I wrote last week that David Cameron will try and stay in Downing Street after the election for as long as he thinks he has the chance of forming a government. To do so would not be illegal or unconstitutional. Precedent is on his side. He is not obliged to resign until he chooses to do so – in practice, the moment when it is clear he is not able to form an administration that commands the confidence of the House of Commons.

To this end it’s entirely plausible that, even if Labour wins more seats than the Tories, Cameron will remain in the role of prime minister – at least temporarily. So long as the electoral arithmetic permits the potential for a Tory-led coalition, or even a Tory minority government, Cameron will do his best to usher one into existence.

But what kind of arithmetic does he need?

I’ve already had a go at calculating the bare minimum Labour needs to do at the election to end up the largest party in parliament.

It’s a slightly different situation for the Conservatives, because they already are the largest party. For them, the question is more what they need to do to remain the largest party in parliament.

The Tories will go into the election with 303 MPs, not including the Speaker. Labour will go into the election with 257:

Conservatives 303, Labour 257

Let’s say both parties win 10 seats each from the Liberal Democrats:

Conservatives 313, Labour 267

Now let’s give the SNP 20 gains at Labour’s expense:

Conservatives 313, Labour 247

This would obviously be a very comfortable position for the Tories, but it assumes they won’t lose a single seat to Labour. Let’s say the election goes particularly badly for Ed Miliband, and his party is only able to take 20 seats from the Conservatives:

Conservatives 293, Labour 267

The Tories are still well ahead. But with the Lib Dems likely to be reduced to at most 30 MPs thanks to gains by the Tories, Labour and the SNP, a Tory-Lib Dem coalition on these numbers would total only 323 MPs: not enough to reach the theoretical target of 326 needed for a majority in the House of Commons.

Is 293 seats too low to run a minority government? My instinct is yes. I’ve always thought that 300 is the sort of benchmark a party needs to achieve in order to survive as a minority government for more than a matter of weeks.

After the February 1974 general election, Harold Wilson’s first Labour government consisted of 301 MPs: 17 short of a majority in the Commons. A present-day government of 301 MPs would be 25 short of a majority.

Of course, there’s always the possibility of David Cameron seeking to bolt on more parties to a Tory-Lib Dem coalition to bump up the numbers: the DUP, for example. There’s also the difference between the theoretical target of 326 and the actual number needed for a majority in the Commons. Take off the Speaker, the two deputy speakers and Sinn Fein and the number falls to 322.

Were the Tories to manage a couple of gains from Labour, this would obviously put them in an even more secure position. But at the same time, there’s the chance of them losing a few more to Ukip in return. And so it goes on.

Perhaps it’s best to say that the Conservatives can afford to lose around two dozen seats to Labour so long as they take 10 or so from the Lib Dems and keep losses to Ukip at a bare minimum. This would leave them roughly where they are now, with around 300 MPs: the sort of number that I’m sure will be treated by David Cameron as appropriate for the foundation of a second term as prime minister.