On the second day of the trial of the defendant on a charge of trafficking in 24.49 grams of cocaine1 both sides rested and presented their summations. The jury were then properly instructed by the trial judge that the sole contested issue was whether the Commonwealth had proved beyond a *753reasonable doubt that the defendant had the specific intent to distribute the drugs that he was concededly hiding on his person when arrested by the police during a warranted and legally unexceptionable search.
The jury began deliberating shortly after noon. At 4:45 p.m., the jury foreperson sent the judge a note stating, “[W]e have taken five votes and have not been able to come to an agreement .... We do not believe that we can come to an agreement with further deliberations.”2 The judge sent the jurors home for the evening with an emphatic warning to avoid discussing the case among themselves or with third parties and to refrain from conducting any “independent research.”3
When the proceedings resumed the following day, the judge immediately asked the jurors whether they had complied with his orders of the previous evening. All of them affirmatively responded that they had followed his instructions. The judge then gave a Rodriguez charge4 and ordered the jury to continue deliberations. A few hours later, the foreperson of the jury sent the judge a note which stated: “Last evening, [a] Juror accessed the Internet and gleaned information about the chemical composition of cocaine. Another Juror approached two police officers and asked about the quantity of drugs necessary for trafficking. Another Juror asked a friend about the cost of cocaine on the street.” The judge, with the agreement of counsel, decided to conduct an individual voir dire of each juror outside the presence of the other jurors.5
With the defendant, his attorney, and the prosecutor in attendance, the judge began each inquiry by reading the foreperson’s note aloud. He then asked each juror whether he or she was one of the individuals referred to in the note. Nine of the jurors denied any such involvement. The judge then asked each *754of those nine — without explicitly inquiring whether the juror had in fact heard or received any information of the sort referred to in the note or what the content of such information was if the juror had heard or received it — whether “the fact that that information has been brought to your attention during your deliberations” would affect the juror’s ability to be fair and impartial and whether it would be taken into consideration in reaching a verdict. Eight of the nine categorically stated they would not consider “that information” and could still render a fair and impartial verdict. One juror, however, said, “It [referring to ‘that information which was brought to your attention by your fellow jurors’] changed my mind,” and that it “ha[d] had an impact in [her] deliberations.” Both the judge and defense counsel agreed that this juror should be discharged.
Early in the course of the voir dire, defense counsel had requested that the jurors be asked specifically “what was the information that was imparted to them on these issues” from their three errant colleagues, in order more precisely to gauge the nature of any prejudice created.6 The judge refused, expressing his concern that such a query would intrude into the nature of the jury’s deliberations. He again offered to entertain a motion for a mistrial, but defense counsel simply registered, “Objection.”
As the voir dire progressed, three jurors separately admitted to engaging in the reported misconduct. The juror who had accessed the Internet stated that he had only done so “out of curiosity” while working at the computer and had gotten no information other than the chemical composition of cocaine. The juror who had asked about the quantity of drugs necessary for trafficking denied having received any information, because the officers he approached “were MBTA cops” who did not know the answer. The third juror also denied receiving any information in response to his inquiry of “a friend” about the street cost of cocaine.
At the conclusion of the voir dire (and still out of the jury’s presence), the judge decided to discharge (with defense counsel’s concurrence) the two jurors who had spoken with others the previous evening. The Internet-surfing juror was allowed *755to remain on the panel, neither side having sought his removal. At that point, there remained only eleven available jurors, nine originals and two alternates. The judge gave the defendant the option of moving for a mistrial or agreeing to submit the case to be decided by the eleven jurors (with any guilty verdict still to be unanimous) as authorized by Mass.R.Crim.P. 19(b), 378 Mass. 888 (1979).7 After some vacillation, the defendant agreed to proceed pursuant to rule 19(b). Following consultation with his counsel and a detailed colloquy with the judge, in which he was fully informed of his rights and options (including the option of a mistrial, which the defendant explicitly acknowledged he had discussed with counsel),8 the defendant orally waived his right to trial by a jury of twelve, agreed to have his case submitted to the eleven remaining jurors, and executed a written waiver to that effect.
Upon the return of the jury to the courtroom, the judge discharged the three jurors as previously determined, replaced them with the two alternates, and ordered the nine original jurors to refrain from discussing what had previously transpired. He then instructed the newly constituted jury to begin deliberations anew.9 Almost two hours later, the jury returned a verdict finding the defendant guilty of trafficking.
*756On appeal the defendant contends principally10 that his constitutional right to trial by an impartial jury was violated. The defect he presses is the judge’s failure to conduct a sufficiently detailed voir dire, designed to elicit the precise nature of the extraneous information communicated to the jury, so as to provide the judge with the data necessary for independently *757evaluating the likely prejudicial effect of the information on the remaining jurors and each juror’s ability to act impartially. The judge’s limitation of the voir dire inquiry, he maintains, violated the procedures mandated in such situations by Commonwealth v. Jackson, 376 Mass. 790, 800-801 (1978), and Commonwealth v. Kamara, 422 Mass. 614, 615-616 (1996).11
The Commonwealth counters that the defendant is not entitled to a new trial because the judge essentially followed the voir dire procedures approved in Jackson and Kamara. It dismisses as unfounded the defendant’s claim that the voir dire was inadequate, because the judge in fact ascertained through his questioning the precise nature of the extraneous information imparted to the jury from the testimony of the three jurors who engaged in the misconduct. The Commonwealth also asserts that the judge acted well within his discretion in permitting nine original jurors to decide the case on the basis of his acceptance of their assurances to him that they could remain fair and impartial.
Given the limited authority relevant to evaluating the adequacy of the judge’s prejudice-probing procedures in this case, we face a close question on the unique facts presented. Although the defendant criticizes the judge’s refusal to elicit the precise nature of the extraneous information communicated to the jurors, the same was true in Jackson. (The court noted in *758Jackson, 376 Mass, at 798, “The record does not disclose what these news reports [on the radio and in the newspaper] stated concerning the defendant,” and the judge’s questions only inquired whether whatever the jurors had seen or read had caused them “to form any opinion or prejudice against the defendant, or in relation to this case”; this uncovered one juror who on further questioning admitted that what she had read would prevent her from rendering a fair and impartial verdict.)
Although the defendant also faults the judge’s acceptance of the nine surviving jurors’ unqualified representations of impartiality as unreliably uncritical, the court in Jackson approved the trial judge’s reliance on the fact that only one juror affirmatively acknowledged exposure to the extraneous report and influence by it: “No other juror answered in the affirmative.” 376 Mass, at 798. See Kamara, 422 Mass, at 618 (the judge accepted jurors’ assurances that they were not influenced by the extraneous information and could be fair and impartial, even though most of them had heard some of it, see note 13, infra).12 Cf. Berlandi v. Commonwealth, 314 Mass. 424, 450-453 (1943) (judge presiding over nonjury criminal contempt trial took a technically objectional view of premises mentioned in the evidence without the consent or knowledge of the defendants or their counsel but stated that he had learned nothing of value and what he saw in no way affected his decision; held, no harm or prejudice ensued, and the judge’s statement that what he did was irrelevant to his decision “is to be given full credence,” on the same principle as the presumption that the jury follow instructions to disregard improper evidence).
The defendant relies on Kamara for the proposition that the *759judge on voir dire in such a situation must ask each juror “extensive questions to learn just what that particular juror heard.” In Kamara, however, the judge was informed by the jury foreperson, sua sponte, of the essential details of the extraneous information in the course of the initial revelation of the fact of the jury’s exposure to that information.13 Finally, the defendant asserts, in a conclusory fashion, that “the offending jurors . . . irreparably altered the impartiality of those [other] jurors who heard the extraneous information and destroyed any chance of a fundamentally fair trial.” But in Kamara the court noted that no authority had been presented or found for the defendant’s equivalent proposition there that, despite an individual voir dire of the unoffending jurors and the trial judge’s conclusion that they could decide the case impartially unaffected by their conceded exposure to the extraneous information, the taint of that information was nonetheless irremediable as matter of law. Rather, the court stressed the discretionary nature of the judge’s decision and refused “to substitute our judgment for that of the trial judge . . . .” 422 Mass, at 620.14
On the other hand, although the Commonwealth asserts that the limited extent of the extraneous information the jurors received demonstrates that the judge was warranted in not delving deeper into what was said in the jury room regarding the fruits of the unauthorized activities, the judge’s acceptance of the three meddlesome jurors’ explanations as to the limited extent of the extraneous information (merely the chemical composition of cocaine) is arguably brought into question by *760several circumstances. First, the three jurors’ reliability was open to challenge in light of their having immediately disobeyed the judge’s specific “no investigation” order, then lied about it when collectively questioned concerning their compliance the next morning. Second, their assertions that they discovered nothing, or at least nothing of significance, are at odds with the fact that they nonetheless felt impelled to communicate something to the other jurors, at least two of whom responded to the judge’s questioning by affirmatively stating that some information had been brought to their attention.
Moreover, the claim of the three offending jurors that their efforts yielded nothing relevant appears contradicted by the confession of one of the other jurors that something about the communications made by one or more of the three not only had had an impact on her deliberations but had actually changed her mind. It seems unlikely that merely learning the chemical composition of cocaine — a matter irrelevant to the jury’s deliberations — could have had such an effect. We are also unable to conclude that asking each of the nonoffending jurors to state what the three intermeddlers had actually said about their illicit investigations, without delving further, would necessarily have required revelation of or intrusion into jury deliberations.
We need not, however, definitively resolve any doubts involving the efficacy of the judge’s inquiry. Even were we to accept the defendant’s contention that the judge’s handling of the voir dire was inadequate and incomplete, we would nonetheless affirm the defendant’s conviction because he effectively waived his right to object to the determination of his guilt by the reconstituted jury. Instead of moving for a mistrial based upon the jury’s presumed receipt of conceivably prejudicial extraneous information — a motion the trial judge expressly invited not once but five times in the course of the jury interrogation — the defendant voluntarily and intelligently chose rather to waive his right to be tried by twelve new jurors and affirmatively agreed to be tried by “the remaining [eleven] jurors” (emphasis supplied). Mass.R.Crim.P. 19(b), 378 Mass. 888 (1979). See discussion at 754-755 and note 7, supra. He did so knowing full well (or at least expressly speculating) at the time that one of those remaining jurors may have learned and conveyed something from the Internet more prejudicial than the chemical composition of cocaine and that the other eight original jurors might have heard something potentially harmful from the two *761discharged investigating jurors despite the pair’s protests that their efforts had produced nothing useful.
In such circumstances, the defendant is bound by the result of his deliberate choice and cannot demand reversal of his conviction on direct appeal, any more than had he competently waived, after proper colloquy, his constitutional right to trial by jury, see Commonwealth v. Rowe, 257 Mass. 172, 175-176 (1926); Commonwealth v. Pavao, 423 Mass. 798, 800-801 (1996); cf. Commonwealth v. Collado, 426 Mass. 675, 677-679 (1998) (even procedurally defective jury waiver sufficient so long as no doubt exists as to its voluntary and intelligent nature), or even his right to any trial at all. See Kuklis v. Commonwealth, 361 Mass. 302, 305 (1972); Huot v. Commonwealth, 363 Mass. 91, 100-102 (1973); Commonwealth v. Lopez, 426 Mass. 657, 660-662 (1998); Commonwealth v. Pingaro, 44 Mass. App. Ct. 41, 45 n.4, 49-50, 54-55 (1997).15
The instant situation is also analogous to that of a defendant who, knowing of a biased or otherwise disqualifiable juror, nonetheless makes no objection and agrees to continue to trial and verdict by a jury including that juror. However valid a timely challenge might theoretically have been, having intentionally forgone it, the defendant cannot rely on that issue on appeal. See Amado v. Commonwealth, 349 Mass. 716, 717-719 (1965); Commonwealth v. Zakas, 358 Mass. 265, 267-268 (1970). Cf. Fox v. Hazelton, 10 Pick. 275, 277-278 (1830) (referees); Gray v. Boston Elev. Ry. Co., 215 Mass. 143, 149-150 (1913).
The very scenario presented here — a defendant’s express consent to continuing trial even though disqualifications during trial reduced the panel to eleven — has been addressed twice by the Supreme Judicial Court, which on both occasions unqualifiedly held that the defendant is precluded from thereafter challenging a resulting adverse verdict. See Commonwealth v. Dailey, 12 Cush. 80, 82-83 (1853); Commonwealth v. Lawless, 258 Mass. 262, 263-264 (1927). Cf. Gallo v. Commonwealth, 343 Mass. 397 (1961) (recognizing that a trial judge has jurisdiction to continue the defendant’s noncapital trial with only eleven *762jurors and that a defendant can effectively waive his right to a jury of twelve, but reversing the conviction there because a since repealed statute, G. L. c. 234, § 26A, required that the defendant’s waiver be in writing, signed, and filed with the clerk, which had not been done).
The rationale for such a principle, as explained by Chief Justice Shaw almost 170 years ago, appears still relevant:
“[V]olenti non fit injuria. ... If a party knows of any prejudice entertained by a juror, and makes no exception when the jury is empannelled, however good his cause of challenge then is, it must be deemed to be waived. Otherwise, knowing of a secret taint to which the verdict may be exposed, he takes his chance for a favorable verdict, reserving a power to impeach it, should it happen to be against him; a proceeding inconsistent with the plain principles of fair dealing, and with the frankness which ought to characterize the whole course of judicial proceedings.”
Fox v. Hazelton, 10 Pick, at 277-278. See Commonwealth v. Dailey, 12 Cush, at 82 (“Having so done, and taken their chance for a verdict [by the eleven remaining jurors], it would be inconsistent with ordinary good faith and fair dealing to turn round and insist on legal exceptions, which they had pledged themselves to the court that they would not take”); Commonwealth v. Cancel, 394 Mass. 567, 571-572 (1985) (“[I]t is not consistent with the purposes of justice, for a party knowing of a secret defect, to proceed and take his chance for a favorable verdict, with the power and intent to annul it, as erroneous and void, if it should be against him,” quoting from Cady v. Norton, 14 Pick. 236, 237 [1833]).
Such a calculation appears attributable to the defendant in this case, given his resistance to reiterated invitations for a mistrial, which would only yield him a new trial. See Donavan v. Commonwealth, 426 Mass. 13, 14-15 (1997). Presumably heartened by the report of five failed jury efforts at unanimity, the defendant could have reasoned that the odds were favorable that at least one of the remaining original jurors had been skeptical of the Commonwealth’s case, so that he would be no worse off if a hung jury resulted from the renewed deliberations than if he moved for a mistrial. Further, he might have inferred that *763the eight original jurors who had obeyed the judge’s orders might well have been the ones inclined to acquittal, whereas the illicit investigators were a minority for conviction who had been motivated to discover inculpatory information in order to sway their fellows; that the most likely proconviction jurors had been discharged from the panel; that the new alternates might be susceptible to persuasion by the original jurors, who had invested time and energy in deliberations; and, consequently, that the prospect of an outright acquittal was bright enough to warrant proceeding with the reconstituted jury.
Whatever the defendant’s tactical considerations might have been, it is clear that he made a deliberate choice — to continue rather than to terminate his arguably tainted trial. That choice was consistent with the underlying constitutional “consideration . . . that the defendant retain[s] primary control over the course to be followed in the event of such error.” United States v. Dinitz, 424 U.S. 600, 609 (1976). “The fact that the defendant . . . might have gambled and lost,” Commonwealth v. McMaster, 21 Mass. App. Ct. 722, 735 (1986), does not entitle him to second-guess his deliberate trial strategy on appeal, so long as his “trial was fair, ... the verdict was not ‘against the weight of the evidence considered in a large or nontechnical sense’ ” (Commonwealth v. Toney, 385 Mass. 575, 589 [1982]), and his counseled choice was not “suicidal” (Commonwealth v. Adams, 374 Mass. 722, 730 n.4 [1978]). See Commonwealth v. Mains, 374 Mass. 733, 736 (1978). Cf. Commonwealth v. Fernette, 398 Mass. 658, 666-667 (1986) (defendant’s trial agreement to allow jury unrestricted access to his taped post-Miranda statement waived objection to such access on appeal: “[T]he theory of law on which by assent a case is tried cannot be disregarded when the case comes before an appellate court for review . . .”); Commonwealth v. Roberts, 407 Mass. 731, 737 (1990); Commonwealth v. Pagan, 35 Mass. App. Ct. 788, 791 (1994).
In light of the defendant’s deliberate waiver of the right to complain of the verdict of the jurors whom he knowingly agreed should determine his fate, he can obtain reversal only if he can demonstrate to us that this is one of the “extraordinary cases,” Commonwealth v. Harrington, 379 Mass. 446, 449 (1980), that justify our employment of the “rarely used power” to consider *764a waived issue in order to avoid a “substantial risk of a miscarriage of justice.” Commonwealth v. Freeman, 352 Mass. 556, 563-564 (1967). See Commonwealth v. Curtis, 417 Mass. 619, 623 (1994); Commonwealth v. Collado, 426 Mass, at 678 & n.5. The defendant has failed to make such a demonstration. Indeed, he has not even explicitly attempted to do so on appeal. To the extent his assertion that the judge’s unobjected-to instructions to the reconstituted jury were somehow insufficient represents an effort to do so, it is wholly speculative, as well as so cursory and devoid of meaningful argument and pertinent citation to authority as to be inadequate to the task. See Mass-.R.A.P. 16(a)(4), as amended, 367 Mass. 921 (1975).16
In this connection, we note that the judge’s charge following the defendant’s agreement to be tried by the nine remaining jurors and two alternates (see note 9, supra at 755-756) forcefully instructed the original group not to discuss with or inform the new members of anything that had previously taken place, to disregard all past deliberations “as if they have not taken place,” and to begin deliberations anew. The charge also reminded the jury to continue to heed the judge’s unobjected-to general instructions of the previous afternoon covering all elements of the entire case (including the obligation to reach a decision solely on the facts in evidence), as well as his Rodriguez charge (which reiterated the Commonwealth’s burden of proof and the defendant’s entitlement to the benefit of any reasonable doubt) and his warning to each interrogated juror not to discuss the nature of the judge’s questioning with the other jurors. See Commonwealth v. Harris, 395 Mass. 296, 301 (1985) (objections to supplemental charge to be evaluated in light of the judge’s instructions in their entirety). No reason appears, aside from the defendant’s conjecture, to depart here from the established principle that jurors are always presumed to follow the instructions they are given. See Commonwealth v. Cameron, 385 Mass. 660, 668 (1982); Commonwealth v. Watkins, 425 Mass. 830, 840-841 *765(1997); Commonwealth v. Kilburn, 426 Mass. 31, 37-38 (1997).
Judgment affirmed.
The defendant was indicted for trafficking in cocaine with a net weight of fourteen grams or more but less than twenty-eight grams (in violation of G. L. c. 94C, § 32E[b][l]) and for conspiracy to distribute cocaine. The Commonwealth moved for trial on the trafficking charge only, and the conspiracy charge was filed with the defendant’s consent after the jury returned their verdict.
During the course of the afternoon, the jury had asked two questions and received brief supplemental instructions which are not at issue on this appeal.
The judge specifically admonished: “Don’t do any independent research and become Inspector Clouseau or Lieutenant — the guy with the bald head — Kojak, or the guy with the raincoat, Columbo. In other words, don’t do any of that.”
See Commonwealth v. Rodriguez, 364 Mass. 87, 101-103 (1973). Neither side objected to the judge’s giving of the charge, which was received by all of the jurors, including the alternates.
Upon informing counsel of the foreperson’s note, the judge asked defense counsel whether he wanted to request a mistrial at that point. Counsel responded that he wished to “reserve” the issue until the end of the voir dire.
Counsel hypothesized that the information about the value of the cocaine might have been that it was worth “thousands of dollars . . . , way over the amount necessary ... for trafficking . . . and way over personal use,” the precise issue the jury had to decide.
Rule 19(b) of the Massachusetts Rules of Criminal Procedure provides in pertinent part: “If after jeopardy attaches there is at any time during the progress of a trial less than a full jury remaining, a defendant may waive his right to be tried by a full jury and request trial by the remaining jurors by signing a written waiver which shall be filed with the court . . .” (emphasis supplied).
Since waiver of the constitutional right to trial by a jury of twelve, like any waiver of a known right, must be express, intelligent, and competent, see Patton v. United States, 281 U.S. 276, 312 (1930); Johnson v. Zerbst, 304 U.S. 458, 464-465 (1938); Commonwealth v. Pavao, 423 Mass. 798, 800-801 (1996), the record must reflect a colloquy that evidences that the defendant’s waiver was voluntary and intelligent, in order to ensure that the defendant understood the choice he was making. Commonwealth v. Pavao, supra. The defendant here raised no objection to the judge’s colloquy at the time it occurred and does not question any aspect of it on this appeal.
The judge charged: “Members of the Jury, as you know, three of your fellow jurors have been excused from this jury, and we have replaced them with two alternate jurors. The reasons for this are entirely personal to those jurors [and] ha[ve] nothing to do with their views in this case or their relationships with the other jurors. You are not to speculate about or consider for any purpose the reasons why those jurors have been excused. Both the prosecution and the defendant have a right to a verdict that has been reached with full participation of all jurors who return that verdict. This right will be assured in *756this case only if the jury begins its deliberations again from the very beginning. I will say that again. This right will only be assured in this case only if the jury begins its deliberations again from the beginning. I therefore instruct you to set aside and disregard all the past deliberations and to begin deliberations anew. This means that each of you, the remaining jurors, must put aside and disregard the earlier deliberations just as if they have not taken place. I ask you now to retire and continue your deliberations in accordance with all of these instructions and all of the other instmctions that I have given you yesterday, this morning and all previous instructions.”
The previous instructions incorporated by reference in this charge had included the following language: “You must [determine the facts] solely from a fair consideration of the evidence. You can’t use guesswork, conjecture, or surmise. You must decide this case on things you see in this courtroom. You may not decide this case on things you read in the newspapers, see on television, or watch in the movies or speculate as to what might have been or what should have been. You must confine your deliberations to the witness stand, all the various testimonial evidence, and any exhibits that are before you.”
Prior to giving his additional instmctions to the reconstituted jury, the judge had informed counsel that the instruction came from the model contained in the “Jury of Six District Court Handbook” and asked whether either side had any objections. Defense counsel said, “No objection,” at that time and made no objection to any part of the charge at any subsequent time until his brief on appeal (see discussion at 763-764, infra).
The defendant also argues that the judge erred in denying his repeated motions for a required finding of not guilty and in allowing a police witness to state his express opinion on the only contested issue, the defendant’s specific intent to distribute the cocaine. We agree with the Commonwealth that the evidence of the quantity of the cocaine possessed by the defendant at the time of his arrest and its physical characteristics was sufficient to survive those motions and warrant a finding beyond a reasonable doubt that the defendant intended to distribute the drugs. (Among other things, the arresting officer testified that in his years as a narcotics investigator he had never seen anyone smoke or buy for personal use rocks of cocaine the size of those discovered on the defendant’s person.) See Commonwealth v. Johnson, 410 Mass. 199, 202 (1991); Commonwealth v. Roman, 414 Mass. 642, 645-646 (1993). We also agree that the police officer’s testimony, while inartfully put, did not create reversible error in light of the other substantial evidence justifying the inference of the defendant’s intent to distribute, much of it based on the same officer’s years of personal experience in drug enforcement. Cf. Commonwealth v. Woods, 419 Mass. 366, 375-376 (1995); Commonwealth v. Barbosa, 421 Mass. 547, 554-555 (1995); Commonwealth v. Rivera, 425 Mass. 633, 645 (1997).
Jackson and Kamara appear to be the only Massachusetts decisions that deal with the nature of the inquiry to be made of jurors exposed to extraneous information during their deliberations. Jackson pertinently held: “When material disseminated [to the jurors] during trial is reliably brought to the judge’s attention . . . [and] the judge finds that the material raises a serious question of possible prejudice . . . [and in the course of a collective voir dire] any juror indicates that he or she has seen or heard the material, there must be individual questioning of that juror ... to determine the extent of the juror’s exposure to the material and its effects on the juror’s ability to render an impartial verdict.” 376 Mass, at 800-801. Kamara put the following gloss on the Jackson ruling: “[The] trial judge must assess the possible prejudicial effect of the jury’s exposure to extraneous information, and weigh the impact of that extraneous information on the jurors by conducting an individual voir dire of each juror. . . . The judge should also consider the efficacy of curative instructions. . . . The facts of the specific case are important.” 422 Mass, at 616. Further, the “possibility of taint because of the [extraneous information] . . . must be appraised in light of the evidence.” Id. at 619. Finally, the principle applies that “ [determination of potential juror prejudice is á matter within the sound discretion of the trial judge.” Id. at 620. Neither opinion explicitly mandated that the judge ascertain the precise nature of the extraneous information that the jurors had received.
The defendant’s attack on the judge’s implicit findings as to the impartiality of the retained original jurors is technically deficient. Whether to accept declarations of juror impartiality after judicial inquiry is a matter within the judge’s discretion, see Commonwealth v. Coleman, 389 Mass. 667, 676 (1983); Commonwealth v. Kamara, 422 Mass, at 620; Commonwealth v. Cokonougher, 35 Mass. App. Ct. 502, 503-504 (1993), a discretion that is particularly broad with respect to findings based, as here, on credibility determinations. The defendant has failed to argue, much less demonstrate, an abuse of that discretion on these facts, i.e., “that no conscientious judge, acting intelligently, could honestly have” made such a decision. Commonwealth v. Bys, 370 Mass. 350, 361 (1976). The defendant’s claim that the judge accepted all juror claims of impartiality uncritically is belied by the fact that the judge dismissed the two jurors who had spoken with third persons notwithstanding their protestations that their activities did not affect their ability to be fair and impartial.
On the morning of the second day of jury deliberations, a juror (the jury foreperson, according to the Appeals Court decision in Kamara, 37 Mass. App. Ct. 769, 770-771 [1994], S.C., 422 Mass. 614 [1996]) brought to the judge’s attention “that a woman juror had said during deliberations that she knew the defendant, that he was a friend of Eric Brown who dated her niece, that she thought the defendant did it [i.e., the second-degree murder for which the defendant was on trial], that he was a member of a gang, and that she was afraid to walk up the street.” 422 Mass, at 616. In the individual voir dire that followed, the judge incorporated these revealed details into his questioning, and “most jurors [acknowledged that they] had heard some of the extraneous information . . . .” Id. at 617.
We also recall the Supreme Judicial Court’s strong statement that in such situations “the utmost caution is required to avoid invading the province of the jury,” Commonwealth v. Connor, 392 Mass. 838, 844 (1984); see id. at 845 n.3, an admonition that the trial judge here conscientiously strove to honor.
The Commonwealth did not rely on waiver in its brief, although the defendant strenuously denied waiver as one of his appellate contentions. We have the authority to consider the issue as apparent on the record even if not argued in any party’s brief. See Commonwealth v. Simpson, 428 Mass. 646, 648-649 (1999).
The defendant’s entire contention regarding those instructions rests on “the [jury’s] rendering of a verdict in less than two hours . . . and the difficulty of the first jury in reaching any verdict.” Not only is this argument entirely speculative, but it is also rejected by the authorities that establish the irrelevance of the length or speed of jury deliberations. See Commonwealth v. Doyle, 392 Mass. 23, 26-27 (1984). Cf. Commonwealth v. Stewart, 375 Mass. 380, 389-390 (1978); Commonwealth v. Haley, 413 Mass. 770, 779 (1992); Commonwealth v. Bregnard, 3 Mass. App. Ct. 489, 493 n.4 (1975).