John Troy King pleaded guilty to killing Djuan Jefferson with a knife. The Texas court found him guilty of murder with a deadly weapon and sentenced him to 45 years in prison. King then sought post-conviction relief in state court, arguing that his trial counsel's performance was constitutionally deficient. After the Texas *603courts denied King's claims of ineffective assistance, he sought a writ of habeas corpus in federal court.
The district court denied the writ, and our Court granted a certificate of appealability on two of King's ineffective assistance of counsel claims: (1) that counsel advised him he was eligible for court-ordered community supervision despite the fact that he was statutorily ineligible and (2) that counsel failed to convey a 15-year plea offer from the State. We affirm because the state court's resolution of these claims was neither contrary to, nor an unreasonable application of, clearly established federal law as determined by the Supreme Court.
I.
A Texas grand jury indicted King for murdering Djuan Jefferson by stabbing him with a knife, after previously having been convicted of felony possession of a controlled substance. King agreed to plead guilty in exchange for the State's agreement to waive the indictment's enhancement paragraph, which lowered the mandatory minimum sentence to 5 years from 15 years. The parties did not reach an agreement as to the sentence length, but agreed that King would be sentenced based on a Presentence Investigation (PSI) report. Pursuant to King's written plea agreement, the judge found King guilty of first-degree felony murder with a deadly weapon and sentenced him to 45 years in prison. King did not appeal.
King then sought habeas relief in state court, arguing that he received ineffective assistance of counsel. As relevant here, King alleged that his counsel advised him that "the Judge could grant him Court ordered Community Supervision"-despite the fact that counsel "knew that Defendant King was not even eligible for Community Supervision." According to King, he "would not have entered a guilty plea ... had his attorney correctly advised him ... that he was not eligible for Judge ordered community supervision." Instead, he "would have insisted upon going to trial."
King also argued that his counsel failed to tell him about a 15-year plea deal the State allegedly offered. King learned of this offer "[o]nly through a website review/response between Gina Chambers and [King's counsel]." As Gina Chambers explained in her affidavit, King's lawyer "replied to my review wherein she stated, 'My client had an opportunity to plead to 15 years in this case ... the last option was a PSI and he opted that route.' " King also asserted that he "would have accepted" the 15-year deal "had he known about it."
The state court ordered King's trial attorney to file an affidavit responding to his allegations, but she failed to do so. The State's attempts to locate her were unsuccessful, but it did inform the court that she was no longer licensed to practice in Texas.
The state court denied the writ, ruling that King failed to demonstrate both (1) "that trial counsel's representation fell below an objective standard of reasonableness" and (2) that there was "a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different" as to both of his claims. As to the failure of King's counsel to communicate the alleged 15-year plea offer, the state court found that King's "[c]onclusory allegations are not enough to overcome the State's denial." See Ex parte Empey , 757 S.W.2d 771, 775 (Tex. Crim. App. 1988). See also Tex. Code Crim. Proc. art. 11.07, § 3(b) ("Matters alleged in the application not admitted by the state are deemed denied."). The court also explained that King's allegation "that *604he did not want to plead guilty, but rather wanted to go to trial renders his argument that he would have accepted a plea bargain of fifteen years ... irrelevant." Finally, the court ruled that King "failed to meet his burden of providing evidence that the State would not have withdrawn the offer or that the trial court would not have refused to accept the plea bargain."
The Texas Court of Criminal Appeals affirmed, without written decision.
King then sought federal habeas, re-urging his ineffective assistance of counsel claims. Regarding his probation-based ineffectiveness claim, King urged that if he "knew his only alternative was jail time[,] he would have never plead[ed] guilty but [would have] went to trial." As to his failure-to-communicate claim, King explained that "had he been properly informed of the 15 year plea offer, he would have accepted the offer rather than going to trial by Judge."
The district court denied the writ, and we now affirm.
II.
"When a state prisoner asks a federal court to set aside a sentence due to ineffective assistance of counsel during plea bargaining, our cases require that the federal court use a doubly deferential standard of review that gives both the state court and the defense attorney the benefit of the doubt." Burt v. Titlow , 571 U.S. 12, 15, 134 S.Ct. 10, 187 L.Ed.2d 348 (2013) (internal quotation marks omitted) (quoting Cullen v. Pinholster , 563 U.S. 170, 190, 131 S.Ct. 1388, 179 L.Ed.2d 557 (2011) ). In other words, King must show not only (1) "that counsel's performance was deficient" and "that the deficient performance prejudiced the defense," Strickland v. Washington , 466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), but also (2) that the state court's decision rejecting his claims "was contrary to, or involved an unreasonable application of, clearly established Federal law, as determined by the Supreme Court of the United States." 28 U.S.C. § 2254(d)(1).
A.
King's argues that his counsel performed deficiently by advising him that, by pleading guilty, he would be eligible for court-ordered community supervision-despite the fact that he was statutorily ineligible for community supervision. To prevail on this claim, King must show both (1) deficient performance (i.e. , "that counsel's representation fell below an objective standard of reasonableness") and (2) prejudice (i.e. , "that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different"). Hill v. Lockhart , 474 U.S. 52, 57, 106 S.Ct. 366, 88 L.Ed.2d 203 (1985) (quoting Strickland , 466 U.S. at 687-88, 694, 104 S.Ct. 2052 ). To "satisfy the 'prejudice' requirement" in the context of a guilty plea, "the defendant must show that there is a reasonable probability that, but for counsel's errors, he would not have pleaded guilty and would have insisted on going to trial." Id. at 59, 106 S.Ct. 366.1
King alleged that he would have gone to trial had he known that he was *605ineligible for probation. But he failed to allege that going to trial would have given him a reasonable chance of obtaining a more favorable result. That omission is fatal to his claim. As we have explained, demonstrating prejudice requires showing not only that the petitioner would have gone to trial, but also "that going to trial ... would have given him a reasonable chance of obtaining a more favorable result." United States v. Shepherd , 880 F.3d 734, 743 (5th Cir. 2018) (alteration in original) (quoting United States v. Batamula , 823 F.3d 237, 240 (5th Cir. 2016) (en banc) ). See also Batamula , 823 F.3d at 241 (ruling allegations and evidence "suggesting only that [petitioner] would have proceeded to trial had he known" are insufficient to demonstrate prejudice); United States v. Kayode , 777 F.3d 719, 726 (5th Cir. 2014) ("Another important factor is whether the defendant has demonstrated that he was likely to succeed at trial."). In other words, "counsel's ineffectiveness is only a basis for vacating a conviction if there is a reasonable probability it made a difference to the outcome of the proceeding." Young v. Spinner , 873 F.3d 282, 285 (5th Cir. 2017). See also Kayode , 777 F.3d at 726 ("In assessing whether a reasonable defendant would have rationally chosen to go to trial under the circumstances, we also consider the risks faced by a defendant in selecting a trial rather than a plea bargain.").
Were that not enough, the evidence against King was strong. See Armstead v. Scott , 37 F.3d 202, 210 (5th Cir. 1994) ("bare allegation" that petitioner "would have insisted upon going to trial" insufficient to establish prejudice-especially where "evidence of guilt against [the petitioner] was strong"). And the only way King could have avoided jail time was acquittal-Texas law precludes community supervision not only if a defendant is convicted of murder but also if the defendant used or exhibited a deadly weapon during the commission of a felony. See Tex. Code Crim. Proc. art. 42.12, § 3g(a)(1)(A), (a)(2) (2010) (currently codified at Tex. Code Crim. Proc. art. 42A.054(a)(2), (b) ). See also Hill , 474 U.S. at 60, 106 S.Ct. 366 (no prejudice even where "petitioner's mistaken belief that he would become eligible for parole ... would seem to have affected not only his calculation of the time he likely would serve if sentenced pursuant to the proposed plea agreement, but also his calculation of the time he likely would serve if he went to trial and were convicted").
Accordingly, we cannot say that the state court's determination was contrary to, or an unreasonable application of, clearly established federal law as determined by the Supreme Court.
B.
King's second ineffective assistance of counsel claim is based on counsel's alleged failure to inform him that the State offered a 15-year plea deal. Again, to prevail, King must show both deficient performance and prejudice. To establish prejudice where "counsel's deficient performance causes a plea offer to lapse or be rejected," a petitioner "must demonstrate a reasonable probability that: (1) he would have accepted the plea offer had he been afforded effective assistance of counsel; (2) the plea would have been entered without the prosecution canceling the offer or the trial court's refusing to accept it; and (3) the end result of the criminal process would have been more favorable by reason of a plea to a lesser charge or a sentence of less prison time." United States v. White , 715 F. App'x 436, 437-38 (5th Cir. 2018) (citing *606Missouri v. Frye , 566 U.S. 134, 147, 132 S.Ct. 1399, 182 L.Ed.2d 379 (2012) ).2
As King concedes, the only evidence demonstrating the existence of the alleged 15-year plea offer is the affidavit of Gina Chambers. According to that affidavit, Chambers wrote a negative review of King's attorney on the website merchantile.com. King's attorney allegedly "replied to [the] review," stating: "My client had an opportunity to plead to 15 years in this case ... the last option was a PSI and he opted that route."3
But there is no evidence that it was actually King's attorney who replied to Chambers's review-King's attorney did not file an affidavit confirming or denying the existence of such a plea offer. Nor did the State confirm the existence of such an offer. See Tex. Code Crim. Proc. art. 11.07, § 3(b) ("Matters alleged in the application not admitted by the state are deemed denied."). As the state court ruled, King's "[c]onclusory allegations are not enough to overcome the State's denial"-a factual finding which "shall be presumed to be correct" in federal habeas. 28 U.S.C. § 2254(e)(1).4
Absent such an offer (or absent counsel's failure to convey such an offer), King cannot demonstrate that his counsel performed deficiently-let alone that the state court's decision was contrary to, or an unreasonable application of, clearly established Supreme Court precedent.
Even assuming that such an offer existed, and that it was never conveyed to King, he still cannot prevail. Under Frye , a petitioner must show "a reasonable probability that he would have accepted the lapsed plea." 566 U.S. at 150, 132 S.Ct. 1399. But here, King pleaded-both in state court and federal court-that he "would have insisted on going to trial" had he known that "he was not eligible for Judge ordered community supervision." There is nothing in the record to suggest that King would have been eligible for community supervision under the alleged 15-year plea offer.
Thus, as the state court explained, King's allegation "that he did not want to plead guilty, but rather wanted to go to trial[,] renders his argument that he would have accepted a plea bargain of fifteen years in TDCJ-ID irrelevant." We cannot say this conclusion is contrary to, or an unreasonable application of, clearly established Supreme Court precedent. See *607Young , 873 F.3d at 288 ("Even if [King] has a plausible argument that he would have [accepted the alleged 15-year deal] had he known [probation] was impossible, that does not establish that the state court's contrary conclusion was unreasonable.").5
Accordingly, the judgment of the district court is AFFIRMED.