On June 5, 1994, there was a confrontation involving guns between the defendant and Ludwin Midence (known as “Chino”) at the Carter Playground in the South End section of Boston. Vilma Flores, a bystander, was shot in the neck and died. The defendant admitted to firing his handgun three or four times; he testified that he shot in the direction of Chino. In brief, the defendant was charged with murder and other crimes (see note 1, infra), and Chino was charged with manslaughter *763and with armed assault with intent to murder the defendant, along with other crimes. Chino pleaded guilty to the charges against him.
We recapitulate the extended prior history of this case in the margin.1 Upon retrial in the Juvenile Court, the defendant was found guilty of murder in the second degree, and he now appeals, making the arguments discussed below.
At the first trial, see note 1, supra, the Commonwealth argued that the defendant fired the shot that killed Flores. At the second trial the Commonwealth offered two theories: (1) that the defendant fired the fatal shot, and (2) that the defendant was guilty of murder because he was engaged in a “shootout” with Chino, as a consequence of which Flores was shot dead.
The second theory was the product of Santiago II, 425 Mass. 491, 503-504 (1997). See note 1, supra. There the defendant claimed that he should not be found guilty as matter of law because the Commonwealth had failed to prove that he fired the *764fatal shot. The court acknowledged that “the evidence at the trial [regarding the identity of the shooter of the bullet that killed Flores] was far from overwhelming. There was no conclusive forensic evidence and the Commonwealth’s case was based solely on the position of the victim . . . relative to the shooters.” Id. at 502.
The court nevertheless held that, “where the defendant chooses to engage in a gun battle with another with the intent to kill or do grievous bodily harm and a third party is killed, the defendant may be held liable for the homicide even if it was the defendant’s opponent who fired the fatal shot.” Id. at 503. The court elaborated: “The defendant’s acts need not be the sole or exclusive cause of death. ... By choosing to engage in a shootout, a defendant may be the cause of a shooting by either side because the death of a bystander is a natural result of a shootout, and the shootout could not occur without participation from both sides.” Id. at 504. The court concluded that the Commonwealth’s inability to prove who fired the fatal shot would not provide the basis for a directed verdict. Id. at 503.
Of special significance for the purpose of this case is footnote 5 of the court’s opinion, which we quote in full: “There is no bar to the Commonwealth’s proceeding at retrial on this theory. See Commonwealth v. Arsenault, 361 Mass. 287, 298 (1972) (‘The Commonwealth made no binding agreement or stipulation locking itself into the theory of the first trial’).” Santiago II, 425 Mass. at 503 n.5.
Discussion. The defendant argues that the due process clause of the Fourteenth Amendment protected the defendant’s “justifiable reliance” at the second trial on the Commonwealth’s theory at the first trial — that it was the defendant who fired the fatal shot. More particularly, the defendant argues that the introduction at the second trial of the new theory outlined and suggested in Santiago II, 425 Mass. at 503 & n.5, “deprived the defendant of due process,” because “when [the judge] instructed on the alternative theory of the defendant engaging in a shootout conviction became a certainty.” The defendant offers no decisions in support of this position, and the argument is not entirely clear. Putting that to one side, it is enough to say that this court is not free to disregard the plain instructions from the Supreme Judicial Court regarding the retrial, supported by the unequivocal statement from Commonwealth v. Arsenault, 361 Mass. at 298, quoted in Santiago II, 425 Mass. at 503 n.5. The defendant *765made a timely objection to the introduction of the Commonwealth’s second theory, and his rights appear to be preserved for further review.
The defendant’s second argument is quite clear. The judge denied the request of the defendant to introduce the record of the guilty pleas of Chino to armed assault with intent to murder the defendant and to manslaughter of Flores. The defendant, citing art. 12 of the Massachusetts Declaration of Rights (“And every subject shall have a right to produce all proofs, that may be favorable to him”), argued at trial, and here, that the proffer was material to the defendant’s claim of self-defense.
There was no error. “|l]n a criminal case the record of conviction or acquittal in another case to which the defendant was not a party is not admissible to establish the truth of any fact involved in such conviction or acquittal.” Commonwealth v. Tilley, 327 Mass. 540, 548 (1951). See Commonwealth v. Robles, 423 Mass. 62, 69 (1996). In Santiago II, 425 Mass. at 504, the court considered the question pressed by the defendant and decided that “[t]he admission of the convictions is within the discretion of the judge on retrial, although the defendant’s contentions lose much of their force if the Commonwealth adopts the alternative theory open to it.”
The Tilley rule is well established in this Commonwealth. It has been applied in cases involving coconspirators, see Commonwealth v. Cerveny, 387 Mass. 280, 285-286 (1982) (holding that the acquittal of one coconspirator in a separate trial does not preclude the subsequent conviction of the other coconspirator), and cases involving joint venturers, see Commonwealth v. Jones, 403 Mass. 279, 290 (1988) (the acquittal of a joint venturer “does not insulate the defendant from being found guilty as a joint venturer. There is nothing inconsistent between one jury’s finding that there was insufficient evidence to prove [the joint venturer’s] guilt beyond a reasonable doubt, and another jury’s finding, in a separate trial, that there was sufficient evidence to prove the defendant’s guilt to that degree of certainty”).
Whatever it was that persuaded Chino to plead guilty and the judge to accept that plea has no bearing on the jury’s verdict in this case. As stated in Santiago II, 425 Mass. at 504-505, the admission of a guilty plea has little value “because the plea is often the result of bargaining with the prosecutor and is not necessarily the equivalent of an admission of full guilt for the *766act alleged. Where the defendant is seeking to introduce the evidence, its introduction might be required if it were critical to the determination of guilt or innocence, such as where another individual has pleaded guilty or been adjudged guilty of the same act for which the defendant is charged, and there is no theory of joint involvement available. ... In this case, . . . there is no inconsistency in finding both shooters criminally responsible for this victim’s death. As to the [conviction of] assault with intent to kill [the defendant,] there was no contention by the prosecutor that the other shooter was acting in ... [a] lawful manner. The case proceeded on the theory that both shooters were trying to kill each other.”
The defendant’s argument, based on an exception to the hearsay rule, does not meet the central point that the guilty plea by Chino in his separate trial has no relevance to the defendant’s trial. The judge acted within his discretion in refusing to admit the record of Chino’s convictions.
The defendant’s third and final argument is that the judge should have declared a mistrial when it was discovered that certain extraneous matter — one juror’s exposure to the fact that the defendant had previously been convicted — had found its way into the jury room.
The judge immediately conducted an individual voir dire of each juror. See Commonwealth v. Kamara, 422 Mass. 614, 616-618 (1996). The judge concluded that only one juror (#3) had become aware of the defendant’s prior conviction, and each of the remaining jurors testified under oath as to their continuing ability to remain fair and impartial. Juror #3 stated to the judge, “I don’t feel like I heard anything different than what I’ve already heard.” The defendant moved for a mistrial, but did not seek to have juror #3 removed from the panel. The judge denied the motion for a mistrial. There was no error.
Judgment affirmed.