The next Prime Minister will be whoever can secure a majority of votes in the House of Commons. That will either be David Cameron, or it will be Ed Miliband.

If push comes to shove, if he's willing to do deals, Ed Miliband will likely be able to get votes of confidence from the SDLP, the SNP, Plaid Cymru, and the Greens. All of these parties have said that they will talk to Labour but won't vote for the Tories. I'll assume for now that speculation about Sinn Fein MPs taking their seats is no more than that. Let's call this grouping the left collection. If George Galloway's re-elected (which I think he won't be) then I think it's clear we can count him in this group too.

There is, on top of this, someone else – the one independent, Lady Sylvia Hermon, MP for North Down. Lady Hermon left the Ulster Unionists in 2010 when they went into an alliance with the Tories - or, as the woman who answered the phone in her office corrected me, “the UUP left Lady Hermon”. When I put it to this friendly staffer that it was reasonable to assume that Westminster's only independent would be more likely to talk to Ed Miliband than David Cameron, she said that she didn't think this was necessarily accurate – though it is true that the MP for North Down is “not a traditional Conservative supporter by any means” (the “Lady” is a product of the fact that her late husband was knighted for being chief constable). Her boss, I was told, is “keeping her powder dry” and “playing her cards close to her chest” regarding who she would talk to. Their analysis is that leadership challenges were possible in both Labour and the Tories post-election, and they implied that this might change things. It's understandable that they don't want to reveal their hand to whichever random journo rings their office, but speaking to friends who know the constituency well, they were pretty clear that, if her vote was enough to swing it, she would almost certainly join the left collection over the right cluster. We'll see.

David Cameron might get the votes of Lib Dems, the DUP, UKIP, and Alliance, though for a number of reasons, these seem less secure: it may be that what he'll have to offer the Lib Dems and what he'll have to offer any UKIP MPs will be incompatible; the Lib Dems may not be very keen on another coalition in any case, particularly after a rough election, and particularly if Nick Clegg has been unseated, and they may prop Labour up instead. Likewise, the DUP have said that they would also be willing to work with Miliband, presumably because they know how to play hard to get in these situations. In any case, the minimum requirement for David Cameron to be returned as Prime Minister is that this collection of parties needs to have a majority. Let's call this grouping the right cluster.

In 2010, our left collection got a total of 271 seats. Our right cluster got 372 seats. There's one floating voter, five Sinn Fein and one speaker. This means that in order for Ed Miliband to become Prime Minister, the left collection needs to take at least 51 seats off the right cluster.

What are the odds of that? Northern Ireland, Wales, Scotland and England all have different stories to tell. These will change through the course of the election campaign, and opinion polls are a moment in time not a projection into the future, but it's worth considering the current position.

Northern Ireland

The Belfast Telegraph (“Bel Tel” to the locals) has a poll predicting that the Lib Dem's sister party Alliance will lose Naomi Long, their only ever MP, to the DUP. But since then, it seems Unionist unity has broken down in Belfast, which gives her a much better chance of hanging on. In any case, that's a swap within our right cluster so may make no difference to who the PM would be. The breakdown of such co-operation probably also means that the SDLP are safe in South Belfast. Mairtin O Muilleoir, a strong Sinn Fein candidate, might just split the vote there and let the DUP through, but that's counteracted, I'm told, by anger with Peter Robinson's party over their behaviour during the flags protest. Similarly, Sinn Fein will probably hold Fermanagh and South Tyrone – the closest seat in the UK in 2010 - against the divided unionists. In any case, my ears on the ground tell me that any Unionist unity candidate would likely be an independent from the left, and so be more likely to add one to our left collection than our right cluster.

In summary, only two changes between our categories seem to be on the cards in Northern Ireland - a possible gain for the right cluster in Belfast South, and an outside chance of the left collection securing a seat from the abstentionist Sinn Fein in Fermanagh and South Tyrone. In practice, neither seems very likely. Let's count that as a score draw.

Wales

The Principality is frustratingly under-polled. However, there was a survey recently, written up by Roger Scully of Cardiff University. The headline is that the Lib Dems would lose two MPs, and Labour gain them. Apart from that, everything else would stay the same. That's a switch of two from our right cluster to our left collection.

Looking more generally, with Leanne Wood now in the leaders' debates and all this chatter about small parties, it seems she's likely to break through at least some of the barrier she described to me when I interviewed her last summer: in this election, people may notice Plaid Cymru more than they have in past UK votes (though the polling isn't yet reflecting that). It seems plausible, in that context, that they could take Ceredigeon back off the Lib Dems (they had it from 1992-2005 and hold it at the Welsh Assembly). That would be another swing from our right cluster to our left collection, but I won't add it to our total, as the polls haven't yet picked up the change.

That leaves Ed Miliband needing a total of 49 seats from Scotland and England - or 48 if Lady Hermon is on board.

Scotland

The polling in Scotland is the polar opposite of that in Wales – it's frequent and brutally dramatic. Currently, our right cluster gets 12 of its seats from North of the border – 11 Lib Dems and a Tory. It's rarely mentioned, but Clegg's party is more proportionally dependent on Scotland for their MPs than Labour is, and the Ashcroft polls last week only confirmed what we already know to be true: we're looking at a wipe-out. The SNP have replaced the Lib Dems in all of their Holyrood constituencies but Orkney and Shetland and look to do the same at Westminster. A few polls have shown David Mundell, the one Conservative, getting the boot too. Some people say Charlie Kennedy will hang on to Ross, Skye and Lochaber through sheer force of personality, but we'll see. I spent some time knocking on doors there last summer, and the word on the street was “numpty”. It's a sad tale, but he's not the man he once was.

Given all that, it seems reasonable to assume our right cluster will defy the polls in two of its twelve seats (ie two out of Kennedy, Mundell and Orkney and Shetland). That swings ten MPs to our left collection. Of course, it also looks like there's going to be a huge swing from Labour to SNP, but that's not a change between our two groups – both are in the left collection. If the question is whether Ed Miliband or David Cameron is likely to be Prime Minister, then this has little baring.

All this leaves the left collection needing 39 seats from England - in other words, before we get to England, Miliband's already nearly a quarter of the way to his winning figure.

England

Ed Miliband is the first Labour leader in my lifetime who grew up in England, and the polling there on its own makes for interesting reading. In 2010, Labour were 11.5 points behind the Conservatives. Mike Smithson of Political Betting has been occasionally tweeting the England-only polls this time, and there is one consistent story – Labour, while behind, aren't nearly as far behind as they were five years ago: an effect masked to some extent by their astounding collapse in Scotland. On the 9th of February, for example, the Tory lead in England was only four points.

And of course, it's not just the swing between Labour and the Tories that matters – taking Lib Dem seats is just as valuable to Miliband in an election that's about pacts as much as parties. Likewise, whilst UKIP may win up to five seats, it's likely all of them will be from the Conservatives, having no bearing on the relative size of our two groups. On the other hand, the two seats in which Greens have some prospect of making gains – Bristol West and Norwich South, are both held by Lib Dems.

This means that the overall question for England seems a simple one: can Labour and the Greens take a total of 39 seats from a combination of the Lib Dems and Tories? Despite Labour's falling lead, I've yet to see a pollster saying that they won't.

This leaves Miliband with a strategic question. He has limited time and campaign funds – significantly less money than the Tories. He could spend that resource on battling the SNP in 40 seats in Scotland. They average 1,500 members per constituency, have the most efficient ground campaign in the UK, and will now have millions of pounds to throw at this election. Labour's likely to lose most of those battles. Ed could throw cash into beating Greens and Plaid in their target seats. Or he could accept the reality that he's almost certainly going to have to do a deal with Sturgeon and others, pick the 40 seats he needs to win in England (or, in practice, a few more to give a buffer), throw everything at them, trust the SNP machine to wipe the Lib Dems out of Scotland, and walk into Downing Street on the 8th of May.

Of course, all of this depends on Miliband accepting the terms of a deal with parties to Labour's left. In normal circumstances, that would mean he would have to put up with those on the right of his party berating them. But, given this strategy means sacrificing the likes of Douglas Alexander and Jim Murphy to the Scottish electorate, at least some of this internal dissent would likely be drowning its sorrows by then. And, in any case, a majority probably isn't possible. The sooner Miliband realises that, the more he focuses on the battles he needs to win rather than the ones he doesn't, the higher his chances of getting into Number 10.