
930 A.2d 693 (2007)
103 Conn.App. 254
Michael McCLEAN
v.
COMMISSIONER OF CORRECTION.
No. 26244.
Appellate Court of Connecticut.
Argued April 23, 2007.
Decided August 14, 2007.
*696 Michael McClean, pro se, the appellant (petitioner).
Nancy L. Chupak, assistant state's attorney, with whom, on the brief, were James E. Thomas, state's attorney, and John F. Fahey, senior assistant state's attorney, for the appellee (respondent).
DiPENTIMA, GRUENDEL and HARPER, Js.
DiPENTIMA, J.
The petitioner, Michael McClean, appeals from the judgment of the habeas court dismissing his amended petition for a writ of habeas corpus. The petitioner claims that the court (1) abused its discretion by excluding certain testimony as irrelevant and (2) improperly concluded that defense counsel had not rendered ineffective legal assistance during his representation of the petitioner. We affirm the judgment of the habeas court.
The following facts and procedural history inform our disposition of the petitioner's appeal. In connection with the shooting death of Jose Vasquez on December 23, 1994, the petitioner was arrested and charged with murder in violation of General Statutes § 53a-54a(a).[1] Pursuant to a plea agreement negotiated by his defense counsel, John W. Watson, the petitioner pleaded guilty to the murder charge under the Alford doctrine[2] on January 5, 1998. The trial court, Clifford, J., thoroughly canvassed the petitioner and found that the plea was made knowingly and voluntarily with the assistance of competent counsel. In exchange for the petitioner's guilty plea, the state recommended a sentence of thirty years incarceration and dropped additional charges and withdrew its request for a sentence enhancement. On March 20, 1998, the court sentenced the petitioner to thirty years incarceration in accordance with the plea agreement.[3]
On November 29, 2004, the petitioner filed an amended petition for a writ of habeas corpus, claiming that he had received ineffective assistance of counsel during the prior criminal proceedings.[4] The petitioner and Watson testified at a hearing on the petition before the court, Hon. Ronald J. Fracasse, judge trial referee, on December 17, 2004. On December 20, 2004, the court dismissed the amended petition and rendered judgment dismissing the petition. The court granted the petition for certification to appeal on December 29, 2004. This appeal followed. Additional facts will be set forth as necessary.
The petitioner sought relief from the habeas court on the grounds that his defense counsel was ineffective both during plea negotiations and before the trial court. "In Strickland v. Washington, 466 U.S. 668, 104 S.Ct. 2052, 80 L.Ed.2d 674 (1984), the United States Supreme Court enunciated the two requirements that must be met before a petitioner is entitled to reversal of a conviction due to ineffective assistance of counsel. First, *697 the [petitioner] must show that counsel's performance was deficient. . . . 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 adversarial process that renders the result unreliable." (Internal quotation marks omitted.) State v. Dixson, 93 Conn.App. 171, 184, 888 A.2d 1088, cert. denied, 277 Conn. 917, 895 A.2d 790 (2006).
In the present case, the petitioner pleaded guilty to the charged offense, thereby forgoing a trial. "For ineffectiveness claims resulting from guilty pleas, we apply the standard set forth in Hill v. Lockhart, 474 U.S. 52, 59, 106 S.Ct. 366,88 L.Ed.2d 203 (1985), which modified Strickland's prejudice prong. . . .
"To satisfy the performance prong, the petitioner must show that counsel's representation fell below an objective standard of reasonableness. . . . A petitioner who accepts counsel's advice to plead guilty has the burden of demonstrating on habeas appeal that the advice was not within the range of competence demanded of attorneys in criminal cases. . . . The range of competence demanded is reasonably competent, or within the range of competence displayed by lawyers with ordinary training and skill in the criminal law. . . . Reasonably competent attorneys may advise their clients to plead guilty even if defenses may exist. . . . A reviewing court must view counsel's conduct with a strong presumption that it falls within the wide range of reasonable professional assistance and that a tactic that appears ineffective in hindsight may have been sound trial strategy at the time. . . .
"To satisfy the prejudice prong, the petitioner must show a reasonable probability that, but for counsel's errors, he would not have pleaded guilty and would have insisted on going to trial. . . . Reasonable probability does not require the petitioner to show that counsel's deficient conduct more likely than not altered the outcome in the case, but he must establish a probability sufficient to undermine confidence in the outcome. . . . A reviewing court can find against a petitioner on either ground, whichever is easier." (Internal quotation marks omitted.) Bowden v. Commissioner of Correction, 93 Conn.App. 333, 339, 888 A.2d 1131, cert. denied, 277 Conn. 924, 895 A.2d 796 (2006).

I
We first address the petitioner's claim that the court improperly excluded certain testimony at the habeas trial. Specifically, the petitioner claims that the court improperly excluded testimony regarding the circumstances surrounding the shooting and testimony relative to whether he would have testified had he elected a trial.[5] As a threshold matter, we note that these rulings were not specifically challenged in the petition for certification to appeal from the court's decision. In the absence of demonstrable prejudice, however, the terms of the court's grant of certification *698 will not limit the specific issues subject to appellate review. James L. v. Commissioner of Correction, 245 Conn. 132, 138, 712 A.2d 947 (1998). Accordingly, we review these claims.
The following additional facts are pertinent to the petitioner's claims. During direct examination at the habeas hearing, the petitioner offered testimony regarding his recollection of the circumstances surrounding the shooting that predicated his conviction.[6] The petitioner also offered testimony that if he had pleaded not guilty, Watson would have opposed his testifying at the criminal trial. The court sustained on relevance grounds each of the objections by the respondent, the commissioner of correction, to this testimony.
"[T]he trial court has broad discretion in ruling on the admissibility [and relevancy] of evidence. . . . The trial court's ruling on evidentiary matters will be overturned only upon a showing of a clear abuse of the court's discretion. . . . We will make every reasonable presumption in favor of upholding the trial court's ruling, and only upset it for a manifest abuse of discretion." (Internal quotation marks omitted.) State v. Pilotti, 99 Conn. *699 App. 563, 567, 914 A.2d 1067, cert. denied, 282 Conn. 903, 919 A.2d 1037 (2007). "Evidence is relevant if it has any tendency to make the existence of any fact that is material to the determination of the proceeding more probable or less probable than it would be without the evidence. . . . The proffering party bears the burden of establishing the relevance of the offered testimony." (Citations omitted; internal quotation marks omitted.) State v. Glenn, 97 Conn.App. 719, 726-27, 906 A.2d 705 (2006), cert. denied, 281 Conn. 913, 916 A.2d 55 (2007).
First, the petitioner claims that the court abused its discretion by excluding testimony regarding the circumstances surrounding the shooting. During direct examination at the habeas hearing, the court allowed the petitioner to testify that he believed the shooting was an accident. The court excluded the petitioner's testimony regarding additional details surrounding the shooting. The petitioner offered this testimony as proof that at the time he entered his plea, he had a viable defense that the shooting was an accident. We are not persuaded that the court's assessment of Watson's competence turned on the petitioner's recollection at the habeas trial of every detail of the shooting. As we have noted, reasonably competent attorneys may advise their clients to plead guilty even if defenses may exist. See Bowden v. Commissioner of Correction, supra, 93 Conn.App. at 339, 888 A.2d 1131. We therefore conclude that the court did not abuse its discretion by excluding this testimony.
The petitioner next claims that the court abused its discretion by excluding his testimony that if he had pleaded not guilty, Watson would not have wanted him to testify at trial. This testimony was offered to show that Watson improperly failed to pursue the petitioner's accident defense. As we have noted, a tactic that appears ineffective in hindsight may have been sound strategy at the time. See id. In this case, the effectiveness of Watson's trial tactics was never tested because the petitioner pleaded guilty. We are not persuaded that speculation could guide the court's assessment of Watson's effectiveness any better than hindsight could. The court did not abuse its discretion by also excluding this testimony.

II
We now turn to the petitioner's claim that the court improperly concluded that Watson had not rendered ineffective legal assistance during his representation of the petitioner. Specifically, the petitioner contends that his plea was not entered knowingly and voluntarily because Watson failed: (1) to discuss adequately with the petitioner the content and admissibility of certain tape-recorded conversations that incriminated the petitioner, (2) to discuss adequately with the petitioner the consequences of his Alford plea, (3) to pursue adequately certain defenses or lesser included offenses, and (4) to challenge the petitioner's mental competence to enter a guilty plea.[7]
"Our standard of review of a habeas court's judgment on ineffective assistance of counsel claims is well settled. In *700 a habeas appeal, this court cannot disturb the underlying facts found by the habeas court unless they are clearly erroneous, but our review of whether the facts as found by the habeas court constituted a violation of the petitioner's constitutional right to effective assistance of counsel is plenary." (Internal quotation marks omitted.) Bryant v. Commissioner of Correction, 99 Conn.App. 434, 438, 914 A.2d 585, cert. granted on other grounds, 282 Conn. 910, 922 A.2d 1098 (2007).
At the habeas trial, the petitioner testified as to the following version of events. Watson had discussed with him a possible alibi defense. On the eve of trial, however, Watson told him that the state had acquired certain tape-recorded conversations that incriminated the petitioner. Watson expressed to him little hope of suppressing these conversations at trial and predicted that his chances of being acquitted on the murder charge were minimal. Watson further explained to the petitioner the concept of an Alford plea and the negotiated thirty year sentence for pleading guilty under the Alford doctrine. The petitioner also testified that he had a limited education and that he and his attorney had difficulty communicating with each other.
Watson's recollection of events differed from the petitioner's. Watson stated that after listening to the incriminating tapes, he filed a motion for continuance to investigate the possibility of suppressing the tapes and discussed the content of the tapes with the petitioner. He discussed with the petitioner possible defenses at trial, including alibi and accident, but ruled out the accident defense because the petitioner indicated that such a scenario was untrue.[8] He advised the petitioner that his chances of success at trial were minimal and that they should seek a plea bargain. He took a substantial amount of time ensuring that the petitioner understood the consequences of an Alford plea. He also had some problems explaining to the petitioner what was happening and the complex legal issues involved, but the petitioner ultimately understood Watson's explanations. The petitioner expressed to him dissatisfaction with the plea bargain he had reached with the state but preferred the plea bargain to risking a murder conviction at trial. According to Watson, if the petitioner had insisted on a trial, he likely faced a sentence greater than the thirty year sentence Watson had negotiated.
The court relied heavily on the credibility of the witnesses in reaching its conclusions. "This court does not retry the case or evaluate the credibility of the witnesses. . . . Rather, we must defer to the [trier of fact's] assessment of the credibility of the witnesses based on its firsthand observation of their conduct, demeanor and attitude. . . . In a case that is tried to the court . . . the judge is the sole arbiter of the credibility of witnesses, and the weight to be given to their specific testimony." (Internal quotation marks omitted.) Logan v. Commissioner of Correction, 68 Conn.App. 373, 376, 791 A.2d 638, cert. denied, 260 Conn. 911, 796 A.2d 557 (2002).
In its memorandum of decision, the court credited Watson's testimony and found that Watson fully discussed with the petitioner the evidence against him, including the tapes, as well as the issues involved, several possible defenses and his guilty plea. The court also found no evidence that the petitioner suffered from *701 any mental defect and found that he was able to understand the criminal proceedings and to assist in his defense. We thoroughly reviewed the record of the proceedings in this case. Our review revealed adequate support for the court's findings, and we therefore conclude that those findings are not clearly erroneous. On the basis of its findings, the court properly concluded that the petitioner failed to prove ineffective assistance of counsel and prejudice.
The judgment is affirmed.
In this opinion the other judges concurred.
NOTES
[1]  General Statutes § 53a-54a(a) provides in relevant part: "A person is guilty of murder when, with intent to cause the death of another person, he causes the death of such person. . . ."
[2]  See North Carolina v. Alford, 400 U.S. 25, 37, 91 S.Ct. 160, 27 L.Ed.2d 162 (1970).
[3]  At the sentencing hearing, the petitioner was represented by Ellen Morrissey, special public defender, who filed a motion to withdraw the petitioner's guilty plea. The petitioner withdrew this motion before the court imposed a sentence.
[4]  The petition addressed only the performance of Watson during the plea negotiations and before the trial court. The petition made no allegations regarding the performance of Morrissey during the sentencing hearing.
[5]  The petitioner additionally claims that the court improperly excluded testimony regarding the results of a physician's evaluation of the petitioner's intellectual capacity. Because the petitioner failed to brief this issue, we decline to review this claim. See Martin v. Martin, 101 Conn.App. 106, 122, 920 A.2d 340 (2007) ("It is well established that [w]e are not required to review issues that have been improperly presented to this court through an inadequate brief. . . . Analysis, rather than mere abstract assertion, is required in order to avoid abandoning an issue by failing to brief the issue properly. . . . Where the parties cite no law and provide no analysis of their claims, we do not review such claims." [Internal quotation marks omitted.]).
[6]  The following colloquy occurred during direct examination of the petitioner by his counsel:

"Q. Let me turn your attention back to December of 2000, excuse me, December of 1994; did you know a person by the name of Jose Vasquez?
"A. Yes, sir.
"Q. Okay. And prior to December 23, 1994, did you know him?
"A. Yes, sir.
"Q. Were you planning to meet him on December 23, 1994?
"A. Actually, I was planning to meet him December 22, but it got rescheduled to [December 23].
"Q. Why were you planning on meeting him?
"A. Because we had discussed him purchasing a handgun.
"Q. From who?
"A. From me.
"Q. Did you have a handgun he could purchase?
"A. Yes, sir.
"Q. Okay. And did you arrange to have a meeting?
"A. Yes.
"[The Respondent's Counsel]: I'm going to object to this line of questioning. The habeas corpus goes to the plea and voluntariness of the plea, and I believe this is beyond the scope and irrelevant.
"The Court: [The petitioner's counsel], your claim?
"[The Petitioner's Counsel]: Your Honor, it's underthis is relevant to paragraph five, subsection (c). I'm making a claim that his attorney did not pursue a defense, and I'm getting into information that should have been available to his attorney to potentially pursue.
"The Court: Well, what does this testimony have to do with that, the failure of counsel to pursue a defense?
"[The Petitioner's Counsel]: Well, I'm putting on the record that there was a defense available. I think that's the first step that I need to take.
"The Court: I'll sustain the objection.
"[The Petitioner's Counsel]: Mr. McClean, did you shoot Jose Vasquez?
"A. Intentionally?
"Q. Well, I'll withdraw that question. Did you intentionally mean to shoot Jose Vasquez?
"A. No, sir.
"Q. Was it an accident?
"A. Yeah.
"Q. On December 23, 1994, when you went to meet him, did you have any intention of shooting him?
"A. No, sir.
"Q. What happened?
"[The Respondent's Counsel]: Objection, relevance.
"The Court: Sustain the objection. . . .
"[The Petitioner's Counsel]: And this witness was Angel Rivera?
"A. Yes.
"Q. Did this person actually see the shooting?
"A. No.
"[The Respondent's Counsel]: Objection.
"The Court: Sustain the objection."
[7]  The petitioner also claims that his plea was not entered knowingly and voluntarily because Watson failed to discuss with him any waiver of his right to a presentence investigation. The amended petition for a writ of habeas corpus did not address the petitioner's waiver of the presentence investigation. Further, the petitioner offered no evidence, and the habeas court made no findings, regarding his waiver of the presentence investigation. We therefore decline to review this claim.
[8]  Rules of Professional Conduct (Rev. to 1998) Rule 3.3(c) states: "A lawyer may refuse to offer evidence that the lawyer reasonably believes is false."
