At a regularly scheduled conference on Thursday, the Court will decide whether to grant full review of the case, Shew v. Malloy, which challenges Connecticut laws enacted after the 2012 massacre at Sandy Hook Elementary School in Newtown, Conn. The shooter in that attack, mainly using an AR-15, murdered 20 children and six educators. (An AR-15 was also used in December’s terror-motivated shootings at the Inland Regional Center in San Bernardino, Calif., which killed 14 people. And it was one of three weapons used at the Aurora, Colo. movie theater shooting in July 2012, which killed 12 people.)

Last October, the U.S. Court of Appeals for the Second Circuit upheld the Connecticut laws, which also ban the use of large capacity magazines. In the Sandy Hook massacre, the shooter used multiple 30-round magazines—which can be very quickly detached and replaced when using an assault-style rifle. The Sandy Hook shooter fired 154 rounds in less than five minutes.

The laws are being challenged by three gun-rights organizations, the Connecticut Citizens’ Defense League, the Coalition of Connecticut Sportsman, and MD (as in Maryland) Shooting Sports. The groups argue that the Second Amendment’s “right to bear arms” either flatly prohibits the ban or that the appeals court used too lax a standard in approving these particular bans. The groups claim that the bans in question focus on too broad a spectrum of weapons and accessories, and that those products can be, and for the most part are, used lawfully. Connecticut is one of seven states that currently bans assault-style weapons.

The betting money is that the Court will not take the case.

“The most likely outcome is denial [of review],” says Andrew Pincus, a Supreme Court practitioner at Mayer Brown, “as these issues continue to percolate through the lower courts.

The Court has batted away several attempts to clarify Second Amendment issues since it established in 2008 that the amendment does, indeed, protect individuals’ rights to own guns (as opposed to their right to possess them as part of a community’s “militia”) and, in 2010, that the right binds not merely the federal government, but state governments as well.

Both of those cases, District of Columbia v. Heller and McDonald v. City of Chicago, were decided by bare 5-4 margins. In each case, Justice Antonin Scalia wrote the majority opinion, and the rest of the Court voted along familiar ideological lines.

Scalia’s death in February and the Senate’s stated determination not to replace him before the November presidential elections leaves the Court evenly split on most Second Amendment issues, which makes it even less likely that the Court would choose to take the Shew case.

Still, the lack of guidance from the Court on these matters is becoming an increasingly pressing matter. While Heller and McDonald made clear that state and federal governments can’t outlaw the possession of handguns for self-defense in the home, they also permit certain reasonable regulations, making it unclear just how far legislators can go.

Since those two cases were decided, two appeals court panels, based in the District of Columbia and Chicago, have upheld assault-style weapons bans, though with slightly different reasoning. A third panel, based in Baltimore, struck a ban down in February. In the last instance, however, the full appeals court for the relevant circuit (the Fourth) has vacated the panel’s decision and agreed to rehear the case, eliminating the circuit split for now. The National Law Journal‘s Marcia Coyle wrote a thorough analysis on this matter.

The AR-15 was originally designed by Armalite as a military weapon. Its military version, with a fully automatic setting—meaning that you can use it like a machine gun—is the M-16. Civilian versions of the AR-15, with only semi-automatic capability, are are now made by many manufacturers, including Colt and Bushmaster.

The various AR-15s are now, according to the gun-rights groups’ briefs, “the best-selling rifle type in the United States.”

Many gun enthusiasts, including the groups bringing the challenge to the Connecticut laws, object to the use of the term “assault rifle” when referring to any weapons other than fully automatic, military ones, like the AK-47, M-16, or the later generation M-4. These groups also argue that the term “assault weapon” is a political creation, and that the definition is arbitrary and too broad.

Nevertheless, even in its civilian, semi-automatic form, the AR-15 allows a shooter to fire single shots in rapid succession (about three rounds per second), and it fires small caliber bullets at unusually high velocity (more than 3,000 feet-per-second, compared to 750-1,400 feet-per-second for most handguns) making it light, easy to aim, and extraordinarily lethal. In the wrong hands, and equipped with high-capacity magazines, it confers enormous might.

The state of Connecticut’s attorneys, defending the assault-style weapons ban, argue that while such weapons amount to just 1% of firearms held by civilians, they “account for up to 6% of murders, up to 16% of killings of law enforcement officers, and 42% of mass public shootings.”

The gun-rights groups contest these figures and assert that handguns account for 71% to 83% of the firearms used in murders, and 84% to 90% of firearms used in other violent crimes.

The Supreme Court could issue an order as early as next Monday on whether it will give a full hearing to the Shew case. If it declines to review the case, the Second Circuit’s ruling will become binding for the states it covers—New York, Connecticut, and Vermont—but not for states covered by other circuits.