MANCHESTER, N.H. — Half a million New Hampshire voters will pour into their polling places on Tuesday, many of them slogging through snow banks and wobbling across ice to get there, in the first primary election of the 2016 presidential campaign.
It is a state built for surprises: a famously independent-minded political battleground, where new voters can register to cast ballots on the day of the election and people unaffiliated with either party can vote in primaries.
Winning New Hampshire, or at least doing well, is such a strategic prize that candidates and “super PACs” have plastered the state’s television screens with more than $80 million in ads and turned its rambling two-lane highways into an endless procession of caravans.
There are few certainties in New Hampshire politics, but for most of the 2016 campaign there have been two: Donald J. Trump has led in statewide polls on the Republican side, and Senator Bernie Sanders of Vermont has led on the Democratic side.
Everything else looks like a big question mark.
A decisive victory by Mr. Trump could restore his momentum after his deflating second-place showing in the Iowa caucuses last week.
Senator Marco Rubio of Florida was poised to do well, possibly finishing second, but his floundering performance in Saturday’s debate might have scrambled the Republican field. In a CNN/WMUR poll released Monday, more than half of Republican voters said they still had not made up their minds.
Among Democrats, Mr. Sanders’s lead over Hillary Clinton here has fluctuated widely, but a Clinton victory would be a staggering upset. She continues to lead in nationwide polling and will be looking for stronger showings as the campaign moves on to other states.
With the race here up in the air, here is a quick guide to what to look for:
The Unpredictable Independents
New Hampshire has an unusual system that allows voters who are not affiliated with a party to cast a ballot in either primary. Under the state’s rules, an independent can basically choose to become a member of a party for just long enough to vote, and then re-register as an independent as soon as they are finished.
The independents here are not some small cluster of voters in the middle of the electorate. They are a big, heterogeneous and potentially decisive bloc.
In the 2012 Republican presidential primary, nearly half the voters were unaffiliated with a party, according to exit polls. Ron Paul, the libertarian-leaning former Texas congressman, tied Mitt Romney with this group.
And in 2008, the last time both parties had competitive primaries, exit polls showed 44 percent of the Democratic primary electorate was independent voters, compared with about a third on the Republican side. Barack Obama beat Mrs. Clinton among independents, despite losing the state over all by a narrow margin.
The more mainstream candidates on both sides end up competing across party lines for this crowd: A moderate voter who votes for Mrs. Clinton in the Democratic primary, for instance, may be a vote taken away from Gov. John R. Kasich of Ohio on the Republican side.
New Hampshire is a high-turnout state in general, and the primary is a normal election, rather than an arcane process like the Iowa caucuses. Campaigns don’t have to work as hard to drag their supporters to the polls.
Bill Gardner, New Hampshire’s secretary of state, has predicted record turnout for Tuesday’s election, forecasting a total of 550,000 votes cast, about 25,000 more than in 2008.
Compared with Iowa, that’s a huge turnout: Iowa Republicans cast about 187,000 votes last week, in a state of about three million people. Mr. Gardner predicted about 282,000 votes in the Republican primary in New Hampshire, a state with less than half of Iowa’s population.
But a campaign that lacks a well-organized operation to communicate with voters and turn them out might still leave a decisive sliver of votes on the table. That is more likely to matter on the Republican side, where four or five candidates are competing closely for second place and below.
New Hampshire’s population is overwhelmingly concentrated at the bottom end of the state, within an hour or so of the border with Massachusetts.
When Mrs. Clinton competed here in 2008, the decisive counties in her victory were three in the southeast corner of the state: Hillsborough, where Manchester and Nashua are located; Rockingham, including the coastal city of Portsmouth; and Strafford.
Watch the state’s more rural western border with Vermont for evidence of Mr. Sanders’s home-field advantage. The last time a Vermont candidate ran in a Democratic primary here was 2004, when Howard Dean lost to John Kerry. But even in losing, Mr. Dean handily won three counties along the Vermont border: Grafton, Sullivan and Cheshire.
The Republican map is likely to be more muddled, but watch Hillsborough and Rockingham — home to more densely settled, conservative-leaning suburbs — for evidence of which mainstream Republican might pose the greatest threat to Mr. Trump.
The Delegate Math
There are relatively few delegates up for grabs here. Each party requires a presidential candidate to amass well over a thousand delegates to clinch the nomination. In New Hampshire, there are just 23 at stake on the Republican side, and 32 for the Democrats.
New Hampshire awards more to candidates in the form of momentum. Traditionally, candidates must perform well in the early primary states to show voters and political donors across the country that they have a message and a political organization capable of winning elections.
On the Republican side, especially, the state is likely to play an important role in determining which of Mr. Trump’s opponents is best positioned to challenge him in the Southern primaries coming this month and in early March.
Polling stations typically close at 7 p.m., though it can vary; in Nashua, for instance, voting goes on until 8. And in the tiny towns of Dixville Notch, Hart’s Location and Millsfield, voting began at 12 a.m. Tuesday and was over in minutes. (Mr. Sanders got a total of 17 votes, to Mrs. Clinton’s nine; Mr. Trump, Mr. Kasich and Senator Ted Cruz led the Republican field with nine votes each.)
In 2012, the Republican primary here was called for Mr. Romney almost immediately after polls closed. But a closer contest could take much longer: In 2008, when Mrs. Clinton defeated Mr. Obama here, The Associated Press did not declare her the winner until around 10:30 p.m.
What Falls From the Sky
The candidates were already slogging through the snow on Monday, and an afternoon storm warning from the National Weather Service predicted a total accumulation overnight of 5 to 8 inches, with the heaviest buildup along the coast.
Conventional wisdom states that candidates with more casually committed supporters would suffer most in extreme weather. Beyond that, it’s hard to game out the consequences.
Does it hurt Mr. Sanders, whose supporters are younger and in many cases newer to the political process, or Mrs. Clinton, who has not seemed to inspire revolutionary zeal in her voters?
Is the snow more likely to undermine Mr. Rubio, whose support has been fluid after the Iowa caucuses and Saturday’s debate, or Mr. Trump, whose fans may like watching him perform on television more than they enjoy driving through the snow?
It’s just unpredictable. That’s why they have to hold an election.