3d 1192, 1195 (7th Cir.1994). The merely strategic guilty plea, which may reflect nothing more edifying than a certainty of conviction if the defendant invokes his right to a trial, does not augur “well for his future behavior. Against this it can be argued that an inquest on the sincerity of a defendant’s repentance neither is feasible, nor should be necessary to earn the discount. Most guilty pleas are strategic, as are most decisions to turn state’s evidence. Why rule out the possibility of rewarding such a decision? A guilty plea confers benefits on prosecutors *576 (and thus on society) by freeing up time that they can use to bring additional prosecutions. It relieves pressure on the courts as well. And the defendant trades higher certainty of punishment for a lower level of punishment. If district judges must insist on sincerity — a real change of heart — strategic pleas will be no good to defendants, who then will go to trial.

But these ruminations cannot help Lo-pinski, who forfeits his acceptance of responsibility discount not because of the state of his heart but because he tried to have things both ways — to have a chance at acquittal plus the discount for foregoing that chance, and because he used up a lot of prosecutorial time by the motion to withdraw the plea (surely as complex as many a trial) and his appeal.

Mr. Lopinski, to put it as charitably as possible, is in the state that psychologists call “denial”; he is also a liar. Far from acknowledging his violation of the wire-fraud statute, he has denied, beginning with his motion to vacate his guilty plea and continuing at his sentencing hearing after the motion was denied, that he intended to defraud anyone; and without such intent he cannot be guilty. Given the nature of his conduct, the denial is unbelievable, and he further lied about what his lawyers told him when he decided to plead guilty. The judge gave him a sentencing bonus for obstruction of justice by repeatedly perjuring himself at the post-plea hearings, and Lopinski does not challenge the ruling. He not only is not repentant, which we have suggested should perhaps not be a condition precedent for the grant of the acceptance of responsibility (despite the language of the cases); he is brazen or deluded.

So how could the judge have thought him deserving of an acceptance of responsibility discount? Because the judge believed that “ultimately, somewhere in his [Lopinski’s] psyche he has the appropriate mental state,” namely the acceptance of “some form of moral responsibility” (emphasis added). What the judge seems to have meant by these unelaborat-ed remarks, in light of Lopinski’s own plea for mercy that preceded them, is that Lo-pinski, while refusing to acknowledge that he had intended to defraud anybody, expressed what the judge considered genuine regret for the harm that he had done, that is, the losses he had caused by his conduct. And it is true if paradoxical that people can feel morally responsible for conduct that is (or that they think is) blameless in the sense of being wholly innocent in intent, as in the case of Oedipus, who not only did not know, but had no reason to know, that he had killed his father and married his mother. So the judge may have been correct in his conclusion, indeed insightful into the complex character of moral responsibility, given his premises. But we do not think that the Sentencing Commission intended acceptance of responsibility in this sense, cf. United States v. Beserra, supra, 967 F.2d at 256; United States v. Mohrbacher, 182 F.3d 1041, 1052 (9th Cir.1999), and so we conclude that the district judge’s error was one of law rather than one of application of law to fact. Acceptance of responsibility is not regret for the consequences of innocent mistakes, but recognition that one has violated the law. If Lopinski does not realize that he committed fraud, he is quite likely to repeat his fraudulent activity when he is released from prison, although he may endeavor to minimize the harm to others, for example by preying entirely on banks and other large institutions rather than on particularly vulnerable individuals. But the more important point is that, as we have already suggested, the law cannot tolerate a situation in which a criminal defendant plays heads I win tails you lose by combining a perjurious attack on his guilty plea with an appeal for mercy if the attack fails. See United States v. Stewart, supra, 198 F.3d at 987; United States v. Martinez, 169 F.3d 1049, 1056 (7th Cir.1999); United States v. Champion, 234 F.3d 106, 110-11 (2d Cir.2000) (per curiam); United States *577 v. Patron-Montano, 223 F.3d 1184, 1191 (10th Cir.2000).

The judgment is vacated insofar as the sentence reflects an adjustment for acceptance of responsibility, and the case is remanded with instructions to resentence the defendant -without that adjustment. In all other respects the judgment is affirmed.

AFFIRMED IN PART, VACATED IN PART, AND REMANDED WITH INSTRUCTIONS.