DENNIS JACOBS, Circuit Judge:
Calvin Johnson appeals from a criminal judgment of the United States District Court for the Northern District of New York (McAvoy, ./.), entered October 20, 2015, on a plea of guilty (without a plea agreement) to a drug conspiracy in violation of 21 U.S.C. §§ 841(a)(1) and 846, and to being a felon in possession of a firearm,_ in violation of 18 U.S.C. § 922(g)(1). A few months after his plea on July 3, 2015, but before his sentencing, Johnson wrote to the district court seeking to withdraw his plea and replace his lawyer, asserting that he did not understand that his guilty plea would necessarily entail a mandatory life sentence. If he understood that the judge would have no discretion, Johnson explained, he would have gone to trial. The district court denied the motion without a hearing, and Johnson also appeals from that denial.
[518] We conclude that Johnson’s plea was not entered voluntarily, knowingly, and intelligently. In the plea hearing, the impression was given that there was a range of sentencing options: the judge spoke of “the potential sentences”; the prosecutor gave an account of multiple maximum and minimum sentences, discussed supervised release, and warned of the forfeiture of rights (including the right to hold public office); and the court and prosecutor discussed Sentencing Guidelines ranges and judicial discretion to weigh the facts and circumstances. Although the prosecutor at one point stated that a minimum sentence of life would “trump” other considerations, that critical advice was overwhelmed by Incompatible advisories. The sentencing transcript suggests that Johnson’s counsel (on whom Johnson would rely to sort it out) may not have understood the inexorable nature of the sentence either. And Johnson’s assertion that he would have gone to trial if he knew that a life sentence was foreordained is rendered plausible by the arresting fact that he derived absolutely no benefit or advantage from the plea.
Accordingly, we vacate the district court’s judgment and Johnson’s plea, direct that the case be reassigned, and remand for further proceedings consistent with this opinion.
BACKGROUND
I
In October 2014, a grand jury indicted Calvin Johnson on one count of participation in a drug-trafficking1 conspiracy in violation of 21 U.S.C. §§ 841(a)(1) and 846 and one count of possession of a firearm by a felon in violation of 18 U.S.C. § 922(g)(1). The statutory determinants of his sentencing exposure appear relatively complex, but his actual sentence if convicted could hardly be simpler.
The firearm count, pursuant to 18 U.S.C. § 924(a)(2), carries a maximum sentence of ten years of imprisonment and no mandatory minimum. The drug count, pursuant to 21 U.S.C. §§ 841(b)(1)(A) and 851, carries a maximum sentence of life imprisonment and a mandatory minimum that depends upon the application of prior-felony enhancements: the baseline is a mandatory minimum of ten years of imprisonment; a prior conviction for a felony drug offense makes a defendant eligible for a mandatory minimum of twenty years; and two such prior convictions make a defendant eligible for a mandatory life sentence. Pursuant to § 851, the “imposition of an enhanced penalty is not automatic,” but is triggered when “the Government files an information notifying the defendant in advance of trial (or prior to the acceptance of a plea) that it will rely on that defendant’s prior convictions to seek a penalty enhancement.” United States v. LaBonte, 520 U.S. 751, 754 n.1, 117 S.Ct. 1673, 137 L.Ed.2d 1001 (1997).
The government did seek an enhancement: it filed an information establishing that Johnson had been twice convicted of criminal sale of a controlled substance in the third degree in violation of New York State Penal Law § 220.39(1). Those judgments were entered nearly 20 years earlier, in September and December of 1995, when Johnson was 19 years old. Johnson was incarcerated from 1995 until 2003. He appears not to have had significant involvement with the criminal justice system after his release until he was indicted in the present case, when he was 38 years old.
[519] This indictment charges Johnson with responsibility for drug trafficking that allegedly occurred in or through a nightclub that Johnson operated in Binghamton, New York. The weapon that gives rise to the firearm count was apparently discovered behind a jukebox. By operation of the prior-felony information, conviction on the drug-trafficking count entails a mandatory sentence of life imprisonment. No other sentence is possible.
II
In March 2015, Johnson and his lawyer, Lee Kindlon, appeared by videoconference from Albany before Senior U.S. District Judge Thomas McAvoy in Binghamton. The purpose of the hearing was to enter a guilty plea. Judge McAvoy advised Johnson that he had a right to appear in the same room and asked whether it was “okay with [him]” that they proceed by videoconference, .and Johnson said that it was. App. 19. Johnson had no plea agreement, but that circumstance was never mentioned at his plea hearing. It is not clear from the record whether his lawyer attempted to negotiate an agreement, or whether the government was willing.
In colloquy, the judge asked Johnson whether Kindlon had explained to him “the potential sentences” (in the plural), “or consequences of pleading guilty,” and Johnson said yes; the judge asked him if he had understood them, and Johnson said that he had. Id. at 20.
Later, the judge asked the prosecutor, Miroslov Lovric, to “please advise Mr. Johnson and the Court what the maximum or any minimum penalties would be.” Id. at 30. Lovric said that “the possible maximum penalty is life imprisonment” and that,“the mandatory minimum pursuant to statute is life imprisonment.” Id. He went on to add that “there’s a supervised release term required of at least ten years”; that “[i]f there’s any violation of the terms of supervised release, the Court would have the power to add an additional five years of imprisonment for any violation thereof’-; that the second count had a “possible maximum sentence” of ten years with “no mandatory minimum required”; and that, with respect to both counts, “in addition to these possible maximum penalties,” Johnson would lose certain rights, including the right to vote, to possess a firearm, to hold certain public offices, and to obtain certain licenses. Id. at 30-31. He summed up, saying that he “believe[s] those are the possible maximum penalties and the statutory minimum penalties.” Id. at 31.
‘Without discussing the prosecutor’s remarks or asking Johnson whether he understood them, Judge McAvoy then addressed Johnson:
[T]he Court also has to inform you that under, and pursuant to certain Sentencing Guidelines that used to be mandatory but are no longer mandatory but still must be considered by the sentencing court, that my discretion in sentencing you is thereby affected and the Court must enforce the law as it stands today but sometimes the Court can sentence you above the Guidelines, below the Guidelines or [e]ven outside of the Guidelines depending upon the facts, the circumstances and the law that’s brought to the Court’s attention at or about the time of sentencing.
Id. at 32. He asked whether Johnson understood “what I just said about the Sentencing Guidelines” and Johnson said yes.
Judge McAvoy asked the prosecutor for a preliminary Guidelines calculation, and Lovric then delivered about two pages of transcript in the jargon of the United States Sentencing Guidelines. He described one calculation with the result that “the guidelines range is 30 to life,” another [520] that is also “30 to life,” another that “would be 262 to 327 months,” another that “would be 151 to 188 months,” another that “is 108 to 135 months” and one that is “188 to 235 months.” Id. at 33-34. He then added:
All of the guideline provisions I’ve just described are nevertheless trumped by the fact that the statutory mandatory minimum is a life term under Section 21 U.S.C. 841(b)(1)(A) [sic] and as I indicated that is the statutory mandatory minimum in this case when I indicated the possible penalties under count one. So the Guidelines are trumped by that statutory mandatory minimum.
Id. at 34. Without commenting on the prosecutor’s description of the Guidelines calculations or asking Johnson whether he understood their applicability (or that, as a practical matter, they simply had no applicability because of the mandatory life sentence), the judge asked Johnson, “now that you’ve heard about the statutory sentence and Guidelines, do you still wish to plead guilty?” Johnson said, ‘Tes, your Honor.”
Judge McAvoy then turned his questioning to Johnson’s lawyer. Kindlon described his background and his experience, including dozens of cases over more than a decade. He also said that he and members of his firm had spent “dozens and dozens of hours” on Johnson’s case, “in preparation, reviewing all the documents, going over them with Mr. Johnson and even trial prep over the past weekend and then meetings yesterday with [Johnson] in preparation for today’s plea.” Id. at 35. The judge asked him whether he knew of any defenses that would prevail at trial and Kindlon answered that “[a]gain, your Honor, after going over this thing from soup to nuts over the weekend, we could think of nothing. No viable defense to the charges.” Id. at 36. The judge asked if Kindlon knew any reason why Johnson should not plead guilty, and Kindlon said no. There is nothing to suggest why Johnson — in the midst of trial preparation — would knowingly elect to plead when a plea could yield no discount from the worst that could happen at trial.
Judge McAvoy accepted and entered the plea.
Ill
On June 24, 2015 — just shy of four months after his plea hearing — Johnson sent a handwritten letter to Judge McAvoy requesting that his plea be withdrawn and that Kindlon be replaced:
My plea was not made knowingly or voluntar[il]y. I was mislead and ineffectively assisted by my attorney into believing that your Honor could sentence me to a sentence lower than the statutory sentence provided in section 841(b)(1)(a) of the sentencing codes.
During my plea allocution you stated that you had the power to go above, below, or even outside the guidelines depending on the laws at the time of my sentencing. I misunderstood you to mean you could sentence outside of the statutory sentences as well.
Without being lead to believe this by my attorney I would never have pleád guilty to charges that sentence me to a mandatory term of life in prison.
I have everything to gain going to trial versus just accepting a life sentence. Mr. Khindlon has provided me with ineffective assistance, not only by advising me to plead guilty to a mandatory life sentence, but also by stating to me as well as stating to your Honor on the plea allocution record that “He cannot come up with a defense.”
Id. at 39-40. It does not appear that Kind-lon was asked to respond. In any event, he [521] did not. The government filed an opposition.
A few days after the date of Johnson’s letter, but one day before it was filed by the clerk, Kindlon filed a sentencing memorandum. That memorandum does not mention the mandatory sentence. It argues that the career-offender enhancement should not apply and that the court should use a 1:1 crack-to-powder ratio. It thus assumes application of the Sentencing Guidelines, even though they could have no effect as a result of the mandatory sentence. (The government’s sentencing memorandum responds to those arguments but also points out that the mandatory life sentence applies.)
On October 5, 2015, Judge McAvoy ruled without a hearing, denying the motion to withdraw the guilty plea and to replace Kindlon. Most of the decision is a detailed restatement of the plea hearing.2 It concludes that Johnson “under oath, informed the Court that he understood the charges against him and the consequences of pleading guilty, and that his attorney had explained both to him,” and therefore that his “claims here are contradicted by his own sworn statements at the plea allo-cution.” Id. at 52.
On October 21, 2015, Johnson and Kind-lon appeared before Judge McAvoy for sentencing. The judge asked Kindlon what he would like to say on behalf of his client, and Kindlon briefly discussed the phenomenon of overly harsh sentences and seemingly asked the judge to use discretion (though he could not lawfully do so):
[W]e stand here next to Mr. Johnson on [sic] watching the sands shift in front of us in terms of the sentencing guidelines and I only ask that the Court take this into consideration so we’re not standing here in five years or ten from now, you know, asking to have Mr. Johnson re-sentenced to something other than'what he may be sentenced to today, something much less. I ask the Court to be prospective in how it sentences Mr. Johnson. Look at all the things he’s done and balance them against the things which he pled guilty to and sentence him accordingly.
Id. at 79. Judge McAvoy said that he thought a “more appropriate” sentence “would be something in the neighborhood of 180 months” but that he was bound by the law. Id. at 80. Accordingly, Johnson was sentenced to life in prison.
With new counsel, Johnson appealed. He argues that his guilty plea should be vacated because it was not knowing, intelligent, and voluntary; that his motion to withdraw the plea should have been granted; and that it was an abuse of discretion to deny his motion to replace counsel without a hearing.
DISCUSSION
I
A guilty plea operates as a waiver of constitutional rights, including the rights to a jury trial and against self-incrimination, and it is therefore “valid only if done voluntarily, knowingly, and intelligently, ‘with sufficient awareness of the relevant circumstances and likely consequences.’ ” Bradshaw v. Stumpf 545 U.S. 175, 183, 125 S.Ct. 2398, 162 L.Ed.2d 143 (2005) (quoting Brady v. United [522] States, 397 U.S. 742, 748, 90 S.Ct. 1463, 25 L.Ed.2d 747 (1970)).
Procedurally, pleas are governed by Rule 11 of the Federal Rules of Criminal Procedure. Given the constitutional implications, “this Circuit has adopted a standard of strict adherence to Rule 11 and ... therefore we examine • critically even slight procedural deficiencies to ensure that the defendant’s guilty plea was a voluntary and intelligent choice, and that none of the defendant’s substantial rights has been compromised.” United States v. Livorsi, 180 F.3d 76, 78 (2d Cir. 1999) (quotations, citations, and modifications omitted). When a Rule 11 violation is raised in the district court, this Court reviews for harmless error. See United States v. Tien, 720 F.3d 464, 469 (2d Cir. 2013). “In demonstrating harmless error, it is not enough to negate an effect on the outcome of the case. Rather, the Government must prove that the error was harmless beyond a reasonable doubt.” Id. (citations and internal quotation marks omitted).
Rule 11 provides that “the court must address the defendant personally in open court” and “must inform the defendant of, and determine that the defendant understands” a long list of things, Fed. R. Crim. P. 11(b)(1), including “any maximum possible penalty” and “any mandatory minimum penalty.” Id. ll(b)(l)(H)-(I). The district judge in this case did not personally inform the defendant of any sentence at the plea hearing, but it is enough that the court directed the prosecutor to do so. The baffling complexity of the prosecutor’s account did, however, render serious the failure by the court to confirm that Johnson understood the sentence that his guilty plea entailed. Johnson says that he was confused, and it is easy to see how that might be. Johnson was not trained in the law.
The most significant fact for Johnson at his plea hearing — a fact that he had to understand for his plea to be voluntary, knowing, and intelligent — was that life imprisonment was the certain consequence of pleading guilty. This was not merely a potential sentence, or one possible maximum among other possibilities, but his certain and inevitable sentence upon conviction. By pleading guilty, he was effectively sentencing himself to spend the rest of his life in prison; yet this fact was not conspicuous at his plea hearing, which included discussion of many other “possible” (though actually impossible) sentences and robotic references to (inapplicable) calculations and judicial discretion.
Johnson’s plea hearing, in relevant part, proceeded in three explanatory stages, each of them comprehensible only from the perspective of a lawyer or judge for whom plea hearings are routine.
The prosecutor’s first lengthy recital, specifying the “possible maximum,” a “mandatory minimum,” the loss of certain rights, and statutory periods of supervised release with additional terms of incarceration for violations, was technically sound, but confusing and difficult to reconcile with the inevitability of Johnson’s sentence. The “possible maximum” was no mere possibility; and while conviction would bar Johnson from obtaining certain licenses and holding certain public offices, discussion of these moot considerations, without effective context, could only bespeak the possibility of a sentence short of life in prison. .
The judge inadvertently compounded the confusion. Without asking Johnson about what the prosecutor had just said, or whether Johnson understood the mandatory life sentence, the judge discussed discretion and the Guidelines, and the court’s ability to sentence “below the Guidelines or [e]ven outside of the Guidelines depend[523] ing upon the facts...App. 32. Everything the court said was accurate, but the better Johnson understood those points, the less he could appreciate that he would be sentenced to life, no matter what. So when Johnson confirmed his understanding, all he could have understood is that judges generally have considerable discretion in sentencing — not that in his sentencing the judge would have none whatsoever.
The prosecutor’s long and technical explanation of the Sentencing Guidelines described several widely-varying potential sentences. When at length the prosecutor came around to saying that the mandatory sentence “trumps” the other potential sentences, it was at cross-purposes to the earlier discussion. Even the government conceded in its brief, Gov. Br. 33 n.ll, and at oral argument that it would have been better to clarify the mandatory minimum. Explaining the statutory minimum in terms the defendant would understand was not just advisable, but essential to a valid plea.
The prosecutor’s recitation would be unremarkable to a lawyer or a judge who is accustomed to calculating a Guidelines range at every plea hearing; indeed, although the Guidelines have been advisory since United States v. Booker, 543 U.S. 220, 125 S.Ct. 738, 160 L.Ed.2d 621 (2005), district courts are still required by statute to “consider” them at sentencing, 18 U.S.C. § 3553(a)(4),3 and the Federal Rules of Criminal Procedure require judges to explain this obligation to defendants and to determine that they understand it before accepting a guilty plea, Fed. R. Crim. P. ll(b)(l)(M). The district court therefore can hardly be faulted for including this discussion at the plea hearing, as is customary and generally required. But the defendant’s understanding remains the paramount consideration. See United States v. Maher, 108 F.3d 1513, 1521 (2d Cir. 1997) (“What is essential ... is that ... the defendant actually understands.”).
Discussion of several “possible” sentences, notwithstanding their definite inapplicability to the defendant, undermined the plea, which can be valid only if the defendant has “sufficient awareness of the ... likely consequences.” Brady, 397 U.S. at 748, 90 S.Ct. 1463. The district court should have avoided confusion by clearly and unambiguously telling the defendant that, notwithstanding everything else being said, the consequence of his guilty plea would be a life sentence, period.
II
A remarkable feature of Johnson’s guilty plea, which seems to have gone unnoticed or unmentioned at his plea hearing, is that Johnson evidently stood to gain nothing from it. He had a constitutional right to a trial, and thereby at least a chance of acquittal. Criminal defendants' routinely waive that right and plead guilty in order to benefit from an offense-level reduction for acceptance of responsibility under § 3E1.1 of the Sentencing Guidelines, or to avoid more serious charges pursuant to a plea agreement. But Johnson had no plea agreement and the mandatory life sentence mooted any offense-level benefit. His options, if he had understood them, were to plead guilty and receive a life - sentence, or to proceed to trial and receive a life sentence if convicted. The latter might not turn out to be much better [524] than the former, but it is no worse, and it offers at very least a bargaining chip. Why, then, would Johnson take a naked guilty plea?
Johnson’s letter seeking to withdraw his plea states that he would not have pleaded guilty if he had understood the mandatory sentencing consequence because he had “everything to gain going to trial versus just accepting a life sentence.” And of course he is correct. In light of the circumstances, and absent any explanation, the plea appears on its face irrational. There might be some motive for a knowing and intelligent waiver in this situation, but none is obvious, and the district judge did not attempt to elicit one. The district court erred by failing to determine that the waiver was knowing and intelligent, “with sufficient awareness of the relevant circumstances and likely consequences.” Brady, 397 U.S. at 748, 90 S.Ct. 1463.
The government contends that imposition of the statutory penalty was “fairly communicated” to Johnson when the prosecutor stated that the statutory sentence “trumps” the guidelines. A footnote in the government’s brief offers the breathtaking understatement that “[t]his is not to say that it would have been inadvisable for the district court thereafter to insure that Johnson understood that the statutory mandatory minimum term of imprisonment was the guidelines sentence.” Gov. Br. 33 n.ll. Considering the context of the long and technical allocutions and the judge’s discussion of (inapplicable) discretion, it is a dubious proposition that anything was “fairly communicated”; but in any case, the district court was obligated to determine that the defendant actually understood. And he needed to understand not just that the mandatory minimum “was the guidelines sentence” (which implies that the judge has discretion to depart from it, since the Guidelines are advisory) but that it was the actual and inevitable sentence. “[A] plea of guilty is more than an admission of conduct; it is a conviction.” Boykin v. Alabama, 395 U.S. 238, 242, 89 S.Ct. 1709, 23 L.Ed.2d 274 (1969). It is “a grave and solemn act to be accepted only with care and discernment.” Brady, 397 U.S. at 748, 90 S.Ct. 1463. And “it cannot be truly voluntary unless the defendant possesses an understanding of the law in relation to the facts.” McCarthy v. United States, 394 U.S. 459, 466, 89 S.Ct. 1166, 22 L.Ed.2d 418 (1969).4
The only way to ensure that such a seemingly irrational plea is made knowingly is to tell the defendant clearly and unambiguously that the judge will have no discretion at sentencing, and that accepting the plea will result in no less than the mandatory sentence — in this case, to tell Johnson that pleading guilty means he will be sentenced to life in prison and that no other outcome is possible. The district judge was required to determine that Johnson understood this. If the judge had explained it, it is unlikely that Johnson, if rational, would have taken the plea. It was clearly not entered voluntarily, knowingly, and intelligently.
[525] Accordingly, we vacate the judgment of conviction and the plea underlying it. Because we hold that it was error to accept and enter Johnson’s guilty plea, we do not reach any arguments he raises with respect to the supposed failure to hold a hearing on his letter motion.
Ill
We usually remand cases “without any directions or suggestions as to the judge before whom they are to be conducted.” United States v. Robin, 553 F.2d 8, 9 (2d Cir. 1977). But there are circumstances in which:
both for the judge’s sake and the appearance of justice, an assignment to a different judge is salutary and in the public interest, especially as it minimizes even a suspicion of partiality. In such circumstances our remand does not imply any personal criticism of the trial or sentencing judge....
[T]he principal factors considered by us in determining whether further proceedings should be conducted before a different judge are (1) whether the original judge would reasonably be expected upon remand to have substantial difficulty in putting out of his or her mind previously-expressed views or findings determined to be erroneous or based on evidence that must be rejected, (2) whether reassignment is advisable to preserve the appearance of justice, and (3) whether reassignment would entail waste and duplication out of proportion to any gain in preserving the appearance of fairness.
Id. at 10 (quotations and citations omitted).
The first factor is either neutral or weighs only lightly in favor of reassignment in this case. The original judge did not rely on erroneous factual findings or on evidence that must be rejected. On remand, he would need to put out of his mind his earlier acceptance- of Johnson’s guilt and any adverse findings from the presentence investigation report; but he would not reasonably be expected to have substantial difficulty doing so.
We nevertheless find, on the basis of the second factor taken in conjunction with the third, that it would be “salutary and in the public interest” for the case to be reassigned “to preserve the appearance of justice.” If Johnson does proceed to trial, the appearancé of justice would best be preserved if he can do so before a judge who has not already accepted his guilt. Even assuming, as we do, that the original judge would be able to put earlier proceedings out of his mind and preside fairly, the “countervailing considerations of efficiency and feasibility” are weak in this case. Id. at 11. Johnson pleaded guilty without extensive earlier proceedings and the case does not appear to be factually complex, so there is no indication that the original judge “has gained familiarity with a detailed factual record” that would be wasteful for another judge to replicate. Id. at 10. Reassignment would therefore not “entail waste and duplication out of proportion to any gain in preserving the appearance of fairness.” Id.
Accordingly, we direct that the case be reassigned on remand.
CONCLUSION
For the foregoing reasons, we vacate the judgment of the district court and the guilty plea, direct that the case be reassigned, and remand for further proceedings consistent with this opinion.