This appeal is successive to last year’s decision that the district court abused its discretion by certifying nationwide classes covering multiple models of Ford vehicles and Firestone tires sold between 1990 and 2001. See In re Bridgestone/Firestone, Inc., Tires Products Liability Litigation, 288 F.3d 1012 (7th Cir. 2002), cert. denied, 537 U.S. 1105, 123 S.Ct. 870, 154 L.Ed.2d 774 (2003). Classes comprising owners of more than 60 million tires and 3 million vehicles, including many different models, are unsuitable for several reasons, we concluded — not the least of which is that different rules of law govern different members of the class. The district court thought that Indiana’s choice-of-law doctrines select a single state’s law to govern each kind of product; we disagreed with this conclusion and held that Indiana would apply the law of the state where the injury occurred. A need to apply multiple states’ laws was among the considerations that rendered certification of nationwide classes improvident, we held.

After the Supreme Court denied class counsel’s petition for certiorari, lawyers representing the plaintiffs decided to try again, in other courts. Class suits have been filed in many jurisdictions; in at least five suits, plaintiffs seek certification of the same nationwide classes that our opinion nixes. One state judge certified a nationwide class on the day complaint was filed, without awaiting a response from the defendants and without giving reasons. Ford and Firestone asked the district judge to enforce our decision by enjoining other class actions — not just other efforts to launch nationwide classes, but any class action, even one limited to a single product in a single state. The district court denied this motion, and the defendants immediately appealed on the authority of 28 U.S.C. § 1292(a)(1).

Throughout this litigation, both sides have gravitated to the extremes. Plaintiffs’ lawyers sought nationwide classes that depended on an implausible uniformity of both law and fact, grinding down all differences among the buyers and the products to make a mega-class manageable. Defendants replied by extolling the virtues of federalism and the wisdom of allowing each state a free hand to resolve these disputes. Once we disappointed the plaintiffs’ ambitions, however, the litigants began to sing each other’s songs. Today the plaintiffs celebrate federalism and trumpet the acumen of state judges in handling complex litigation, while defendants seek a uniform outcome, which would forbid any state court to entertain any class action of any kind concerning these products. Plaintiffs were off the mark the first time, and defendants are off the mark now — though neither side has been wholly right, then or now.

The Anti-Injunction Act, 28 U.S.C. § 2283, forbids any federal injunction or stay of state litigation “except as expressly authorized by Act of Congress, or where necessary in aid of its jurisdiction, or to protect or effectuate its judgments.” Defendants contend that an anti-class-action injunction is necessary to carry out our *766decision of last year. Yet the only classes that had been certified had national scope, and the only judgment that could be protected or effectuated is one concerning such classes. (The first appeal did produce a “judgment”; courts of appeals, like district courts, enter judgments, see Fed.R.App. P. 36, and § 2283 refers to all “judgments” rather than just “final judgments.”) The district court had not certified, and our opinion thus did not address, any statewide class. Although we suggested that even a single-state class covering multiple models of tire or SUV would be unmanageable and inferior to supervision by the National Highway Transportation Safety Administration, see 288 F.3d at 1018-21, this assessment did not become part of our judgment. State courts are free to decide for themselves how much effort to invest in creating subclasses (so that each model of tire or SUV receives appropriate consideration); advice designed to ward off what a federal court deems an unproductive investment of judicial time does not create a “judgment” that forbids any state tribunal to make the effort. Indeed, our opinion contemplated that states would certify narrower classes; we gave, as an example, “1995 Explorers in Arizona equipped with a particular tire specification”, id. at 1020. So the district court properly denied Ford’s request , for an injunction that would preclude any class suit in any state court. Each state may apply its own choice-of-law rules (and its own substantive law, if otherwise appropriate) in a way that a federal court, trying to apply nationally homogenized law, could not.

What we did hold is that a class covering owners in every state may not be certified over the defendants’ opposition. (We did not consider the possibility of settlement classes, which pose different issues. See Amchem Products, Inc. v. Windsor, 521 U.S. 591, 117 S.Ct. 2231, 138 L.Ed.2d 689 (1997); In re Mexico Money Transfer Litigation, 267 F.3d 743, 746-47 (7th Cir. 2001).) This holding is the basis of our judgment reversing the district court’s order certifying nationwide classes. The Anti-Injunction Act permits a federal court to protect and effectuate that judgment by equitable relief. Normally the second court determines the preclusive effect of a judgment, see Maintenance of Way Employees v. Burlington Northern R.R., 24 F.3d 937, 940 (7th Cir. 1994), so the appropriate course is to deny a request for an anti-suit injunction even when § 2283 does not itself close the door. But when federal litigation is followed by many duplicative state suits, it is sensible to handle the preclusive issue once and for all in the original case, rather than put the parties and state judges through an unproductive exercise. That these suits are multiplying suggests that some lawyers have adopted a strategy of fifing in as many courts as necessary until a nationwide class comes into being and persists. (We assume that the ex parte certification already mentioned ultimately will be vacated as an obvious violation of procedural requirements.)

Relitigation can turn even an unlikely outcome into reality. Suppose that every state in the nation would as a matter of first principles deem inappropriate a nationwide class covering these claims and products. What this might mean in practice is1 something like “9 of 10 judges in every state would rule against certifying a nationwide class” (in the federal courts, it has meant that 3 of 4 judges have ruled against the proposed nationwide classes). Although the 10% that see things otherwise are a distinct minority, one is bound to turn up if plaintiffs file enough suits— and, if one nationwide class is certified, then all the no-certification decisions fade into insignificance. A single positive *767trumps all the negatives. Even if just one judge in ten believes that a nationwide class is lawful, then if the plaintiffs file in ten different states the probability that at least one will certify a nationwide class is 65% (0.910 = 0.349). Fifing in 20 states produces an 88% probability of national class certification (0.920 = 0.122). This happens whenever plaintiffs can roll the dice as many times as they please — when nationwide class certification sticks (because it subsumes all other suits) while a no-certification decision has no enduring effect. Section 2288 permits a federal court to issue an injunction that will stop such a process in its tracks and hold both sides to a fully litigated outcome, rather than perpetuating an asymmetric system in which class counsel can win but never lose.

Nonetheless, class counsel tells us, the legal system entitles them to the benefit of this heads-I-win, tails-you-lose situation. This is so, class counsel contend, for three principal reasons: first, this federal action has not produced a final judgment; second, states may employ their own rules of preclusion; third, the federal court lacks personal jurisdiction over state-court plaintiffs who did not participate in the federal proceeding. None of these arguments is sound.

Although claim preclusion (res judicata) depends on a final judgment, issue preclusion (collateral estoppel) does not.

The rules of res judicata are applicable only when a final judgment is rendered. However, for purposes of issue preclusion (as distinguished from merger and bar), “final judgment” includes any prior adjudication of an issue in another action that is determined to be sufficiently firm to be accorded conclusive effect.

Restatement (Second) of Judgments § 13 (1980). Our decision that no nationwide class is tenable is “sufficiently firm” for this purpose. It was the result of focused attention by counsel in both the district court and this court; both courts addressed the issúe exhaustively in published opinions and brought the debate to a conclusion; certiorari was sought and denied. Class counsel filed a master complaint in the court assigned to resolve pretrial matters in this multidistrict litigation, precisely so that a single disposition could be reached that would cover all suits, no matter where they had originally been filed. Because the decision stemmed from a complaint filed in the Southern District of Indiana, Lexecon Inc. v. Milberg Weiss Bershad Hynes & Lerach, 523 U.S. 26, 118 S.Ct. 956, 140 L.Ed.2d 62 (1998), has no bearing; the district court had original jurisdiction and was not acting as a transferee court under 28 U.S.C. § 1407 with respect to this complaint. Having sought and obtained a decision on the master complaint, class counsel are in no position to treat the resolution as irrelevant and start anew. Cf. In re Rhone-Poulenc Rorer, Inc., 51 F.3d 1293, 1299-1300 (7th Cir. 1995).

The preclusive effect of a judgment rendered by a federal court depends on national rather than state law. Semtek Int'l Inc. v. Lockheed Martin Corp., 531 U.S. 497, 121 S.Ct. 1021, 149 L.Ed.2d 32 (2001). Although Semtek adds that federal law usually incorporates state law when the federal judgment stems from litigation under the diversity jurisdiction, this does not assist class counsel: the master complaint included two claims under federal law. What is more, the norm stated in Semtek has a proviso: state rules that undermine the finality of federal judgments are not incorporated. To the extent plaintiffs want to urge state courts to disregard our judgment on the ground that it was not final, but “merely” resolved one *768contested issue, that course is cut off by Semtek’s proviso; it is incompatible with federal law for states to ignore federal interlocutory judgments as class counsel propose. Nothing in Baker v. General Motors Corp., 522 U.S. 222, 118 S.Ct. 657, 139 L.Ed.2d 580 (1998), on which class counsel heavily rely, undermines this conclusion. Baker holds that one state court’s decision about a procedural issue need not bind another, state court. It does not discuss the effect of federal judgments under the federal law of preclusion. And the sort of procedural issue at stake in Baker — who may give evidence, and under what restrictions — is very different from a ruling on class certification, which determines the identity of the parties and stakes of the case. Determining the permissible scope of litigation is as much substantive as it is procedural. Our judgment was based not simply on a belief that managing national classes would consume too much of a federal court’s limited supply of time; it also was based on a conclusion that certification of national classes would compromise the legitimate interests of defendants. Baker thus has no bearing on the preclusive effect (in state court) of rulings about class status made by a federal court.

Class counsel’s jurisdictional argument starts from the premise that only named class representatives, and not members of putative classes, are treated as parties to litigation. Unnamed class members cannot be brought in involuntarily, class counsel insist, because federal courts lack the authority to issue process nationwide. As a result, class members other than the named representatives cannot be bound by an adverse decision and are free to file their own class actions elsewhere. The proposition that the federal court lacks the power to issue nationwide process must be qualified by the proviso “unless a federal statute authorizes this step”; and one of the claims in the master complaint rested on RICO, which does authorize nationwide service of process. See 18 U.S.C. § 1965(b); Lisak v. Mercantile Bancorp, Inc., 834 F.2d 668, 671 (7th Cir. 1987). What is more, unnamed class members have the status of parties for many purposes and are bound by the decision whether or not the court otherwise would have had personal jurisdiction over them. See Phillips Petroleum Co. v. Shutts, 472 U.S. 797, 105 S.Ct. 2965, 86 L.Ed.2d 628 (1985). Just as they receive the fruits of victory, so an adverse decision is conclusive against them. See Williams v. General Electric Capital Auto Lease, Inc., 159 F.3d 266 (7th Cir. 1998) (district court may enjoin state-court suit brought by absent class member). Devlin v. Scardelletti, 536 U.S. 1, 122 S.Ct. 2005, 153 L.Ed.2d 27 (2002), holds that unnamed class members are entitled to appeal or seek certiorari without intervening; any would-be member of the class could have sought certiorari from our adverse decision. The premise of allowing class members to seek review by a higher court is that otherwise they would be bound by defeat. District courts with authority over the original class claim may issue writs under 28 U.S.C. § 1651 in aid of that jurisdiction. See Williams and Winkler v. Eli Lilly & Co., 101 F.3d 1196 (7th Cir. 1996). They do not need a separate grant of subject-matter jurisdiction. See also Syngenta Crop Protection, Inc. v. Henson, 537 U.S. 28, 123 S.Ct. 366, 154 L.Ed.2d 368 (2002) (although § 1651 does not create federal jurisdiction, district courts may issue writs ancillary to cases over which they otherwise have original jurisdiction).

A decision with respect to the class is conclusive only if the absent members were adequately represented by the named litigants and class counsel. That *769requirement has been met. The district court found that both the named plaintiffs and their lawyers furnished adequate representation to the other members of the putative classes. 205 F.R.D. 503, 518-19 (S.D.Ind. 2001). That decision was not challenged on the first appeal and is not contested now. Holding the absent class members to the outcome is no more an exercise in virtual representation than it is to hold them to a decision on the merits. “Virtual representation,” a doctrine that we disapproved in Tice v. American Airlines, Inc., 162 F.3d 966 (7th Cir. 1998), would permit the outcome of one non-class suit to control another if the plaintiffs are similarly situated; Tice holds, to the contrary, that, outside the domain of class actions, precedent rather than preclusion is the way one case influences another. Our suit, by contrast, was commenced as a class action, and oné vital issue was litigated and resolved on a class-wide basis: whether a national class is tenable. Absent class members are bound provided that the named representatives and their lawyers furnished adequate representation, which they did.

True, the district court did not offer unnamed class members an opportunity to opt out of the certification decision. Plaintiffs now contend that this is fatal to any invocation of preclusion. Yet no statute or rule requires notice, and an opportunity to opt out, before the certification decision is made; it is a post-certification step. See Fed.R.Civ.P. 23(c)(2). No one is entitled to opt out of the certification, a decision necessarily made on a class-wide, all-or-rione basis; one opts out of a certified class. And a person who opts out receives the right to go it alone, not to launch a competing class action. Preserving the right to litigate individually, as one’s own champion, is the point of opting out. The opt-out avoids any risk of the class’s loss on the merits and also forswears any opportunity to take advantage of the class’s victory. See Premier Electrical Construction Co. v. National Electrical Contractors Ass’n, Inc., 814 F.2d 358 (7th Cir. 1987). Every person included in the district court’s class definition still has the right to proceed on his own. What such a person now lacks is the right to represent a national class of others similarly situated; that’s the upshot of a fully contested litigation in which every potential class member was adequately represented on this issue.

Our prior judgment is binding in per-sonam with respect to the unnamed class members. The district judge must enforce that judgment by issuing an injunction that prevents all members of the putative national classes, and their lawyers, from again attempting to have nationwide classes certified over defendants’ opposition with respect to the same claims. The case is remanded for the entry of such an injunction. To the extent defendants seek broader relief, however, the district court’s decision is affirmed.