Wilkins, C.J.
The defendants, convicted of deliberately premeditated murder in the first degree of Joseph John Bottari and Frank Angelo Chiuchiolo, appeal, raising a multitude of issues.2 We reversed the defendants’ previous convictions of murder in the first degree because recorded testimony of Richard Storella, a witness who was unavailable at trial, had been improperly admitted. Commonwealth v. DiBenedetto, 414 Mass. 37, 41, 44 (1992). See Commonwealth v. Tanso, 411 Mass. 640, 650, cert. denied, 505 U.S. 1221 (1992) (retrial ordered).
By the time of the defendants’ retrial, Storella was available. He testified that he knew the defendants and that on the night of February 19, 1986, he had seen them, along with Paul Tanso, shoot the victims in Slye Park in the North End of Boston.3 According to Storella, the defendants told him that they had each shot both victims. Storella had given a number of different and [416]*416inconsistent accounts of what he had seen that night, including one in which he claimed that he himself had been one of the murderers. He had been given immunity from prosecution. With good reason, the defendants strenuously challenged the reliability of Storella’s testimony.
Another witness testified that he had watched the murders take place. At 9:30 p.m. that night, Joseph Schindler, a Boston lawyer, was sitting in his third-floor apartment overlooking the park when he heard four or five “cracks or pops” that he thought were fireworks. He had an unobstructed view of the park from his apartment. He looked out and saw orange-red flashes in the area of the hand of a man whom he later identified as Costa. He went to another, darkened room to obtain a better view. The sounds continued. The park was lit by the moon and artificial lights. He saw five men. Two of them fell to the ground, and the other three left the park. Leaving the park, the defendants came toward Schindler, first Costa, then Tanso, and finally DiBenedetto. Schindler called the police. He described the defendants to the police, descriptions which were not entirely accurate, and later identified them in separate lineups and in three different court proceedings.
The major question for the jury was whether the defendants were two of the murderers. Convictions depended on (a) the credibility of Storella, who knew the victims and claimed to have witnessed the killings, but had repeatedly and admittedly lied about the killings and (b) the reliability of Schindler’s identification of the defendants, whom he did not know. The only other incriminating evidence, the subject of vigorous challenge in this appeal, was marginally instructive testimony that a small trace of blood was found on one of DiBenedetto’s sneakers.
Able appellate counsel have raised multiple challenges to various decisions and rulings in the trial court. Many of their arguments fail because the judge made rulings that lay within his discretion. There was no prejudicial error. We affirm the convictions and deny relief under G. L. c. 278, § 33E.
1. The defendants object to the admission of evidence indicating the presence of blood on one of DiBenedetto’s sneakers. They argue first that the evidence should have been suppressed [417]*417because it was the product of an unconstitutional arrest.4 They next argue that, in any event, the tests that led to the indication of blood on DiBenedetto’s sneaker were conducted in violation of the pretrial conference report and consequently their admission violated the defendants’ due process rights. They also claim that the Commonwealth did not take adequate steps to protect the sneakers from contamination. We shall not discuss this last point beyond stating that the defendants were able fully to explore the possibility of contamination at trial. It was for the jury to decide what weight, if any, to give the tests. See Commonwealth v. Ortiz, 424 Mass. 853, 860 (1997).
On February 23, 1986, between 5 a.m. and 6 p.m., police executed a search warrant and a warrant for DiBenedetto’s arrest at an apartment on North Margin Street in Boston. A judge later ruled that the search warrant was defective and suppressed all evidence seized at the apartment. The sneakers were taken from DiBenedetto at the police station when he was booked. The lawfulness of this seizure depends on the validity of his arrest made in execution of the arrest warrant. If the arrest was lawful, any clothing that could have been evidence was properly taken from him. See Commonwealth v. Gliniewicz, 398 Mass. 744, 750 (1986).
The defendants argue that the police lacked a constitutionally sufficient basis for believing that DiBenedetto was in the North Margin Street apartment when they entered it and arrested him. The police were acting on information about the apartment obtained from an identified person who knew DiBenedetto, had verified that DiBenedetto had a bedroom there, and told the police that he had been in that bedroom with DiBenedetto four days before the arrest. There was no reason to believe that DiBenedetto had left. A police officer confirmed that the name DiBenedetto was assigned to the apartment. The early morning entry and the fact that the police found that the front door was ajar justified an expectation that someone was likely to be there.
This evidence surely meets the requirement of the Fourth Amendment to the United States Constitution that, if an arrest warrant is issued on probable cause (a point not challenged here), the police may enter a suspect’s dwelling if they have reason to believe that the suspect is there. Payton v. New York, 445 U.S. 573, 603 (1980). The arresting officer need not have [418]*418probable cause to believe the suspect is at home. Id. at 602. The evidence here easily meets the “reason to believe” standard of the Payton case. See United States v. Magluta, 44 F.3d 1530, 1535 (11th Cir.), cert. denied, 516 U.S. 869 (1995) (“officers may presume that a person is at home at certain times of the day”); United States v. Terry, 702 F.2d 299, 319 (2d Cir.), cert. denied sub nom. Williams v. United States, 461 U.S. 931, and cert, denied sub nom. Guippone v. United States, 464 U.S. 992 (1983) (police need not “first conduct a thorough investigation to obtain evidence of an arrestee’s actual presence before entering his residence”).
This court has not yet decided whether art. 14 of the Massachusetts Declaration of Rights requires that police, with a valid arrest warrant, have more than reason to believe a suspect is in a dwelling. See Commonwealth v. Acosta, 416 Mass. 279, 282 (1993). The defendants argue that art. 14 requires that the police have probable cause to believe that the subject of an arrest warrant is present. We need not answer this question because the information the police had when they entered the apartment satisfied even the higher probable cause standard.
The next question is whether the judge erred in admitting expert testimony that a test showed the presence of blood on one of DiBenedetto’s sneakers. Neither the sneakers nor testimony concerning tests conducted on them were introduced at the first trial. In fact, the Commonwealth did not conduct its testing until December 31, 1993, shortly before the second trial. This date was well after the May 27, 1993, deadline, set pursuant to the pretrial conference report, for the delivery of “[scientific test reports” and the names of all Commonwealth witnesses.
On December 31, 1993, David Brody, director of the Boston police crime laboratory, tested the sneakers for the presence of blood. No test had been conducted on the sneakers since the laboratory received them on February 26, 1986. There was no apparent sign of blood on either sneaker. The test, a sensitive one using phenolphthalein followed by hydrogen peroxide, indicated blood on a small portion of the left sneaker and no blood on the right one. The blood was not necessarily human. Brody wrote a report that was promptly delivered to DiBenedetto’s counsel.
One week later, in Brody’s presence, a defense expert tried unsuccessfully to replicate Brody’s tests. He found nothing on [419]*419the left sneaker (where Brody had obtained a positive result), but he obtained a positive result on the right sneaker (where Brody’s tests had produced a negative one). Brody testified that the defense expert had probably found nothing on the left sneaker because Brody’s wiping of it had removed all traces of blood.5
There is no doubt that the Commonwealth failed to comply with the pretrial conference report. The question is whether the defendants were prejudiced by the breach. See Commonwealth v. Gliniewicz, 398 Mass. 744, 748-749 (1986). In the Gliniewicz case, the pretrial conference report explicitly obliged the Commonwealth to make certain evidence available for inspection. In the course of its testing, the Commonwealth destroyed a portion of the defendant’s boots with the result that the defendant could not possibly duplicate the tests. We held that the Commonwealth’s test results should not have been admitted. Id. at 749. “[Wjhen potentially exculpatory evidence is lost or destroyed, a balancing test is employed to determine the appropriateness and extent of remedial action. The courts must weigh the culpability of the Commonwealth, the materiality of the evidence and the potential prejudice to the defendant.” Commonwealth v. Willie, 400 Mass. 427, 432 (1987). To establish prejudice, the defendant must show “a ‘reasonable possibility, based on concrete evidence rather than a fertile imagination,’ that access to the [material] would have produced evidence favorable to his cause.” Id. at 433, quoting Commonwealth v. Neal, 392 Mass. 1, 12 (1984).
The test conducted by each expert in this case was substantially the same. The chance to replicate the test on the left sneaker was probably lost because Brody’s testing removed the very small amount of blood at the test site. The defendant’s expert found indications that blood was present on the other sneaker. There seems to be little doubt that one or both of the defendant’s sneakers tested positive for the presence of a minute amount of what was either the blood of a human or some other animal or perhaps certain plant peroxidases. The judge did not abuse his discretion in admitting the blood test results. The defendants have failed to demonstrate that they were prejudiced by Brody’s testing of the sneakers for blood. This case, therefore, differs from Commonwealth v. Gliniewicz, supra at [420]*420748-749, where the Commonwealth prejudicially destroyed sections of the defendant’s boots in violation of the pretrial conference report, thereby making any similar test by the defendant impossible.
2. We have recently considered, and need not revisit, the question of the admission of expert testimony concerning the reliability of eyewitness identifications. See Commonwealth v. Santoli, 424 Mass. 837, 841-844 (1997); Commonwealth v. Walker, 421 Mass. 90, 96 (1995); Commonwealth v. Hyatt, 419 Mass. 815, 818 (1995). The judge knew he had discretion to admit or exclude such evidence that the defendants offered. He did not abuse his discretion in excluding it. This is not a case in which there was a single eyewitness and little or no evidence to corroborate the identification. Commonwealth v. Santoli, supra at 842.
We also adhere to the position we took in our Santoli opinion that only in cases tried thereafter must the statement that the jury may consider the strength of a witness’s identification be omitted from the standard charge concerning eyewitness identification. See Commonwealth v. Payne, 426 Mass. 692, 698 (1998); Santoli, supra at 845. No significant constitutional question is presented by the giving of that instruction in this case.
The judge also did not err in declining to supplement his eyewitness identification instruction. The matters on which additional instructions were sought are appropriate for final argument but need not be included in a judge’s charge.6
3. The judge did not abuse his discretion in excluding testimony intended to show that the victims, strong-arm men in a crew of La Cosa Nostra (LCN) criminals, were killed by fellow LCN members as “fallout” from an earlier LCN murder of one Vincent Limoli. The judge concluded that the Limoli murder was remote and that the proffered evidence was complicated and would divert the jury’s attention. The defendants did not offer evidence, other than speculation, that some third person or [421]*421persons had a motive to kill the victims because of Limoli’s murder. Nor did they show that the killings in this case were sufficiently similar to the Limoli killing to warrant admission. See Commonwealth v. Rosa, 422 Mass. 18, 22-23 (1996); Commonwealth v. Harris, 395 Mass. 296, 300 (1985).
The defendants further argue that the judge improperly restricted their cross-examination of Storella on the same subject to show his bias. The judge barred DiBenedetto’s counsel from seeking to establish on cross-examination that, because of the Limoli murder, Storella had accused the defendants falsely, out of fear, in order to protect the real killers. This was a matter within the judge’s discretion. Commonwealth v. LaVelle, 414 Mass. 146, 153 (1993). The defendants did not make a plausible showing that circumstances existed on which the alleged bias could be based. See Commonwealth v. Bui, 419 Mass. 392, 401, cert. denied, 516 U.S. 861 (1995); Commonwealth v. Souza, 39 Mass. App. Ct. 103, 108 (1995).
4. The defendants were also not improperly restricted in cross-examining Storella about his immunity agreement. They were able to question him at length about that agreement and how it affected his different accounts of the events surrounding the murder. They wanted to elicit whether Storella thought that he was protected from prosecution for murder when he made his fourth statement, the one in which he incriminated himself. The judge forbade inquiry into statements Storella’s attorney had made to him regarding the consequences of the immunity agreement “unless it appears it is the only way to get at the information.” Because defense counsel did not fully pursue the issue of Storella’s belief, it never became clear that it was necessary to discover what Storella’s attorney had told him about the immunity agreement. Only then would the defendants have been entitled to invade the attorney-client privilege to learn this information. Commonwealth v. Michel, 367 Mass. 454, 460-462 (1975). See Commonwealth v. LaVelle, 414 Mass. 146, 154-155 (1993).
5. The defendants assert that the judge erred in using a blackboard during his jury instructions to set forth the elements of murder because this process overemphasized those elements. The defendants did not object to the use of the blackboard when the judge inquired if there was any objection to his doing so. Their objection came only after the charge had been given, and, in response, the judge told the jury that all his instructions were important and that any question about them would be answered.
[422]*422The judge did not err. The defendants consented to the use of the blackboard. Even if they had not, the judge was entitled to place the elements of the crime on the blackboard. We have endorsed jurors’ use of notebooks during the judge’s charge. See Commonwealth v. St. Germain, 381 Mass. 256, 265-266 (1980). If we allow jurors to try to write out the elements of a crime as a judge recites them, it would be strange to forbid a judge from following a more rehable course and giving the jury those elements in writing or setting them forth on a blackboard. In Commonwealth v. Dilone, 385 Mass. 281, 287 n.2 (1982), we endorsed any reasonable procedure by which all or any portion of a charge could, by agreement, be given to the jury. See Commonwealth v. Martin, 424 Mass. 301, 311 n.5 (1997); Commonwealth v. Lavalley, 410 Mass. 641, 652 n. 15 (1991).
Whatever we may have said before, it is now time to recognize that reasonable steps to assist a jury in performing their function should be encouraged. As long as the judge makes it clear that the jury must find each element of the crime beyond a reasonable doubt, a judge may, in the exercise of discretion, provide a jury with an accurate statement of the elements of each crime charged. We hope and expect that in time, at least in the trial of serious crimes, technology will be in place that will make a judge’s entire charge available to jurors promptly following its conclusion.
6. The judge gave an instruction on joint venture that Costa’s counsel requested and to which DiBenedetto’s counsel did not object at any time. We do not review jury instructions in such a situation (Commonwealth v. Callahan, 401 Mass. 627, 631, 634 n.9 [1988]), except to determine whether they created a substantial likelihood of a miscarriage of justice (see Commonwealth v. Ward, 412 Mass. 395, 398 [1992]). The instruction on joint venture erroneously combined language concerning guilt as an accessory before the fact (not requiring proof of the defendant’s presence at or near the crime scene) with language concerning guilt as a joint venturer and thus failed to make explicit that guilt as a joint venturer required the defendant’s presence at or near the crime scene. See Commonwealth v. Lafayette, 40 Mass. App. Ct. 534, 539-541 & n.7 (1996). However, the instruction could not have led to an unjustified verdict. There was evidence of conduct by the defendants before the trial that would have warranted a finding that each was an accessory before the fact, a charge that was [423]*423within the scope of the indictment. See G. L. c. 274, § 2; Commonwealth v. Perry, 357 Mass. 149, 151 (1970). The challenged instruction did not create a substantial likelihood of a miscarriage of justice. In practical terms, the case was tried and argued on the theory that the defendants were the shooters. The invited error in the judge’s charge could not have had any effect on the verdict.
7. In these circumstances, where there was evidence that the victims’ deaths were caused by the combined actions of two people, but it was not clear who dealt the fatal blows, each defendant may properly be convicted based on joint venture liability. See Commonwealth v. Drumgold, 423 Mass. 230, 253-254 (1996); Commonwealth v. Semedo, 422 Mass. 716, 720-721 (1996). Cf. Commonwealth v. Green, 420 Mass. 771, 780 (1995) (evidence that only defendant was shooter bars joint venture liability). The judge did not err in denying the defendants’ motions for findings of not guilty on the theory of joint venture.
8. We discuss briefly the defendants’ other arguments.
a. The defendants’ motions to dismiss the indictments were properly denied. (1) The Commonwealth did not know that Storella’s grand jury testimony was in part false. It did not knowingly present any false testimony. See Commonwealth v. Sullivan, 410 Mass. 521, 532 (1991); Commonwealth v. Mayfield, 398 Mass. 615, 620 (1986). (2) The Commonwealth’s failure to present evidence to the grand jury that would have impeached Storella’s credibility does not warrant dismissal of the indictments. It is unlikely that, if the grand jury had heard the evidence, they would have decided differently. See Commonwealth v. Trowbridge, 419 Mass. 750, 754 (1995); Commonwealth v. McGahee, 393 Mass. 743, 747 (1985). (3) Costa makes an argument that he could have raised in the first appeal, but did not, contending that the prosecutor improperly, but accurately, told the grand, jury that a Juvenile Court judge had transferred him to the Superior Court. The issue is waived. See Commonwealth v. Kater, 409 Mass. 433, 445 (1991). In any event, the prosecutor did not tell the jury that the judge had found probable cause, and it was unlikely that the jury would have drawn such an inference. See Morrissette v. Commonwealth, 380 Mass. 197, 200 (1980); Commonwealth v. Seminara, 20 Mass. App. Ct. 789, 793-794 (1985). There was no error.
b. Costa’s argument that Storella’s perjured testimony [424]*424requires a new Juvenile Court transfer hearing lacks merit. In his numerous versions of the crime, Storella never wavered from his position that Costa was one of the shooters.
c. The defendants assert that the Commonwealth’s failure to locate Storella to testify at their first trial bars a retrial. We have already rejected the double jeopardy argument. Commonwealth v. DiBenedetto, 414 Mass. 37, 45-46 (1992). A retrial of a defendant found guilty, but granted a new trial because of prejudicial error, is not inappropriate. Id. at 45. The defendants have made no showing that they were not given a fair retrial. Commonwealth v. Drumgold, 423 Mass. 230, 246 (1996).
d. Costa’s argument that his trial counsel had a conflict of interest as a result of Costa’s previous claim of ineffective assistance lacks merit. The same lawyer represented Costa at both his trials. In the appeal that led to the reversal of his first conviction and a new trial, Costa’s appellate counsel argued that trial counsel had been ineffective, an issue we did not reach. Costa, nevertheless, wanted the same trial counsel at his second trial, and, on his petition, a single justice of this court directed that Costa be allowed to have the same counsel. Because there is no evidence of an actual conflict at the time of trial, the argument fails. Commonwealth v. Davis, 376 Mass. 777, 781 (1978).
e. The judge properly denied (1) Costa’s motion to suppress Storella’s testimony as unreliable, and (2) Costa’s motion for a psychiatric examination of Storella to determine his competency. Credibility is for the jury. See Commonwealth v. Ianello, 401 Mass. 197, 202 (1987); Commonwealth v. Bohannon, 376 Mass. 90, 94 (1978). An expert opinion in effect commenting on Storella’s credibility would be inadmissible. See Commonwealth v. Ianello, supra; Commonwealth v. Widrick, 392 Mass. 884, 889 (1984).
f. The judge did not err in barring Costa’s counsel from inquiring of Schindler whether other individuals in the lineup from which he identified Costa looked in any way like a person that Schindler had seen committing the murders. The judge ruled that Schindler’s opinion on that point was not admissible because any infirmities of the identification procedure were for the jury, which saw a videotape of the lineup. The ruling was well within the judge’s discretion. Commonwealth v. Nassar, 351 Mass. 37, 41-42 (1966). See Commonwealth v. Austin, 421 Mass. 357, 365-366 (1995).
g. The defendants’ claim that two remarks in the prosecutor’s [425]*425final argument to the jury, not objected to, created a substantial likelihood of a miscarriage of justice has no merit and requires no discussion.
h. The judge’s instruction that the jury not “go off into the realm of conjecture and speculation” was appropriate in context. The judge made clear that he meant that the jury should make their decision on the evidence.
i. Costa’s two challenges, not raised below, concerning the judge’s instructions on malice lack merit. First, the judge’s malice instruction included the frame of mind definition of malice that we disapproved, after the trial of this case, in Commonwealth v. Eagles, 419 Mass. 825, 836 (1995). It, however, also properly defined malice by reference to its three aspects. See Commonwealth v. Grey, 399 Mass. 469, 470 n.l (1987). Costa’s argument that the frame of mind language created a substantial likelihood of a miscarriage of justice fails. See Commonwealth v. Richardson, 425 Mass. 765, 769 (1997); Commonwealth v. Torres, 420 Mass. 479, 487 (1995). Second, the judge’s malice instruction did not give the jury the option of convicting the defendants of deliberately premeditated murder without a finding that the defendants intended to kill the victims. See Commonwealth v. Diaz, 426 Mass. 548, 552-554 (1998); Commonwealth v. Hamilton, 426 Mass. 67, 75 (1997); Commonwealth v. Richardson, supra at 768. No substantial likelihood of a miscarriage of justice was created.
j. Costa challenges the denial of his motion to sever his trial from DiBenedetto’s. His sole argument is that their proposed alibis were inconsistent. At the first trial, the defendants presented an alibi that, at the time of the killings, they were together with others at DiBenedetto’s home. Before the second trial, Costa asserted that he had a witness who would testify that he was at her home at the time of the killings, although, contrary to his interests, she would also testify that “the kids were in and out all night.” The distance between the two homes was small. Neither defendant presented any alibi evidence at the second trial. DiBenedetto does not challenge the denial of his motion to sever.
The judge did not abuse his discretion in denying the motion to sever the trials. Because the two defendants’ defenses were not antagonistic and the potential alibi evidence was not irreconcilable, the judge was warranted in concluding that there was no prejudice to Costa in denying the motion and that Costa [426]*426could receive a fair joint trial. See Commonwealth v. Smith, 418 Mass. 120, 125-126 (1994); Commonwealth v. Cunningham, 405 Mass. 646, 654 (1989).
Judgments affirmed.