Where to Watch

An old rule in Montana politics — that the winner of a statewide election could be gleaned by watching who won Yellowstone County, home to Billings — has receded in recent years. But the county, Montana’s most populous, still merits a close eye. If Mr. Gianforte does not amass a significant margin of victory there, the race could prove competitive. Similarly, if Mr. Quist does not come out of Cascade County, where Great Falls sits, with a substantial advantage, it will be difficult for him to keep the contest close.

But the most important task for Mr. Quist in a special election where turnout is so crucial may be to drive up his margins in the two liberal-leaning counties that are home to Montana’s large state universities: Missoula and Gallatin.

A Libertarian in the Mix

As Montana Republicans know all too well, Libertarians here have a history of siphoning enough votes to hand statewide races to Democrats. And there is a Libertarian, Mark Wicks, on the ballot Thursday. While Democrats have not overtly tried to promote Mr. Wicks, as they have Libertarian candidates in previous elections, both parties acknowledge that he could capture about 5 percent of the vote — enough to make a difference.

Prepare for a Long Night

If we have piqued your curiosity about this race, here is a suggestion: Get some coffee. It’s going to be a long night. The polls close at 10 p.m. Eastern, and The Associated Press is often slow to make projections in Montana.

The race for governor in November was not called until 10 a.m. the next day, even though Steve Bullock, the Democrat, was re-elected by a fairly comfortable four-point margin. Similarly, the Democratic presidential primary wasn’t called until after 2 a.m.; Bernie Sanders ultimately won by seven points.

Why? It often takes a long time for Montana’s conservative and rural areas to report. It is also tricky because so many ballots are cast by mail. More than 250,000 have been returned already, a significant enough portion of the just over 699,000 registered voters in the state to potentially mitigate the effects of Mr. Gianforte’s assault charge. The substantial early vote will also make it harder to get a quick grasp on the race, since the mailed votes can differ from those cast on Election Day.