The White House’s address may be 1600 Pennsylvania Avenue, but the real road to the presidency runs through the state of Pennsylvania, the biggest prize among the electoral battleground map.

According to calculations by elections analyst Nate Silver, the candidate who wins Pennsylvania has more than a 90% of winning the White House.

“It’s the granddaddy of all the swing states,” said former Congressman Patrick Murphy, who represented a northeastern Pennsylvania as a Democrat from 2007 to 2011.

With its 19 electoral votes, Pennsylvania – the fifth most populous US state – is the lynchpin of the swing-state electoral firewalls for both Kamala Harris and Donald Trump.

If the Democrats win Pennsylvania, Wisconsin and Michigan, along with one congressional district in Nebraska, she’s the next president. If the Republicans carry Pennsylvania, North Carolina and Georgia, Trump is back in the White House next year.

Without Pennsylvania, there is no way Trump can win without flipping at least three of the states Joe Biden won in 2020.

Nicknamed the Keystone State, Pennsylvania could in fact be the key to the White House.

Pennsylvania is not only the most valuable swing state, it also can be seen as a microcosm of the US as a whole – demographically, economically and politically.

It is a former manufacturing state that has been transitioning to newer industries and businesses, but it has a large energy sector because of its abundant oil shale deposits. Agriculture is still the second-largest industry in the state.

The majority of the population is white, but there are growing immigrant communities. Some areas, like Allentown – the working-class factory city made famous by a Billy Joel song – are now majority Hispanic. The state’s black population, at 12%, is just under the US total of 13%.

As for the politics, the state’s two large urban areas, Philadelphia and Pittsburgh, heavily favour the Democrats. Between the two are vast stretches of rural territory where Republicans dominate. And the suburb that once were reliably conservative are now tilting to the left.

That gives rise to the old quip that Pennsylvania is Philadelphia and Pittsburgh with (deeply Republican) Alabama in the middle.

Somehow, all these political cross-currents and shifting dynamics have kept Pennsylvania at a near dead-even balance when it comes to presidential elections. President Joe Biden won the state by about 80,000 votes in 2020. Donald Trump carried it by about 40,000 in his surprise 2016 win over Hillary Clinton.

Only once in the last 40 years has a candidate won Pennsylvania by double-digits – Barack Obama in his 2008 electoral landslide.

Current polling puts the race between Harris and Trump in the state at a virtual dead heat. According to the 538/ABC News poll tracker, Harris holds a lead by less than a percent – a margin that has hardly shifted over the course of this tumultuous political year.

Both the Harris and Trump campaigns have been pouring enormous resources into Pennsylvania. They are spending more on television advertising there than any other swing state. Both candidates make regular visits.

Harris introduced her running mate pick, Tim Walz, at a rally in Philadelphia. She spent days preparing for her presidential debate in Pittsburgh. She made a tentpole economic speech there two weeks ago.

Last Saturday, Trump held a massive rally in Butler, where in July he was nearly assassinated. On Wednesday he was in Biden’s hometown of Scranton and Reading.

And when the principals aren’t around, both campaigns have other politicians and officials to drum up support.

“A candidate can’t go into a county to talk to 1,200 people,” says former Democratic Pennsylvania Governor Ed Rendell. “The state is too big. There’s just not time. That’s what surrogates are for.”

Rendell notes that the current governor, Democrat Josh Shapiro, is a big help for Democrats here, as he is very popular in the state and a dynamic speaker – qualities that had made him the odds-on favourite to be Harris’s vice-presidential pick.

For Harris, her keys to victory are to post dominating numbers in Philadelphia and Pittsburgh and win the suburbs by enough to offset Trump’s margins in the rest of the state.

An essential part of this strategy is to win over moderate voters and some Republicans – including the more than 160,000 who turned out to vote for former South Carolina Governor Nikki Haley in the state’s Republican primary, held earlier this year, well after Trump had already locked up the party’s nomination.

“What these people need to hear is ways in which both the past record of Kamala Harris and the future plans of Kamala Harris are basically centrist positions – that she is not this crazy, wild-eyed radical leftist,” said Craig Snyder, former Republican Senate staffer who is running Pennsylvania’s “Haley Voters for Harris” effort.

He added that the Harris campaign is making the most extensive effort to reach Republican voters that he’s seen in a generation.

Trump’s strategy is to squeeze all the support he can out of the conservative parts of the state, including by registering and mobilising those who may not have participated in past elections – a move Trump’s campaign officials say is a central focus of their grass-roots effort.

There are signs their work may be paying off, too. Registered Democrats still outnumber Republicans in the state, but the margin is just a few hundred thousand – the smallest its been since the state first began releasing figures in 1998.

While the college-educated voters in the suburbs may be difficult to convince, the Trump team thinks it can also chip away at traditionally Democratic support among blue-collar union voters and young black men.

“We’ve seen nationally that Trump has made some real inroads with African American men,” said Farah Jimenez, a conservative education activist. “They’re here in Philadelphia, and if you can convince them that he speaks more clearly to the things that concern them, it can at least start to provide a base for Republicans in Philadelphia.”

• the BBC’s flagship political debate programme heads to Pennsylvania on Thursday, 10 October
• it will be recorded at the National Constitution Center in Philadelphia, presented by Fiona Bruce and featuring a local audience
• panel will include the BBC’s Anthony Zurcher, former Trump campaign adviser Bryan Lanza and commentator Mehdi Hasan
• will be streamed on BBC website from 16:00 EST (21:00 BST)
• UK audiences can also watch on BBC One and iPlayer, global audiences on the BBC News channel

Four years ago, the results in Pennsylvania took days to come in – due, in large part, to the more than two million mail-in ballots cast because of the Covid pandemic. Major media outlets didn’t project Biden as the winner until four days after the election.

Mail-in voting is expected to be lower this year, but the state reports that it has already received 217,000 completed ballots that, by Pennsylvania law, cannot be opened and tabulated until election night.

Another wildcard is the more than 27,000 military and overseas voter ballots that have been distributed by Pennsylvania state officials so far. If the race is as close as polls indicate, those votes could make a difference – even if they take longer to arrive and be recorded.

“I can’t imagine that it’s not going to take several days after to get a count,” said Snyder. “And if the count is very close, we’re going to get into lawsuits and recounts and all the rest of it. So everybody needs to buckle up.”

North America correspondent Anthony Zurcher makes sense of the race for the White House in his twice weekly US Election Unspun newsletter. Readers in the UK can sign up here. Those outside the UK can sign up here.