The General Election numbers game what will the next government look like?

The magic number is not three, it’s 323. That’s how many seats are needed to produce a majority and, in the hifalutin phrase, “command the confidence of the House of Commons”.

And it’s anybody’s guess who will get over that line. The final result is scheduled around noon on Friday but with so many contests expected to be tight there could be multiple recounts.

Received wisdom says we’re used to majority governments in this country, mainly swinging between the Conservatives and Labour. But, of the 20 governments during the 20th century, only half were majority administrations with a further five coalitions and five minority governments. No-one’s expected to get a majority on their own on Thursday and that’ll open up all sorts of potential partnerships and coalitions. Here, we take a look at the potential options for government after Thursday’s vote.

Tory/Lib Dem

Odds: 4-1

Analysis:

A good night for the Tories which included Nick Clegg keeping his seat would make this outcome a whole lot more likely. Despite some public trash talking during the campaign Clegg and Cameron have a decent personal relationship and would happily work together again if the numbers add up. The Lib Dems are making increasingly encouraging noises at the Conservatives for example by saying they’ll speak to the party with most seats first and ruling out any administration that relies on SNP support both of which are aimed squarely at cooling Labour ardour. Clegg has expressed concern about a coalition with only a slim majority fearing the sort of Tory headbangers who got up to silly japes in the last parliament like trying to bring in laws abolishing him would make hay and hold the administration to ransom. But those worries could probably be eased by the thought of five more years with a ministerial limo at hand.

Pros/Cons:

Both parties could claim that a second coalition offers stability and both could claim to be finishing the job of fixing the nation’s finances and hope to reap the electoral reward in five years’ time.

The potential pitfalls arise around leadership issues. Can Clegg continue as leader of the Lib Dems if his parliamentary party is scythed in size? How long can Cameron hold off the ambitions of Boris Johnson given he’ll have failed yet again to beat a duff Labour opponent outright? The continuation of the coalition could be very reliant on the key personnel at the top.

Labour/SNP

Odds: 11-1

Analysis:

Don’t waste your money on this option. Both parties have ruled out a formal coalition meaning whatever happens there’ll be no SNP MPs round the UK Cabinet table and bookies won’t pay out. However there are other ways to govern together. A confidence and supply arrangement means the nationalists promise to back Labour’s budgets and support them in the face of any confidence vote but everything else is up for grabs. It’s been categorically ruled out by Miliband but that may still not be the end of the matter.

Pros/Cons:

Confidence and supply would allow the SNP to try extract maximum benefit for them, and for Scotland in their eyes, in return for backing bills.

For Labour it would give them more security than minority Government.

The Fixed Term Parliaments Act introduced by the Coalition means it’s quite hard to force another General Election. Strathclyde University election boffin Professor John Curtice has compared going into minority government under the new arrangements as entering the lion’s cage but giving the key to the opposition because it’s now easier for the opposition to collapse a parliament than for the PM to do so. So there’s clear benefit to Labour in knowing the SNP have got their back. Given there’s no love lost between the two parties in the wake of the independence referendum and they’ll be the two main protagonists for the next 12 months leading up to the Scottish elections it would make for a volatile mixture which the money markets for one will not like.

Labour/Lib Dem

Odds: 10-1

Analysis:

The Sheffield Hallam constituency is the one to watch on election night. It’s Nick Clegg’s seat and his fate will likely determine who the Lib Dems might team up with in the next Parliament. Clegg doesn’t appear to have any affinity with Labour but plenty in his party do. If he’s a goner, then it’ll be a lot easier for Ed Miliband to do a deal with the Lib Dems albeit there could be a delay while the Lib Dems decide who is their new leader. Trouble is, the numbers might not add up. If Labour and the Lib Dems together don’t have enough seats to make up a majority then it’s hard to see the benefit for Miliband in having them round the Cabinet table when he could govern alone and hand out ministerial jobs to his own team. Labour would need to have a good night for this option to add up.

Pros/Cons:

The big advantage for Labour in coming to an accommodation with the Lib Dems is it would stop them having to rely on the SNP for support. But if the numbers don’t add up to a majority they’d still need some help to get over the line on a vote-by-vote basis though they might find it easier to persuade or buy off Plaid Cymru, Green or Northern Irish SDLP MPs. For the Lib Dems, there’d be a big concern that, having lost a lot of voters on the left because they got into bed with the Tories, they would then see right-leaning Lib Dems switch to the Tories damaging the party even further. It’s worth pointing out that minority coalitions are not unheard of and in countries like New Zealand are actually the norm.

Labour in power

Odds: 7/4

Analysis:

Ed Miliband is favourite to be the next Prime Minister but the odds on him getting a majority are as long as 77-1. He’s in a good position because Labour have significantly more allies in the Commons than the Tories. The party’s Scottish collapse will likely cancel out most of the gains they’ll make elsewhere but, since the SNP have ruled out putting the Tories in power, Miliband can form a minority administration fairly quickly knowing his Queen’s Speech will have the backing of the SNP and others in the so-called “progressive alliance” such as the Greens and Plaid Cymru.

Pros/Cons:

Minority government doesn’t have to be unstable but a Labour administration would struggle to stay operational from the very outset. If Miliband doesn’t get most seats there’d be questions about his legitimacy to be in No. 10, especially if he relied on a party that wants to break up the UK to govern. In the run-up to the 2016 Scottish elections the SNP won’t want to be blamed for putting the Tories in power so they’ll likely behave themselves for the first year but they’ll still want to be able to show the Scottish electorate that they are making gains for Scotland. Thus they’ll look to extract the greatest possible reward for making Miliband PM and backing his programme of government. Labour could then face five years of misery as the SNP embarks on a campaign of torturing them for rewards and the Tories can then claim they’re selling out English voters.

Tories in power

Odds: 5-1

Analysis:

The polls are looking increasingly positive for David Cameron. He’s unlikely to win an outright majority but is currently favourite to emerge with most seats. Add that to the fact the rules state that the incumbent Prime Minister gets first shot at forming a government and Cameron is in pole position to try and stay in power. But, first of all, he needs to get enough seats. According to insiders, 284 is the magic number for the Tories. That’s the total they think will allow them to govern with support from the Lib Dems, Ukip and Northern Ireland’s unionist MPs when needed. The three others are likely to have at least 40 MPs between them. For the Tories, governing alone has its attractions. First, it allows the PM to dish out plum ministerial posts to his own people. Secondly, they can blame everyone else when they can’t get their EU referendum bill through and then go to the country next time out hoping the election will essentially be a referendum on the referendum.

Pros/Cons:

The Tories know about minority government from both sides. In Holyrood they propped up Alex Salmond’s 2007 administration in return for favours. And John Major ran a minority administration in the dog days of his time in office. But that got increasingly chaotic with the PM held to ransom by the rabid wing of his own party before the whole thing ended in crushing defeat to Tony Blair. Tories hope the election will be a re-run of 1992, but they won’t want to re-run the five years that followed.