An end to Republican presidential front-runner Donald Trump's candidacy? It could be within reach. Could be.

Trump's closest rival, Texas Senator Ted Cruz, celebrated his victory in the Wisconsin primary on Tuesday night as a "turning point" in the race for the nomination.

For pundits, two other words came to mind: brokered convention. That's when no candidate has enough delegates to win during the first round of voting.

Here's why that matters.

Good news for the establishment

It's not a sure thing. But a scenario that would involve wheeling and dealing for an alternative nominee looks more probable than ever so far this year, reviving arguments that a "Dump Trump" option remains viable.

Former Republican U.S. presidential nominee Mitt Romney pauses and smiles as he delivers a speech criticizing current Republican presidential candidate Donald Trump at the Hinckley Institute of Politics at the University of Utah. (Jim Urquhart/Reuters)

At the very least, the odds of Trump securing enough delegates to win a simple majority on the first ballot at the national convention in July have slimmed.

The Republican brass are hedging their bets on an open convention. If they get their way and neither Cruz nor Trump has a majority of delegates locked up before the end of primary season, "that's when that gambit gets dangerous," warns Steve Jarding, a public policy professor with Harvard's Kennedy School of Government.

A little on delegate math

There's a number that Republican candidates keep on referencing in their stump speeches: 1,237.

That's how many delegates any GOP candidate needs to nab 50 per cent, plus one, of the 2,472 delegates. In other words, a simple majority that would win the nomination outright.

Ted Cruz, shown greeting voters in Wisconsin, has called the concept of a contested convention a 'fever dream' of the Republican establishment. (Jim Young/Reuters)

Before the Wisconsin primary — in which Cruz added 36 delegates and Trump took six — Trump would have needed to win 61 per cent of all remaining delegates going forward. Even then, he was tracking to underperform in the West, according to political statisticians with the FiveThirtyEight blog.

With the Wisconsin loss behind him, the incline tilts steeper. Trump now needs to take 63 per cent of delegates in the states that have yet to vote in primaries or caucuses, according to updated number-crunching by the Washington Post.

How likely this scenario will play out

Delegate analysts agree that Cruz prevailing in Wisconsin has bumped the Republican Party closer to a contested convention. But they split on the degree to which that's likely.

A 2012 file photo shows Romney and his running mate Rep. Paul Ryan at the end of the Republican National Convention in Tampa, Fla. (Patrick Semansky/Associated Press)

Former Republican National Convention chief of staff Mike Shields told CNN it looks "very unlikely" that Trump will avoid such a scenario by meeting that 63-per-cent threshold.

Jarding is less certain.

"I don't think 63 per cent is out of the question," he says. "It's a little on the out range, a little at the high end, but the system is so prone to momentum."

If Trump racks up big delegate counts in the coming northeastern states, including his home state of New York on April 19, Jarding expects the momentum will swing back to Trump, quashing speculation of an open convention.

When a convention is 'brokered'

Both contested and brokered conventions qualify as "open" conventions, as both follow scenarios in which no candidate wins the nomination on the first ballot, forcing another round of voting.

Republican U.S. presidential candidate John Kasich has vowed to remain in the nomination race through to the July Republican National Convention. (Charles Mostoller/Reuters)

What drives a brokered convention, Jarding notes, is mediation and deal-making, which historically occurred in "smoke-filled rooms."

"You literally would go in the backroom and you try and cut some deals. So, for example, Marco Rubio could cut a deal and say: 'Put me on the ticket, and I'll swing my delegates to Ted Cruz,'" Jarding says.

The concept operates on the assumption that delegates will follow their chosen candidate's lead.

When a convention is 'contested'

Contested conventions involve releasing delegates after the first ballot, allowing them to become "free agents."

Candidates who have suspended their campaigns, like Marco Rubio, will be able to release their delegates at the Republican National Convention. (Carlo Allegri/Reuters)

"Although they were with you on the first ballot, without committing anybody, there are no guarantees they have to follow you [on the next ballot]," Jarding explains. "You effectively just open the thing wide."

Ohio Gov. John Kasich is keen to see either of the multi-ballot scenarios. Despite being pressured by Trump and Cruz to drop out and make it a two-man race, Kasich has vowed to stick it out until the national convention in Cleveland this July. He hopes multiple ballot calls will cause delegates to drift his way and give him the nomination.

"It's going to be so much fun," Kasich told ABC's This Week.

Why multi-ballot conventions are rare

If there's a secret ingredient for a multi-ballot convention, it's divisiveness.

That doesn't bode well for a party that has called for unity in order to defeat likely Democratic nominee Hillary Clinton in a general election come November.

Usually by the time the primary calendar winds down, the parties have a clear idea of who will emerge as their nominees, making conventions little more than what U.S. historian James Paterson called "scripted, anachronistic rituals."

Not so in this election cycle. As the Republican field winnowed during the primaries, a strong anti-establishment base has resisted backing candidates viewed as ideologically moderate insiders. No obvious delegate favourite has yet materialized.

The last time this happened

After 103 ballot calls, John W. Davis, former U.S. ambassador to the U.K., was chosen as a compromise candidate to be the Democratic presidential nominee during the 1924 Democratic National Convention. (U.S. Library of Congress)

Republicans were last forced into a brokered convention in 1948, when it took three ballots for the party to nominate former New York governor Thomas Dewey.

Nobody won the first ballot in the 1952 Democratic national convention either and it again took until the third ballot for delegates to coalesce behind then-Illinois governor Adlai Stevenson.

The nightmare scenario

The most contested convention was the infamous 1924 Democratic national convention, a 16-day contest that at times devolved into fistfights, obscenity-laced screaming and even a gathering of tens of thousands of Ku Klux Klan members, according to historical accounts.

After an absurd 103 ballots were called, the party finally settled on relative outsider John W. Davis, former U.S. ambassador to the U.K.

In this June 23, 1948, file photo, delegates with posters and state signs crowd down the centre aisle at Convention Hall in Philadelphia during a demonstration for Gov. Thomas E. Dewey after his name was placed in nomination during the Republican National Convention. (Associated Press)

The rowdy conclave was held in July at the old Madison Square Garden in New York City.

Davis was finally chosen as a compromise candidate to break a deadlock between the two front-runners: then-New York governor Al Smith, a Catholic who was despised by the KKK, and former treasury secretary William McAdoo, who was endorsed by them.

Davis was handily beaten in the general election by Republican candidate Calvin Coolidge.

What Republicans should worry about

Democratic U.S. presidential candidate Hillary Clinton waves as she speaks to supporters at a campaign rally in West Palm Beach, Fla., March 15, 2016. (Carlos Barria/Reuters)

As Jarding warned, the prospect of a brokered Republican convention this year is "dangerous" because it risks alienating a large voter base. "There has been no precedent for this level of rejection for the will of the people," he says.

Cruz has said he sees no problem with a contested convention allowing delegates to align themselves with whomever they wish if a first ballot goes undecided. But he slammed a brokered convention as "the fevered dream of the D.C. establishment," in which a party approves another candidate and "swoops in with their White Knight."

Unless Trump or Cruz becomes the nominee, the Texas senator warned "you would see an open revolt, and it would all but concede the election to Hillary Clinton."

Trump going forward

It's not the end of the road, though, not by a long stretch.

Five winner-take-all-states remain for the Republicans, giving Trump several opportunities to mount huge delegate totals. California is a big prize on June 7, with 172 Republicans delegates.

April 19 is another big day — the day of the New York primary — and Trump is expected to reap some big returns in his home state.