New York, New York.

The state in which Donald Trump started his real estate empire gave his Republican presidential nomination bid a much-needed boost on Tuesday.

A huge boost. One of the greatest boosts anyone has ever seen. You wouldn't believe how big of a boost it was.

Trump was expected to do well in his home state, leading Ohio Gov. John Kasich by about 30 points in the polls going into Tuesday's vote with an average of 53 per cent support, according to RealClearPolitics. The question was not whether Trump would win the New York Republican primary; the question was about how many delegates Kasich and Texas Senator Ted Cruz could deny the front-runner.

In the end, they denied him only a handful of the 95 delegates on offer. With just over 60 per cent of the vote, Trump won all but five or six of the delegates — getting him closer to the 1,237 delegates he will need to secure the nomination at the Republican National Convention to be held in Cleveland in July.

Delegate math is hard

Because of the convoluted delegate system on the Republican side, Trump may not need 1,237 pledged delegates prior to Cleveland to still win the nomination on the first ballot and avoid a contested convention that he could very well lose.

He needs to avoid a second ballot as, in addition to his unpopularity within the party's establishment, his team has trailed the Cruz campaign on securing delegate support after the first ballot, when more and more delegates become unbound.

Senator Ted Cruz and Trump have been tangling as both seek the Republican presidential nomination. Cruz came in third in the New York primary. (Joe Skipper/Reuters )

How many pledged delegates does Trump currently have? One indication of the byzantine nature of the Republican delegate awarding process is that no two sources seem to agree. According to the New York Times, Trump has 844 delegates. RealClearPolitics puts him at 845. FiveThirtyEight estimates he has 846 delegates to his name.

That gives him a lead of between 286 and 302 delegates over Cruz, who for all intents and purposes cannot win the majority of delegates prior to the convention. Mathematically, Kasich can't — he even trails Marco Rubio in pledged delegates, despite the Florida senator having dropped out of the race more than a month ago.

(Unlike in the Democratic primary, where 'superdelegates' represent a significant portion of total delegates and are free to vote as they please at the convention, there are fewer 'superdelegates' on the Republican side, and they are bound to vote for the candidate that won their state's primary or caucus.)

Trump favoured in the next 'Super Tuesday'

Five states will be voting in primaries on Tuesday, all in the northeast: Connecticut, Delaware, Maryland, Pennsylvania, and Rhode Island. Trump is favoured to win all of them.

He enjoys average leads of between 15 and 22 points over Kasich and Cruz in Connecticut, Maryland, and Pennsylvania. Delaware is the kind of state Trump should win, while his big win in Massachusetts in March bodes well for his chances in Rhode Island.

Ohio Gov. John Kasich took second in New York, but mathematically, he's not even in the race. (Joe Raedle/Getty Images)

If Trump outperforms his polls like he did in New York, he could do even better than some expect — again inching him closer to the 1,237 mark.

How close he gets could be very important because of how delegates are awarded in a state like Pennsylvania.

The state is a big prize, with 71 delegates available. But just 17 of them will be awarded to the primary winner. The remaining 54 will be awarded to no one. Those 54 delegates will be elected at the congressional district level and will be unbound to any presidential candidate. Some of the people standing for election as a delegate have already pledged to support one candidate or another, others have not.

And voters need to know the difference as, unlike some other states, the names of the presidential candidates each delegate is supporting will not be on the ballot.

But even if those 54 delegates have promised to support a particular candidate, they can vote however they please once they get to Cleveland.

The race to 1,237-ish

FiveThirtyEight, surveying a panel of experts, suggests that after Trump's win in New York the real estate mogul could end up with 1,191 pledged delegates by the time the convention rolls around. That puts him just 46 short of the number he needs to clinch.

But those 54 Pennsylvania delegates will not be the only uncommitted ones on the convention floor. FiveThirtyEight puts the number of uncommitted delegates at 132. That means that if Trump ends up with 1,191 delegates at the end of primary season, he will need just 35 per cent of those uncommitted delegates to be put over the top.

That is not a particularly high bar for Trump to meet, considering that he has the support of about 42 per cent of Republican voters and has won 38 per cent of votes cast so far in the race.

Had he not won the 20 or so more delegates than expected in New York, however, he would have needed 50 per cent of those uncommitted delegates — a taller order for such a divisive candidate.

Nevertheless, Trump still has a lot of wiggle room. FiveThirtyEight's panel estimates he could win 93 of the 172 delegates in California on June 7. Winning 10, 20 or 30 more delegates is easily plausible, along with picking up a few other delegates here and there along the way.

The closer he gets to 1,237, even without reaching that number before the convention begins, increases his chances of being the nominee.

The scenarios that end in a Trump nomination multiplied after his New York win. The potential for a contested convention still exists, and is a stronger one than has been the case in American politics for some time. But the hope that the Republican convention could deny Trump the nomination that Republican voters seem to want to give him is diminishing in a New York minute.