*569The petitioner, Rafael Abreu, appeals from the judgment of the habeas court denying his amended petition for a writ of habeas corpus, which alleged ineffective assistance of prior habeas counsel.1 The petitioner claims on appeal that the habeas court improperly rejected his claim that his prior habeas counsel provided ineffective assistance by failing to pursue adequately three claims of ineffective assistance of trial counsel. Specifically, the petitioner claims that trial counsel improperly failed (1) to conduct an adequate investigation regarding a potentially exculpatory witness, (2) to offer certain evidence in support of the petitioner's self-defense claim, and (3) to advise the petitioner properly regarding his potential sentence exposure should he proceed to trial. We affirm the judgment of the habeas court.
The following facts and procedural history are relevant to our disposition of the petitioner's appeal. The *570petitioner was charged with murder following the October, 2002 shooting death of Juan Carlos Martinez (victim) outside of a Waterbury cafe. State v. Abreu , 106 Conn.App. 278, 281, 941 A.2d 974, cert. denied, 286 Conn. 919, 946 A.2d 1249 (2008). The facts underlying the victim's death were set forth by this court in its opinion affirming the petitioner's judgment of conviction. "Several days prior to October 20, 2002, the [petitioner] and some others, including Elvis Castro and Castro's girlfriend, Vanessa Garcia, were at the Los Amigos pool hall in Waterbury. At some point, an altercation ensued between the [petitioner] and a group of patrons, which included the victim .... During the altercation, the [petitioner] was beaten and struck in the head with beer bottles.
"On October 20, 2002, the [petitioner], Castro and a few others went to the Eldorado Cafe in Waterbury. While having drinks, the [petitioner] recognized one or more persons in the cafe as having been part of the group of people who had been at the pool hall days earlier and had beaten him. Thereafter, the [petitioner] exited the cafe. A confrontation subsequently occurred between the [petitioner], the victim and others. The [petitioner] shot the victim, and the victim died." (Footnote omitted.) Id.
The petitioner never disputed that he shot the victim, but asserted that he was not the initial aggressor and had shot the victim in self-defense. Id., at 281, 288, 941 A.2d 974. On May 20, 2005, a jury found the petitioner guilty of the lesser included offense of first degree manslaughter with a firearm in violation of General Statutes § 53a-55a (a). Id., at 281-82, 941 A.2d 974. He was sentenced on August 8, 2005, to a total effective term of thirty-eight years of incarceration. Id., at 282, 941 A.2d 974.
*571As indicated, this court affirmed the petitioner's judgment of conviction on direct *1080appeal.2 Id., at 281, 941 A.2d 974. On January 9, 2008, the petitioner filed a pro se petition for a writ of habeas corpus (first habeas petition). The court appointed Attorney Paul Kraus to represent the petitioner. The first habeas petition was tried before the habeas court, Sferrazza , J. , which issued a memorandum of decision on August 1, 2011, denying the petition.
Although the petitioner raised a number of claims in his first habeas petition, the sole claim pursued at the habeas trial was that the petitioner's trial counsel, Attorney Martin Minnella, had failed to investigate and to call as a defense witness Luis Vicente, a fourteen year old boy who had observed the shooting from an apartment located over the cafe.3 Judge Sferrazza determined that the petitioner had failed to prove that he received ineffective assistance of trial counsel because, even if Vicente had testified, his testimony likely would have been damaging to the petitioner's self-defense claim considering that, in his statement to the police, the boy had stated that the petitioner had been chasing the victim at the time of the shooting. Accordingly, there was a reasonable strategic reason for Minnella not to call Vicente as a witness. The court also found that the petitioner had failed to prove that the absence of the boy's testimony prejudiced the petitioner in any appreciable way.
*572The petitioner appealed, following the denial of certification. This court dismissed the appeal by memorandum decision. Abreu v. Commissioner of Correction , 140 Conn.App. 904, 62 A.3d 1182, cert. denied, 308 Conn. 917, 62 A.3d 1132 (2013).
Prior to a final resolution of the appeal from the denial of his first habeas petition, the petitioner filed this second pro se habeas petition on August 17, 2012, commonly referred to as a "habeas on a habeas." Kaddah v. Commissioner of Correction , 324 Conn. 548, 550, 153 A.3d 1233 (2017). In it, he claimed that Kraus had provided ineffective assistance in his representation of the petitioner in his first habeas action. The court later appointed the petitioner habeas counsel. The respondent, the Commissioner of Correction, filed a return in which he asserted, by way of special defense, procedural default, waiver and res judicata.
The habeas court, Oliver , J. , conducted a trial on the second habeas petition on March 4, 2015. The only witness called to testify at the trial was the petitioner. The court admitted into evidence, without objection, exhibits that were premarked by agreement. Those exhibits included transcripts of the criminal trial and the trial on the prior habeas petition.
On June 18, 2015, the habeas court issued a decision finding in favor of the respondent on all issues and denying in part and dismissing in part the petition. The court first dismissed all claims raised by the petitioner except those directed at prior habeas counsel, concluding that the petitioner was procedurally defaulted as to claims directly challenging trial counsel's performance and that "the petitioner has *1081failed to sufficiently establish good cause to excuse the defaults ...."4 The *573court nevertheless proceeded in the alternative to review several "defaulted" claims raised against trial counsel, rejecting each on its merits. The habeas court then turned to the petitioner's claim that his prior habeas counsel provided ineffective assistance. After setting forth the proper standard of review, the habeas court concluded that "because the petitioner failed to set forth a prima facie case regarding the ineffective assistance of his trial counsel, he has not set forth a prima facie case of ineffective assistance of his habeas counsel. Additionally, a full review of the habeas trial transcript as well as the habeas trial court's memorandum of decision reveals no deficiencies in Attorney Kraus' representation at the trial of the previous habeas corpus petition in the preparation, investigation and prosecution of the petition." The habeas court later granted certification to appeal, and this appeal followed.5
The petitioner claims on appeal that the habeas court improperly rejected his claim that Kraus was ineffective because he failed either to raise or adequately pursue in his prior habeas corpus action three claims of ineffective assistance by Minnella. Specifically, the petitioner *574asserts that Minnella failed (1) to conduct an adequate investigation regarding a potentially exculpatory witness, (2) to introduce crucial evidence in support of the petitioner's claim of self-defense, and (3) to advise the petitioner properly regarding his sentence exposure if he proceeded to trial. The habeas court addressed each of these claims against Minnella, rejecting them all, and, on that basis, also rejected the petitioner's claims against Kraus. We agree that the petitioner has failed to demonstrate that Minnella's performance was ineffective as to any of these claims or that Kraus failed to adequately prosecute them. Accordingly, we conclude that the habeas court properly rejected his claim that Kraus' performance amounted to ineffective assistance of counsel.
The standard of review and legal principles that govern our consideration of the petitioner's claims on appeal are well settled. "The use of a habeas petition to raise an ineffective assistance of habeas counsel claim ... was approved by our Supreme Court in Lozada v. Warden , 223 Conn. 834, 613 A.2d 818 (1992). In Lozada , the court determined that the statutory *1082right to habeas counsel for indigent petitioners provided in General Statutes § 51-296(a) includes an implied requirement that such counsel be effective, and it held that the appropriate vehicle to challenge the effectiveness of habeas counsel is through a habeas petition. ... [T]he court explained that [t]o succeed in his bid for a writ of habeas corpus, the petitioner must prove both (1) that his appointed habeas counsel was ineffective, and (2) that his trial counsel was ineffective. ... As to each of those inquiries, the petitioner is required to satisfy the familiar two-pronged test set forth in Strickland v. Washington , [466 U.S. 668, 687, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984) ]. First, the [petitioner] must show that counsel's performance was deficient. *575... Second, the [petitioner] must show that the deficient performance prejudiced the defense. ... Unless a [petitioner] makes both showings, it cannot be said that the conviction ... resulted from a breakdown in the adversary process that renders the result unreliable. ... In other words, a petitioner claiming ineffective assistance of habeas counsel on the basis of ineffective assistance of trial counsel must essentially satisfy Strickland twice ...." (Citations omitted; emphasis added; internal quotation marks omitted.) Gerald W. v. Commissioner of Correction , 169 Conn.App. 456, 463-64, 150 A.3d 729 (2016), cert. denied, 324 Conn. 908, 152 A.3d 1246 (2017).
"The habeas judge, as the trier of facts, is the sole arbiter of the credibility of witnesses and the weight to be given to their testimony. ... The application of historical facts to questions of law that is necessary to determine whether the petitioner has demonstrated prejudice under Strickland , however, is a mixed question of law and fact subject to our plenary review." (Citation omitted; internal quotation marks omitted.) Small v. Commissioner of Correction , 286 Conn. 707, 717, 946 A.2d 1203, cert. denied sub nom. Small v. Lantz , 555 U.S. 975, 129 S.Ct. 481, 172 L.Ed.2d 336 (2008).
I
The petitioner first asserts that Kraus' performance was deficient because he failed to adequately present the petitioner's claim that Minnella provided ineffective assistance by failing to conduct an adequate pretrial investigation regarding Vicente, the teen who witnessed the shooting. The petitioner claims that an adequate investigation by trial counsel would have unearthed exculpatory evidence supporting his self-defense claim, namely, that Vicente would have testified that someone removed an unidentified object from the victim's waistband after the shooting that the petitioner claims was *576a gun or some other weapon. The petitioner argues that if the jury believed that the victim was armed with a weapon, that evidence would have bolstered his claim of self-defense because it would have helped to corroborate that he was not the aggressor and had shot the victim only because he feared for his own life. The petitioner further claims that, although Kraus raised an inadequate investigation claim in the first habeas action, Kraus' performance nevertheless was deficient because he failed to call Vicente as a witness at the first habeas trial in support of the claim.
The habeas court concluded that the petitioner's claim against his trial counsel failed because he did not satisfy his burden of showing how he would have benefited from additional investigation regarding Vicente. In other words, the habeas court, like the judge in the first habeas action, rejected the petitioner's claim against trial counsel on Strickland 's prejudice prong, and this necessarily was also fatal to his claim against prior habeas counsel. The *1083habeas court also concluded that Kraus' performance in prosecuting this claim in the first habeas action was not deficient. We agree with the habeas court.
The facts underlying this claim were set forth by the first habeas court in its memorandum of decision, which was entered into evidence as a full exhibit in this action and quoted by the habeas court in the present case. "On the date of the shooting, [Vicente] was a fourteen year old boy who was visiting his sister, who resided in an apartment above the Eldorado Cafe. The next day, October 21, 2002, Vicente gave a written statement to the Waterbury police and disclosed that he heard gun-fire from the street below his sister's home and ran to the window to investigate. He observed the petitioner, whom he positively identified, firing shots at someone. Vicente then ran downstairs and watched the petitioner *577pursue the victim and fire additional shots. He saw the victim attempt to flee and then collapse.
"Eight and one-half years later on April 4, 2011, an investigator for the petitioner interviewed Vicente, who is now an inmate at the Osborn Correctional Institution. During this oral interview, Vicente stated that he heard an argument on October 20, 2002, but never heard any gunshots. Vicente ran outside, and it was only then that he learned that someone had been shot. He denies ever knowing the identity of the shooter. He also adds, however, that he now recalls seeing someone approach the body lying in the street and remove an object from the victim's waistband. Vicente could not say whether the object was a weapon or not."
At the first habeas trial, Kraus pursued the claim that trial counsel was ineffective because he had not adequately investigated Vicente prior to trial or called him as a witness. As previously indicated, the first habeas court rejected that claim primarily because the state never called Vicente to testify at the criminal trial, it was not known when Vicente changed his story regarding the events of the shooting, and it was "too speculative to assume that his version of events in 2005, when the jury trial occurred, would correspond to either his October 21, 2002 written statement [to the police] or his April 4, 2011 oral statement. The fact that, nearly six years after the trial and eight and one-half years after the occurrence, Vicente, a sentenced prisoner, presently avers that the victim possessed some unknown object in his waistband hardly supports an allegation that, had Vicente been called as a defense witness in 2005, he would have related the same story."
The petitioner was not entitled to relitigate in the present action his claims against trial counsel, which were thoroughly addressed and rejected in his first habeas action, and affirmed by this court on appeal.
*578Rather, he now claims that Kraus' performance was deficient because he did not call Vicente to testify at the first habeas trial. The petitioner, however, has failed to satisfy either prong of the Strickland test with respect to that claim.
The habeas court summarily rejected the petitioner's assertion that habeas counsel's performance was deficient, finding on the basis of its review of the record that Kraus' performance was not deficient "in the preparation, investigation and prosecution of the petition." (Emphasis added.) Making strategic decisions about who to call to testify at the habeas trial is part of prosecuting a petition. It is axiomatic that "[j]udicial scrutiny of counsel's performance must be highly deferential" and that "a court must indulge a strong presumption that counsel's conduct falls within the wide range of reasonable professional assistance; that is, the [petitioner] must overcome the presumption *1084that, under the circumstances, the challenged action might be considered sound trial strategy." (Internal quotation marks omitted.) Spearman v. Commissioner of Correction , 164 Conn.App. 530, 539, 138 A.3d 378, cert. denied, 321 Conn. 923, 138 A.3d 284 (2016). The petitioner has failed to demonstrate that the habeas court's assessment of Kraus' performance was reversible error.
The record shows that although Kraus did not call Vicente to testify at the habeas trial, he did offer into evidence a summary of Vicente's 2011 statement prepared by the petitioner's investigator, which included Vicente's recollection that an object was removed from or near the waistband of the victim. Accordingly, Kraus presented relevant information necessary for the first habeas court to evaluate the petitioner's claim and to determine whether Vicente's testimony would have helped the petitioner. See Andrews v. Commissioner of Correction , 45 Conn.App. 242, 247, 695 A.2d 20 (in support of claim that trial counsel was ineffective by *579failing to call witness, petitioner should either present witness at habeas trial "or otherwise present evidence to establish that [the witness'] testimony at trial would be favorable to him" [emphasis added] ), cert. denied, 242 Conn. 910, 697 A.2d 364 (1997). Furthermore, it is unknown which version of events Vicente would have given if he had been called to testify at the habeas trial, or how he would have fared under cross-examination if confronted with his inconsistent statement to police.
The petitioner did not call Kraus, Vicente or an expert to testify at the habeas trial, and, thus, the record before us simply is silent as to why Kraus chose not to call Vicente as a witness or whether that choice was less than competent under the circumstances. The petitioner has the burden of rebutting the presumption that counsel acted within the bounds of reasonable professional assistance. See Safford v. Warden , 223 Conn. 180, 193, 612 A.2d 1161 (1992). The petitioner has failed to demonstrate that Kraus' decision to refrain from presenting Vicente as a witness was not an objectively reasonable trial strategy.
Moreover, even if the petitioner was able to demonstrate that Kraus' failure to call Vicente to testify at the first habeas trial amounted to deficient performance, he has not established how he was prejudiced. "With respect to the prejudice component of the Strickland test, the petitioner must demonstrate that counsel's errors were so serious as to deprive the [petitioner] of a fair trial, a trial whose result is reliable. ... It is not enough for the [petitioner] to show that the errors had some conceivable effect on the outcome of the proceedings. ... Rather, [t]he [petitioner] must show that there is a reasonable probability that, but for counsel's unprofessional errors, the result of the proceeding would have been different." (Internal quotation marks omitted.)
*580White v. Commissioner of Correction , 145 Conn.App. 834, 841, 77 A.3d 832, cert. denied, 310 Conn. 947, 80 A.3d 906 (2013).
As the respondent correctly argues in his brief, the petitioner failed to present any evidence at the second habeas trial that demonstrated why Vicente's live testimony, rather than the summary, would have been helpful to the petitioner's ineffective assistance of trial counsel claim, or that the result of the previous habeas trial would have been different if Vicente had testified. That failure is, by itself, fatal to the petitioner's claim.
The petitioner failed to demonstrate in his prior habeas action that he was prejudiced by trial counsel's alleged failure to conduct a thorough pretrial investigation of Vicente, and his assertion that habeas counsel provided ineffective assistance by *1085failing to call Vicente as a witness in support of that claim likewise fails.
II
The petitioner next claims that habeas counsel was ineffective because he failed to pursue in the prior habeas action a claim that trial counsel had failed to ensure that other crucial evidence in support of the petitioner's claim of self-defense was introduced into evidence. In particular, the petitioner claims that trial counsel failed to have admitted into evidence the contents of a toxicology report that would have shown that the victim had alcohol in his system at the time of the shooting. The petitioner takes the position that the jury reasonably could have inferred from the fact that the victim had been drinking alcohol that the victim was more likely to have been violent and aggressive toward the petitioner, making the petitioner's claim of self-defense more credible.
The record shows that the toxicology report was the subject of a pretrial motion in limine by the state, which sought to preclude the admission of evidence of the blood alcohol content of the victim. Trial counsel, therefore, *581did not fail to offer the evidence as suggested by the petitioner, but instead its admission was precluded by the court. This court affirmed on direct appeal the trial court's decision to exclude the toxicology report.6
The habeas court concluded that the petitioner's claim that he was prejudiced by his trial counsel's failure to have admitted forensic evidence showing that the victim was intoxicated at the time of the shooting was unavailing because he had not demonstrated that the admission of such evidence would have led to a different result at trial. The habeas court observed that the petitioner failed to present any evidence or call a witness during the habeas trial to support his premise that alcohol caused the victim in this case to be more aggressive.7
*582This court held in the petitioner's direct appeal from his conviction that, in order to introduce evidence of the victim's *1086alcohol content in support of the defense theory linking inebriation and aggressive behavior to bolster the petitioner's testimony that the victim was the initial aggressor in this case, the petitioner effectively needed to present expert testimony. State v. Abreu , supra, 106 Conn.App. 288-89, 941 A.2d 974. Trial counsel failed to do so in this case. In so holding, this court tacitly rejected the notion that such a linkage was within the ken of the average juror.8 See Conn. Code Evid. § 7-2, commentary (expert testimony limited to scientific, technical and specialized information beyond common knowledge and comprehension of average juror). The habeas court was bound by that decision and, therefore, in order for the petitioner to establish that habeas counsel was ineffective by failing to challenge trial counsel's failure to present expert testimony, the petitioner needed to show that it would have been possible to present such testimony by presenting a witness to that effect at the habeas trial. He failed to do so.
On the basis of our review of the evidence presented, we agree with the habeas court that the petitioner has failed to satisfy the prejudice prong of Strickland with respect to his claim that trial counsel was ineffective for failing to ensure that the toxicology report was *583admitted into evidence at the criminal trial. The claim simply fails to rise above "[m]ere conjecture and speculation," which we have indicated on numerous occasions is insufficient to establish prejudice. (Internal quotation marks omitted.) Sinchak v. Commissioner of Correction , 126 Conn.App. 670, 678, 14 A.3d 348, cert. denied, 301 Conn. 901, 17 A.3d 1045 (2011). Accordingly, because the petitioner failed to establish that he had a viable claim of ineffective assistance of trial counsel, his assertion that his prior habeas counsel provided ineffective assistance by failing to raise that claim similarly lacks merit. See Lapointe v. Commissioner of Correction , 113 Conn.App. 378, 403, 966 A.2d 780 (2009) (rejecting claim that habeas counsel was ineffective for failing to raise claim of ineffective assistance of trial counsel because petitioner failed to establish prejudice prong in claim against trial counsel).
III
Finally, the petitioner claims that prior habeas counsel failed to raise in his first habeas action a claim that trial counsel was ineffective because, at the time he was retained by the petitioner, he promised that he could ensure that the petitioner would serve a sentence of no more than twenty years if he went to trial. Because the petitioner failed to establish that trial counsel ever made such a promise or that he inaccurately advised him regarding his sentence exposure, the petitioner's claim lacks merit, and prior habeas counsel was not ineffective in declining to raise this claim.
*1087At the underlying habeas trial, the petitioner testified that he made the decision to retain Minnella because Minnella had promised him that "he was connected, [and] that he would get [the petitioner], if not released, less than twenty years." The petitioner also stated that his decision to go to trial was made on the basis of *584that promise. The petitioner acknowledged on cross-examination, however, that Minnella never used the words, "I promise," and that there was no written agreement with Minnella. He testified that he was aware that sentencing decisions were made by the trial court, not counsel, and that the only plea offer made by the state was for a fifty year sentence on the murder charge. The petitioner indicated that he never informed the trial court that he expected a twenty year sentence and never filed a grievance against Minnella.
The petitioner asserted at the habeas trial that he informed Kraus of Minnella's alleged promise and asked him to pursue a claim of ineffective assistance, but that Kraus did not do so. The petitioner was not asked, and thus did not indicate for the record, whether Kraus provided him with an explanation for not pursuing the claim. As previously indicated, Kraus was not called as a witness, and no other evidence was presented regarding whether Kraus' decision not to raise the claim was strategic in nature.
The habeas court, in rejecting the petitioner's claim, found that the only evidence of a promise by Minnella was the testimony of the petitioner, which the habeas court found was not credible "on this and [in] several other respects." Because we are bound by the credibility determinations of the habeas court; Sanchez v. Commissioner of Correction , 314 Conn. 585, 604, 103 A.3d 954 (2014) ; there is simply no evidence in the record to support the petitioner's claim against trial counsel and, therefore, his claim against Kraus also fails.
In sum, the petitioner has failed to establish that he received the ineffective assistance of prior habeas counsel. Accordingly, the habeas court properly denied the petition for a writ of habeas corpus.
The judgment is affirmed.
In this opinion the other judges concurred.