538 published an article, titled "*Itâ€™s Probably First Ballot Or Bust For Donald Trump At The GOP Convention*", which basically elaborates on the idea contained in its title: if Trump doesn't manage to win in the Convention's first ballot, delegates will no longer be under obligation to vote for him, and as they are not necessarily his loyalists, his chances take a steep turn down.

I posted this on 538's comment box:

*I think this article is right: Trump has a considerable chance of getting to 1,237 delegates, but if he doesn't, it is way more likely that he will not be the nominee (what that bodes for the GOP is a different issue).*

*But let's see what are the actual possibilities.*

*1. Trump gets 1,237 delegates and grabs the nomination before the convention.*

*2. Cruz gets 1,237 delegates and grabs the nomination.*

*3. Trump doesn't get 1,237, but is close enough that he can fill the gap by adding Carson's, Christie's, and some of the non-committed delegates to his side.*

*4. Cruz doesn't get 1,237, but is close enough that he can fill the gap by adding ex-candidates delegates and some of the non-committed ones to his side.*

*5. Trump doesn't get 1,237 delegates but reaches a deal with Kasich and gets the nomination.*

*6. Cruz gets more delegates than Trump, reaches a deal with Kasich, and gets the nomination.*

*7. Cruz gets less delegates than Trump, but reaches a deal with Kasich and gets the nomination even so.*

*8. Cruz and Kasich reach a deal to give Kasich the nomination.*

*9. Cruz and Kasich reach a deal to give the nomination to a non-candidate, likely Ryan or Romney.*

*10. The first round fails to reach a majority, chaos ensue, and Trump emerges as the nominee in the n-th ballot.*

*11. Same as 10. but Cruz emerges as the victor.*

*12. Same as 10. and 11., but Kasich gets the nomination.*

*13. The first round fails to reach a majority, chaos ensue, and a non-candidate (most probably Romney or Ryan) emerges as the nominee in the n-th ballot.*

*14. The first round fails to reach a majority, chaos ensue, the convention splits, with each of its separate pieces chosing a different nominee.*

*15. The convention is unable to reach a result in time to the GOP effectively run in the general election.*

*16. Same as 15. but any number of different GOP candidates register to run as third party candidates.*

*In any case, a predict a sustained boom in the popcorn market up to July.*

Now, elaborating on these possibilities, #1 is still the most probable of them, probably slightly under 50%. And all others are still far shots.

#2. is increasingly unlikely: Cruz would have to win practically all delegates from now on in order to it materialise. This includes getting at least 27 delegates in New York on April 19th, and then winning every single delegate in every remaining state. And New York is quite a difficult state for Cruz - a state where Trump is highly favoured, and Kasich is the more likely runner up. So I would put the chances of this happening below 1%. *Update: Cruz got zero delegates out of New York, so #2 is no longer a possibility*.

#3. is quite unlikely too. In practice, Trump would need to finish with 1,228 to 1,236 delegates, so that, added to Carson's 9, he would clinch the nomination. It is not impossible, of course, that Trump could earn the vote of a few uncommitted delegates, but, realistically, Cruz will get most, quite probably all or almost all of them, so in order for this possibility to materialise, Trump cannot end with much less than 1,228 delegates. There is definitely a path to that, but it is narrow just like the "window" between 1,228 and 1,237 is narrow. So I would say it's probability is something like 1 to 3%.

#4. is much more likely than #2, but that isn't much by itself. Anyway, Rubio, Bush, Fiorina, Paul and Huckabee have 188 in all, and there are some 100 uncommitted delegates available. That's 288, and Cruz will quite certainly be able to get the votes of most of them. This means that Cruz would theorically be able to perform this magic if he finishes the primary process with 949 delegates or more. He has already 545, so he needs 404 more, and there are still 854 to be chosen in the primaries. So he needs slightly less than 50% of the remaining delegates - assuming he is able to secure the votes of the candidateless delegates; each defection from those will increase the number of delegates he has to win in the primaries. Big problem is, he has not been getting anything close to 50% of delegates up to now, and, considering that a considerable part of the Northeast (and California and Maryland, which are not Northeast but tend to vote similary) are still to vote, it is quite unlikely that he will end the primary process with more than 949 delegates. So I would rate this at some 3 to 5%.

Up to now we are dealing with a "normal" convention, ie, one where the result is either known beforehand or decided on the first ballot. From #5 on we are on the terrain of a contested convention (tough technically some of the following, especially #5 and #6, could be reached in a smoke filled room **before** the convention. Whether they would be **publicised** before the convention is a different question altogether, nevertheless). So, also from now on, the possibilities depend not only on mathemathics, but fundamentally on politics.

#5 depends basically on whether the GOP establishment - or rather, the various subsets of the GOP establishment, especially, but by no means exclusively - the ones in which John Kasich is involved - prefers, Trump or Cruz. Mathematically, Trump and Kasich have, as of now, 886 delegates together; plus Carson's 9, we can make that 895, which is 342 short of 1,237, which in turn means 40% of the remaining delegates. That's in line with which Trump has been winning up to now, and if Kasich is able to grab a few more of his own, it is quite probable, perhaps over 90% of the remaining chances after the first four possibilities are discounted, or some 40-45% of the total. But the true issue is political: how probable is that, in a convention where Kasich is a king maker, the GOP establishment will decide to back Trump over Cruz (and how probable it is that Kasich will follow such GOP-e decision?) I would say it is relatively low but far from impossible, perhaps at about 15-20%, which would put possibility #5 at around 6 to 9% overall.

#6 and #7 are symmetrical to #5: they depend on Kasich being the king maker, the GOP establishment deciding to back Cruz over Trump, and Kasich abiding by such decision. Mathematically, Cruz has 545, which, added to the 288 delegates who are uncommitted or were elected to support one of the fallen, makes 859, meaning Cruz and Kasich would need 378 more delegates among them from the remaining 854 yet to be chosen. That would mean they getting, together, about 44% of the remaining delegates, which is something somewhat above what they have been doing, but not by much. Then comes the political issue, and I would estimate that the probability of the GOP establishment preferring to back Cruz against Trump is about 45-50%, so leaving us with some 40% to 45% to distribute among possibilities #6 and #7. Since #6 is much more likely that #7, this is probably 30-35% to 5-10%.

- 8 and #9