There are a total of 2472 delegates going to the Republican convention in July. At the moment, Donald Trump has 756. He needs 1237 to win the nomination on the first ballot (I think it's extremely unlikely he could win any other way), a difference of 481. There are 769 delegates left to choose, so Trump needs to win about 64% of them. That's a tall order. To date, 1703 delegates have been selected, and Trump has only won 44% of those, so he needs to improve his performance by 50% to avoid a brokered convention. That seems unlikely.
But there is a fly in this mathematical ointment in the form of a huge non-linearity: California, the most populous state, has 172 delegates, and it's a winner-take-all state. Trump could bag that prize with a plurality of the votes if John Kasich stays in the race that long. Even if Kasich drops out, it's conceivable that Trump could win California anyway. Could he win then?
California happens last so we won't know until the very end, but let's suppose Trump wins it. That would take him to 756+172 = 928. Of what's left, 238 delegates are selected by proportional vote, so it's probably safe to assume that Trump would win roughly half of those, or 119. That brings his total to 1047, with 359 delegates in 9 winner-take-all states left to assign. Trump would need 190 of those to put him over the top, or 53%. That's very possible.
What is more interesting is the fact that there is no way that Trump could sew up the nomination before California votes. California by itself is not big enough to swing the decision unilaterally, but four other states vote at the same time, and between them they have 303 delegates. The remaining 466 to be selected before June 7 are not enough to put Trump over the top even if he wins them all. Likewise, for Trump to definitively lose before June 7 he'd need to perform spectacularly badly even by Trumpian standards, winning only 177 of the 466 available delegates (38%). That too, is extremely unlikely.
So the math says that it's going to be a nail biter, and California is going to be the deciding factor. But don't blame me, I'm voting for Bernie.
"I think it's extremely unlikely he could win any other way"
To be fair, if Trump comes close (say, 1200 delegates), and the next #2 candidate (Cruz?) is far, far below him ... it's actually not at all clear how the convention would go. Tough for Trump to lose on the first ballot. But also tough for anyone else to assemble a majority, on a later ballot.
I know Cruz is playing the "defect to me on the 2nd ballot!" game. And he might indeed get a lot of delegates that way, with his subtle 2nd-order game. But he has to eventually get to 1237 (at the convention) too. You really think that's easier, than Trump convincing another 100 to join his side?
As Carl Sagan once said, prophecy is a lost art. The outcome of a brokered convention depends on whether the party decides it would rather win or make a statement. Current polls show the only candidate with a chance of beating Hillary (and Hillary will win the Democratic nom) in November is John Kasich, and I think it's possible that Cruz and Trump are widely enough disliked that delegates might come to their senses and rally around him.
Of course, the mere fact that Trump is in the lead proves that there are waaaayyyy more crazy people in the Republican party than I (or anyone else six months ago) would have thought. So who the fuck knows?
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