KETHLEDGE, J., delivered the opinion of the court in which BATCHELDER, GIBBONS, ROGERS, SUTTON, McKEAGUE, GRIFFIN, and THAPAR, *884JJ., joined, and WHITE, J., joined in the analysis of judicial estoppel. MOORE, J. (pp. 892-909), delivered a separate dissenting opinion in which COLE, C.J. and CLAY, STRANCH, and DONALD, JJ., joined, and WHITE, J., joined in all except part II.C. regarding judicial estoppel. STRANCH, J. (pp. 909-11), delivered a separate concurrence to Judge Moore’s dissent.
OPINION
KETHLEDGE, Circuit Judge.Roughly two decades have passed since the plaintiffs in this case murdered their victims. Ronald Phillips raped a three-year-old girl and beat her so badly that her internal organs ruptured. For two days she suffered intense abdominal pain and vomiting, until her heart collapsed. See State v. Phillips, 74 Ohio St.3d 72, 656 N.E.2d 643, 650-52 (1995). Gary Otte entered the home of an Ohio man, robbed him, and then shot him in the head. Two nights later, Otte pushed his way into a woman’s home and did the same things to her. After each murder Otte went out partying. See State v. Otte, 74 Ohio St.3d 555, 660 N.E.2d 711, 715-16 (1996). Raymond Tibbetts killed an elderly man and his caretaker. Police found the man slumped in his chair with butcher knives protruding from his chest and back. His caretaker lay on the floor in a pool of blood with her skull cracked open and its contents scattered nearby. See State v. Tibbetts, 92 Ohio St.3d 146, 749 N.E.2d 226, 237-39 (2001).
Phillips, Otte, and Tibbetts now claim that Ohio’s Execution Protocol would cause them to suffer severe pain in violation of the Eighth Amendment. In a sense the claim is unprecedented: the Supreme Court “has never invalidated a State’s chosen procedure for carrying out a sentence of death as the infliction of cruel and unusual punishment.” Glossip v. Gross, — U.S. -, 135 S.Ct. 2726, 2732, 192 L.Ed.2d 761 (2015) (internal quotation marks omitted). The State’s chosen procedure here is the same procedure (so far as the combination of drugs is concerned) that the Supreme Court upheld in Glossip. Every other court of appeals to consider that procedure has likewise upheld it, including most recently the Eighth Circuit, which rejected a nearly identical challenge in a procedural posture identical to the one here. See McGehee v. Hutchinson, 854 F.3d 488, 492 (8th Cir. 2017) (en bane) (per curiam), cert. denied, — U.S. -, 137 S.Ct. 1275, 197 L.Ed.2d 746 (2017); Glossip, 135 S.Ct. at 2739-40 (collecting cases); Brooks v. Warden, 810 F.3d 812, 818-22 (11th Cir. 2016); cf. Jordan v. Fisher, 823 F.3d 805, 811-12 (5th Cir. 2016). Yet here the district court thought the same procedure is likely invalid. We respectfully disagree and reverse the court’s grant of a preliminary injunction.
I.
The litigation that produced this appeal began in 2004, when death-row inmates challenged Ohio’s then-existing three-drug protocol under 42 U.S.C. § 1983. That protocol called for the injection of sodium thiopental (which anesthetizes the prisoner) followed by pancuronium bromide (which paralyzes the prisoner’s muscles) and finally p'otassium chloride (which stops the prisoner’s heart). By 2008, 30 of the 36 states with the death penalty had adopted that three-drug protocol. See Baze v. Rees, 553 U.S. 35, 42-44, 128 S.Ct. 1520, 170 L.Ed.2d 420 (2008). Yet the Ohio inmates argued that the protocol created an unacceptable risk that, if the sodium thiopental were improperly administered, inmates would feel the painful effects of the second and third drugs. In 2008, the Supreme Court rejected that argument and upheld Kentucky’s nearly identical three-drug protocol. See id. at 41, 128 S.Ct. 1520.
*885Nevertheless, the next year, Ohio announced that it was switching to the same one-drug protocol favored by the losing plaintiffs in Baze: a massive, lethal dose of either sodium thiopental or another barbiturate, pentobarbital. From 2010 to 2013, Ohio executed 20 inmates using those barbiturates. Meanwhile, opponents of the death penalty successfully pressured the pharmaceutical companies who make the drugs to stop selling them to states. See Glossip, 135 S.Ct. at 2733-35. Ohio’s supplies soon ran out, as did other states’. See id.; R. 941 at 31942-44.
The shortage led some states with three-drug protocols to turn to midazolam, a sedative in the same family of drugs as Valium. See Glossip, 135 S.Ct. at 2733-34. In 2014, Oklahoma adopted a protocol that called for the administration of 500 milligrams of midazolam—about 100 times the usual therapeutic dose—followed by a paralytic agent (pancuronium bromide, roeu-ronium bromide, or vecuronium bromide) and potassium chloride. Death-row inmates filed a § 1983 action alleging that Oklahoma’s protocol violated the Eighth Amendment. AlS relief, the inmates sought a stay, which the district court denied. The Supreme Court affirmed the denial for two “independent reasons”: that the district court “did not commit clear error when it found that midazolam is highly likely to render a person unable to feel pain during an execution”; and that Oklahoma was unable to acquire either pentobarbital or sodium thiopental. Id. at 2731, 2738-39.
In October 2016, Ohio adopted a lethal-injection protocol using the same three drugs that Oklahoma uses. Like the Oklahoma protocol, the Ohio protocol contains several procedural safeguards to ensure that executions are carried out humanely, including guidelines for identifying viable IV sites, detailed requirements for training execution team members, and a “consciousness cheek” after the 500-milligram injection of midazolam. If the prisoner is found to be conscious, a qualified drug administrator can inject another 500 milligrams of midazolam. After confirming that the prisoner is unconscious, the team can then administer the second and third drugs. See R. 667-1 at 19828-29.
Ohio planned to use this protocol to execute Phillips, Otte, and Tibbetts during the first four months of this year. The three inmates then filed complaints and moved for a preliminary injunction, claiming among other things that Ohio’s three-drug protocol violates the Eighth Amendment’s ban on “cruel and unusual punishments.” The plaintiffs’ theory here is the same one the Court rejected in Glossip: that the first drug—a massive dose of midazolam—will not prevent them feeling severe pain after injection of the second and third drugs.
After an evidentiary hearing, the district court found that “use of midazolam as the first drug” in Ohio’s three-drug protocol would create a “substantial risk of serious harm” under Baze and Glossip. The court separately held that Ohio was estopped from using the paralytic and heart-stopping drugs because of Ohio’s putative representations when it switched from its original three-drug protocol to the one-drug protocol in 2009. Thus, the court held that the plaintiffs had demonstrated a likelihood of success on their claims, and stayed the plaintiffs’ executions. This appeal followed.
II.
A.
The plaintiffs first argue that Ohio’s three-drug protocol violates their Eighth Amendment right to be free from cruel and unusual punishment. As to that claim, we begin with two areas of common ground. First, we agree with the plaintiffs *886and the district court that the protocol’s second and third drugs—the paralytic and potassium chloride, which stops the inmate’s heart—would cause severe pain to a person who is fully conscious. (Hence the need for the first drug—the 500-milligram dose of midazolam.) Second, we reject the State’s argument that the Supreme Court’s holding in Glossip categorically bars the plaintiffs’ claim here. The Court’s holding—that the district court there “did not commit clear error when it found that midazolam is highly likely to render a person unable to feel pain during an execution[,]” 135 S.Ct. at 2739—is couched expressly in terms of a standard of review that cuts the other way here. But neither, as the plaintiffs suggest, is Glossip irrelevant here. Quite the contrary: the Court’s opinion contains plenty of reasoning that was not confined to the record there—and which therefore binds us just as much as the reasoning in any other opinion of the Supreme Court.
1.
Yet here the district court’s opinion was seriously flawed nonetheless. To begin with, that opinion did not apply the relevant legal standard, which by now the Supreme Court and our court have recited a total of four times. Specifically, to challenge successfully a State’s chosen method of execution, the plaintiffs must “establish that the method presents a risk that is sure or very likely to cause” serious pain and “needless suffering[.]” Glossip, 135 S.Ct. at 2737 (emphasis in original) (internal quotations marks omitted); see also Baze, 553 U.S. at 50, 128 S.Ct. 1520 (same); Cooey v. Strickland (Cooey II), 604 F.3d 939, 944 (6th Cir. 2010) (same); Cooey v. Strickland (Cooey I), 589 F.3d 210, 220 (6th Cir. 2009) (same). Instead, the district court addressed only whether Ohio’s procedure presents a “substantial risk of serious harm,” Baze, 553 U.S. at 50, 128 S.Ct. 1520 (internal quotation marks omitted). That standard is correct so far as it goes; but it elides the more rigorous showing—that the method of execution is sure or very likely to cause serious pain— that the Supreme Court and our court have repeatedly said is necessary to satisfy the “substantial risk” standard in the particular context present here. Accord McGehee, 854 F.3d at 492.
Nor, respectfully, did the district court offer much reasoning in support of its decision. (To some extent that omission is understandable, given the tight timelines applicable here.) The bulk of the court’s opinion merely summarized the expert testimony on both sides. The relevant question, to reiterate, is whether the plaintiffs met their “heavy burden,” Baze, 553 U.S. at 53, 128 S.Ct. 1520, to show that an inmate who receives a 500-milligram dose of midazolam is “sure or very likely” to be conscious enough to experience serious pain from the second and third drugs in the protocol. Glossip, 135 S.Ct. at 2737. As to that question the experts- offered diametrically opposed conclusions: the plaintiffs’ experts argued that serious pain was “highly likely” or a “virtual certainty,” while Ohio’s experts testified that the risk was “very, very low” or “speculative.” Compare R. 923 at 30802-03 and R. 844-1 at 24944 with R. 924 at 31063-64 and R. 852-2 at 25831-32. Yet the district court offered virtually no reason for its decision to adopt the conclusions of the plaintiffs’ experts wholesale. The court did say, “[wjithout knowing precisely why,” that inmates who are “administered midazo-lam” (including doses as low as ten milligrams—one fiftieth of the dosage at issue here) “take longer to die and exhibit different bodily behaviors in the process.” R. 948 at 32227. The court also noted that “there was little support in the record for the idea that midazolam would be used alone” (again, at doses that are a tiny fraction of the dosage at issue here) “for *887surgeries other than those performed on an outpatient basis.” Id. at 32228. The latter observation has little relevance in light of a passage from Glossip that does bind us here: “the fact that a low dose of midazolam is not the best drug for maintaining unconsciousness during surgery says little about whether a 500-milligram dose of midazolam is constitutionally adequate for purposes of conducting an execution.” 135 S.Ct. at 2742 (emphasis in original). And taken even on their own terms, neither of the district court’s observations provides much support for the conclusion that a 500-milligram dose of midazolam is very likely to leave an inmate conscious enough to feel serious pain.
The court also drew what it called “reasonable inferences” from the abandonment of midazolam-based protocols by three states. R. 948 at 32228. First, the district court noted that, in 2014, Ohio abandoned the midazolam-opioid protocol that it used to execute Dennis McGuire. Id. But McGuire’s dose of midazolam was only 10 milligrams, so again his execution says little about the effectiveness of a 500-milli-gram dose. Second, the district court found that Florida, “despite having conducted many executions using midazolam, abandoned the drug while this case was in hearing.” Id. But the court did not explain why Florida changed its protocol or why that decision helps the plaintiffs here. And meanwhile, in Glossip, the Supreme Court observed that Florida had used midazolam in 11 executions, apparently “without any significant problems.” 135 S.Ct. at 2734, 2746. Third, the district court noted that Arizona had “abandoned midazolam shortly before [the hearing below] as a result of settling litigation over its use.” R. 948 at 32228. But Arizona’s settlement agreement says nothing about why the State abandoned midazolam, other than that the State had run out of it. See R. 976-2 at 36214. None of these states’ actions, therefore, provide reason to infer that 500 milligrams of midazolam is sure or very likely to leave an inmate conscious enough to feel serious pain.
Otherwise, the district court merely observed that “there are not now and never will be clinical studies of the effect of injecting 500 mg of midazolam into a person[,]” and that “we certainly cannot ask the executed whether they experienced pain after the injection of midazolam[J” R. 948 at 32227-28. Those observations are obviously correct, but the district court’s reliance on them effectively shifted the burden of proof to the State. Fairly or not, the applicable legal standard requires the plaintiffs to prove their allegations to a high level of certainty; yet the district court based its decision, at best, on uncertainty.
2.
The district court’s findings thus provide little support for its conclusion that Ohio’s three-drug protocol creates an unconstitutional risk of pain. Since we can affirm the district court’s decision on any ground supported by the record, however, we must consider whether the plaintiffs met their burden for reasons the court did not articulate. The plaintiffs’ evidence as to risk of pain fell into two main categories: testimony about midazolam’s effects, and testimony about executions carried out with midazolam. We address each in turn.
Each side offered testimony from two experts as to midazolam’s effects. The plaintiffs offered testimony from Dr. Sergio Bergese, M.D., an anesthesiologist, and Dr. Craig Stevens, Ph.D., a pharmacologist. The State offered testimony from Dr. Joseph Antognini, M.D., an anesthesiologist, and Dr. Daniel Buffington, Ph.D., a pharmacologist.
The experts generally agreed that mi-dazolam ultimately has a “ceiling” above which an increase in dosage will not have *888any greater anesthetic effect. (On that point Dr. Buffington was the only dissenter.) Dr. Stevens attempted to estimate the ceiling using two different methods. One method, based on extrapolations from pe-tri-dish experiments, suggested that the ceiling effect occurs at 228 milligrams. R. 923 at 30800. Another method, based on extrapolations from clinical studies, yielded an estimate of 25 milligrams. R. 836-1 at 24827. That Dr. Stevens’s estimates vary by a factor of nine, however, underscores that they are highly speculative. Moreover, even Dr. Stevens’s estimates suggest that any ceiling effect arrives only at doses five to 45 times greater than the usual therapeutic dose. And in any event the relevant question is not whether the ceiling effect arrives at the equivalent of five doses or 45, but whether, once it arrives, an inmate is sure or very likely to experience serious pain from the second and third drugs. See Glossip, 135 S.Ct. at 2743.
As to that point, Dr. Stevens testified that midazolam cannot produce “general anesthesia,” the level of unconsciousness appropriate for major surgeries. Studies indicate that midazolam—at doses in the therapeutic range—produces “deep sedation,” a level of brain depression just short of general anesthesia. But none of those studies involved the massive doses at issue here. See id. at 2742 (“The effect of a small dose of midazolam has minimal probative value about the effect of a 500-milligram dose”). Meanwhile, the experts for both sides agreed that midazolam is sometimes used alone for intubation, a medical procedure in which a tube is inserted into a person’s windpipe. Dr. Antognini, one of Ohio’s experts, testified that intubation is “incredibly stimulating.” R. 924 at 31052. Dr. Bergese likewise acknowledged that intubation is “very reactive,” meaning that “people react to [it] quite a bit.” R. 923 at 30900. True, Dr. Bergese asserted in his expert report that the protocol’s second and third drugs are more painful than intubation. But Dr. Bergese did not cite any medical evidence to support that assertion. And Dr. Antognini did cite studies showing that injection of the paralytic drug has no effect on a sedated person’s level of consciousness as measured by a brain scan, even when the person appears to flinch in response. R. 924 at 31066. Dr. Antognini further testified that midazolam would reduce or remove any sensation of suffocation (commonly referred to as “air hunger”) caused by the paralytic. See id. at 31072, 31088-89.
Thus, even Dr. Bergese—the plaintiffs’ principal expert as to whether Ohio’s execution protocol would cause inmates to experience severe pain—admitted that the science on this issue “could go either way.” R. 923 at 30844, 30909. What tipped the balance for him, rather, was “the eyewitness reports” from laymen who attended executions involving midazolam. Id. at 30909; see also id. at 30870. But that data came with a raft of problems of its own. First, the sample size was small: in his expert report, Dr. Bergese discussed only nine midazolam-based executions. See R. 844-1 at 24972-80. Second, most of those accounts came from witnesses who, according to the district court, were likely to be “highly biased”-—such as relatives of executed inmates, capital-defense attorneys, and even the inmates’ own lawyers. R. 923 at 30869. And none of these witnesses had any medical training. See, e.g., R. 922 at 30644, 30713. Thus, as Dr. Bergese himself admitted, “the quality of the data is not there.” R. 923 at 30910; see also id. at 30869.
The reliability of Dr. Bergese’s opinion does not improve when one considers the evidence of the nine executions themselves. Two of them—the execution of Clayton Lockett in Oklahoma and the execution of Joseph Wood in Arizona—are ones that the Supreme Court has specifically said *889have “little probative value” because they “did not involve the protocol at issue here.” Glossip, 135 S.Ct. at 2746. And notwithstanding the plaintiffs’ assertion to the contrary, we are not free to disregard that reasoning simply because the plaintiffs’ experts have to some extent testified to the contrary here. Moreover, Lockett’s IV line was not properly connected. See R. 948 at 32147; Glossip, 135 S.Ct. at 2734, 2746. A third execution—the McGuire execution in Ohio—involved a dose of 10 milligrams of midazolam rather than 500. And the district court in McGuire’s case found that McGuire had a condition that “might make him susceptible to an airway obstruction.” R. 948 at 32191 n.26. Hence that execution too has “little probative value[.]” Glossip, 135 S.Ct. at 2746.
That leaves six executions that were conducted using the same protocol at issue here. But five of those involved reports only of eyes opening, “head movements,” and “foot movements” after the injection of midazolam. R. 844-1 at 24974-80. And the plaintiffs concede that “evidence of slight movements might, in a vacuum, not be compelling evidence of consciousness.” Ap-pellee Br. 54. Dr. Bergese likewise testified that minor movements are possible even under general anesthesia. R. 923 at 30834, 30850. Moreover, even in executions involving barbiturates, inmates may have “convulsions” without a paralytic. Workman v. Bredesen, 486 F.3d 896, 909 (6th Cir. 2007). We upheld the use of a paralytic in executions for that very reason, finding legitimate a state’s concern that “lethal injection without [the paralytic] would typically result in involuntary movement,” which “might be misinterpreted as ... an indication of consciousness.” Id.
That leaves only the execution of Ronald Smith in Alabama. The district court heard testimony about that execution from Spencer Hahn, a federal defender in the Alabama Capital Habeas Unit. According to Hahn, at some point after the injection of midazolam, Smith began coughing, clenching and unclenching his fists, flailing his arms, and moving his lips. R. 922 at 30619. Both sides’ experts agreed, however, that people’s bodies can move at reduced levels of consciousness. Dr. Antognini explained that surgical patients under anesthesia can respond to noxious stimuli in complex ways, sometimes by thrashing about violently. R. 852-1 at 25792; R. 924 at 31037, 31044, 31063-64. That is why patients’ arms are strapped down and their eyes taped shut. R. 924 at 31044. Indeed, as the “Lazarus phenomenon” illustrates, even brain-dead persons can move their limbs and seemingly respond to stimuli. See id. at 31036-37. Dr. Stevens agreed that “reflexive withdrawal from a noxious stimulus is not considered a purposeful movement.” R. 948 at 32196. Similarly, Dr. Bergese testified that “movement is ... in the spinal cord,” so “patients are going to move even when the consciousness is depressed.” R. 923 at 30834. And a reporter for the Columbus Dispatch, who witnessed 19 executions using barbiturate-based protocols, said that he had sometimes seen “clenching and unclenching of the hands.” R. 922 at 30708.
As for coughing or gasping, neither demonstrates that the inmate is feeling air hunger. Dr. Antognini testified that mi-dazolam, like other anesthetics, can remove the sensation of air hunger by depressing the drive to breathe. R. 924 at 31071-73, 31088-93. Even Dr. Bergese admitted that an inmate who gasps repeatedly during an execution might not be conscious, and that involuntary respirations associated with the process of dying are hard to distinguish from purposeful attempts to breathe. See R. 923 at 30860-61. Dr. Antognini also testified that patients can cough vigorously while under anesthesia for surgery, though this behavior may *890signal that the patient is shifting to a lighter level of anesthesia. R. 924 at 31037, 31043, 31157, 31178.
All that said, Hahn’s description of the Smith execution is the plaintiffs’ best evidence in support of their claim. But that evidence is far from compelling. Some people react differently to drugs than other people do, see R. 923 at 30896; and the amount of movement reported in Smith’s execution appears to be the exception, not the rule, for executions with the three-drug protocol. More fundamentally, as Dr. Bergese himself explained, consciousness falls on a “spectrum.” Id. at 30830. Yet he appeared to treat consciousness as binary when he opined that an inmate sedated with 500 milligrams of midazolam would feel pain the same way a conscious person would, simply because the inmate clenches his fists or coughs.
In sum, we will grant that the plaintiffs have shown some risk that Ohio’s execution protocol may cause some degree of pain, at least in some people. But some risk of pain “is inherent in any method of execution—no matter how humane[.]” Baze, 553 U.S. at 47, 128 S.Ct. 1520. And the Constitution does not guarantee “a pain-free execution[.]” Cooey I, 589 F.3d at 220. Different people may have different moral intuitions as to whether—taking into account all the relevant circumstances— the potential risk of pain here is acceptable. But the relevant legal standard, as it comes to us, requires the plaintiffs to show that Ohio’s protocol is “sure or very likely” to cause serious pain. Glossip, 135 S.Ct. at 2737, 2745. The district court did not meaningfully apply that standard here. And the plaintiffs have fallen well short of meeting it.
B.
That shortcoming by itself is sufficient to defeat the plaintiffs’ claim under Glossip. But the district court also erred in its analysis of Glossip’s second prong— which requires the plaintiffs to prove that an alternative method of execution is “available,” “feasible,” and can be “readily implemented,” among other things. Id. at 2737. The court found this requirement met as to one of the plaintiffs’ proposed alternatives, namely a one-drug, barbiturate-only method using either sodium thio-pental or pentobarbital. The court acknowledged, however, that Ohio no longer has any supplies of these drugs, that “Ohio’s efforts to obtain the drug from other States and from non-State sources have not met with success[,]” and that Ohio is “not likely” to overcome these obstacles anytime soon. R. 948 at 32229. Yet the court concluded that barbiturates are “available” to Ohio because “there remains the possibility” that Ohio can obtain the active ingredient of pentobarbital and have it made into injectable form by a compounding pharmacy. Id.
The district court was seriously mistaken as to what “available” and “readily implemented” mean. (For that reason the district court’s error is legal, and thus subject to de novo review. See Highmark Inc. v. Allcare Health Mgmt. Sys., Inc., — U.S. -, 134 S.Ct. 1744, 1748, 188 L.Ed.2d 829 (2014).) To obtain pentobarbi-tal or its active ingredient, Ohio would need to receive an import license from the Drug Enforcement Administration. R. 948 at 32229. Ohio’s application for that license has been pending, without apparent action by the DEA, for more than four months. See R. 966-13 at 34506-10; R. 966-14 at 34512-17. Ohio does not know whether the DEA will approve its application, or even when that decision might be made. R. 948 at 32229. And even if that application is approved, Ohio might not be able to locate a willing supplier or manufacturer, for reasons the Supreme Court explained at some length in Glossip. See 135 S.Ct. at 2733. As *891the district court acknowledged, even the plaintiffs’ expert, Dr. Stevens, “was unable to identify any manufacturers or suppliers of thiopental and/or pentobarbital who were willing to sell those drugs, or even those drugs’ active'pharmaceutical ingredients, to Ohio for the purposes of conducting lethal injection executions.” R. 948 at 32163. The plaintiffs, for their part, rely on Dr. Buffington’s testimony about an affidavit he filed in a prior Alabama case, in which he stated that he believed “there are pharmacists in the United States that are able to compound pentobarbital for use in lethal injections because other states have been reported to have obtained compounded pentobarbital for use in executions.” R. 925 at 31440-41. But that is quite different from saying that any given state can actually locate those pharmacies and readily obtain the drugs. And Dr. Buffington testified that he personally contacted 15 pharmacies to that end without success. Id. Indeed, in the very case in which Dr. Buffington submitted his affidavit, the Eleventh Circuit rejected the claim that pentobarbital was available to Alabama. Arthur v. Comm’r, Ala. Dep’t of Corr., 840 F.3d 1268, 1296 (11th Cir. 2016), cert. denied sub nom. Arthur v. Dunn, — U.S. -, 137 S.Ct. 725, 197 L.Ed.2d 225 (2017). Meanwhile, Ohio itself contacted the departments of correction in Texas, Missouri, Georgia, Virginia, Alabama, Arizona, and Florida to ask whether they would be willing to share their supplies of pentobarbital. All refused. See R. 905-1 at 30313-14. Granted, for the one-drug protocol to be “available” and “readily implemented,” Ohio need not already have the drugs on hand. But for that standard to have practical meaning, the State should be able to obtain the drugs with ordinary transactional effort. Plainly it cannot. The reality is that the barbiturate-only method is no more available to Ohio than it was to Oklahoma two years ago in Glossip, for precisely the same reasons.
C.
That leaves the district court’s determination that Ohio is judicially estopped from returning to a three-drug protocol. The plaintiffs ask us to review that determination for an abuse of discretion, citing the Supreme Court’s reference to judicial es-toppel as an “equitable doctrine” in New Hampshire v. Maine, 532 U.S. 742, 750, 121 S.Ct. 1808, 149 L.Ed.2d 968 (2001). But we have twice rejected that argument and “continue[d] to apply de novo review.” Mirando v. U.S. Dep’t of Treasury, 766 F.3d 540, 545 n.1 (6th Cir. 2014); Lorillard Tobacco Co. v. Chester, Willcox & Saxbe, LLP, 546 F.3d 752, 757 (6th Cir. 2008). And here, as in a recent Second Circuit case, “the choice between the two standards is immaterial, for under either,” the doctrine of judicial estoppel “is inapplicable[.]” Chevron Corp. v. Donziger, 833 F.3d 74, 128 (2d Cir. 2016).
The doctrine’s purpose is to prevent a party “from abusing the judicial process through cynical gamesmanship” by changing positions “to suit an exigency of the moment.” Mirando, 766 F.3d at 545. And when, as here, the doctrine is invoked against a state, it must be “construed narrowly.” See United States v. Owens, 54 F.3d 271, 275 (6th Cir. 1995).
According to the plaintiffs, Ohio’s plan to use a three-drug protocol contradicts Ohio’s statements in 2009 that it was switching to a one-drug protocol and that “going forward, pancuronium bromide [the paralytic drug] no longer will be used as part of the lethal injection process.” R. 718-3 at 22390. Ohio also stated in a motion for summary judgment that a then-pending challenge to its prior three-drug protocol was moot—because Ohio was no longer using it. R. 966-2. The district court never granted Ohio’s motion, but our court soon held that any challenge to Ohio’s old three-drug protocol (using sodium thiopental) *892was “now moot.” Cooey v. Strickland, 588 F.3d 921, 923 (6th Cir. 2009) (per curiam). Thus, the plaintiffs argue, Ohio prevailed by “permanently” renouncing the paralytic and potassium chloride—a promise on which Ohio has putatively now reneged.
The argument is meritless. As an initial matter, the plaintiffs nowhere explain how they have been harmed in the current litigation, or how the State has been helped, by the fact that the parties in the prior litigation did not have a trial about-the sodium-thiopental three-drug protocol in 2009. To the contrary, by all appearances, the absence of that trial has made zero difference in this litigation. The effects of the two drugs that the old and new protocol share (namely, the paralytic and the heart-stopping drug) are undisputed. What is disputed, rather, is the effects of midazolam; and there is no reason to think that a trial about sodium thiopental would have affected that issue one way or the other.
More to the point, Ohio represented in 2009 that it was switching to a one-drug protocol in the context of a particular case involving particular named plaintiffs, which apparently do not include the named plaintiffs here. Ohio then proceeded to execute 20 death-row inmates with the new one-drug protocol, which should be proof enough of the State’s truthfulness in making those representations. Ohio did argue in support of its summary-judgment motion (which the State itself later withdrew) that “[tjhere is absolutely no reason to believe that defendants will reinstate-the previous ‘three-drug protocol’ if the plaintiffs’ suits were dismissed.” R. 966-2 at 34329. But that was before death-penalty opponents successfully prevented Ohio (along with other states) from obtaining the drugs necessary to use the one-drug protocol. See Glossip, 135 S.Ct. at 2733-34. Ohio then ceased executions altogether for about three years, before switching to the three-drug protocol that the Supreme Court had recently upheld in Glossip.
A state’s change in policy in response to unforeseen circumstances like these is hardly the kind of inconsistency that warrants estoppel. See New Hampshire, 532 U.S. at 749-50, 121 S.Ct. 1808; Owens, 54 F.3d at 275. Judicial estoppel prohibits “playing fast and loose with the courts”—that is, “abusing the judicial process through cynical gamesmanship” by changing positions “to suit an exigency of the moment.” New Hampshire, 532 U.S. at 749-50, 121 S.Ct. 1808; Mirando, 766 F.3d at 545. Suffice it to say that, if any gamesmanship led us to this pass, it was not gamesmanship by the State.
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The plaintiffs have failed to demonstrate a likelihood of success on their claims. That failure is “dispositive.” Cooey II, 604 F.3d at 946. We therefore vacate the district court’s January 26, 2017 preliminary injunction.