A resurgent Rick Santorum hopes to spring his next big surprise in Michigan. Newt Gingrich looks for a campaign revival in the South. Mitt Romney has his home state of Massachusetts, and the luxury of picking his spots elsewhere, if not everywhere, as the race for the Republican presidential nomination roars back to life.

After a brief midwinter lull, the Republican field faces a cross-country series of nine primaries and four caucuses between 28 February and Super Tuesday on 6 March. At stake are 518 convention delegates, more than three times the number awarded so far in the unpredictable competition to pick an opponent for President Barack Obama.

A debate on 22 February in Arizona, the first in three weeks and possibly the last of the Republican campaign, adds to the uncertainty.

The political considerations are daunting as Romney, Santorum, Gingrich and Ron Paul weigh the cost of competing in one state against the hope of winning in a second or perhaps merely running well but gaining delegates in a third.

It will take 1,144 delegates to win the Republican presidential nomination at the August convention in Tampa, Florida.

According to numerous strategists inside and outside the campaigns, the Michigan primary on 28 February shapes up as a particularly important contest as Romney tries to fend off a charging Santorum one week before a 10-state night on Super Tuesday.

Yet, of the 13 states, Georgia has the biggest delegate haul at stake, 76, and Gingrich can ill afford to lose now where his political career was launched in 1978.

Sensing an opportunity, the pro-Romney group Restore Our Future is targeting Gingrich in television ads in Georgia, hoping to deny the former House speaker a sweep of the delegates and leave some on the table for Romney to scoop up.

No such manoeuvre is possible in Arizona. There, all 29 delegates go to the winner, and Romney, a former Massachusetts governor, is heavily favoured. Texas Rep. Ron Paul, the only of the four contenders without a victory so far, eyes four chances to break through: caucuses in Washington on 3 March, and in North Dakota, Idaho and Alaska three days later. An unusual presidential campaign trip to Alaska is possible.

Nor are the candidates the only ones working to shape the race.

Restore Our Future, the political organisation that supports Romney and has devastated Gingrich with attack ads in two states, is turning its attention to Santorum, a former Pennsylvania senator.

Already, the group has spent $5 million on television advertisements combined in Arizona and Michigan through 28 February, and Ohio, Tennessee, Oklahoma and Georgia through Super Tuesday. The group also has commercials airing in Mississippi and Alabama.

Santorum responded with a commercial in Michigan designed to blunt the attacks and tarnish Romney. It shows a Romney lookalike wielding a machine gun that sprays mud in Santorum’s direction.

When the weapon jams, the gunman tries to fix it, and ends up splattering himself instead.

The Red White and Blue Fund, which supports Santorum, is advertising in Michigan, but the former senator and his allied group are being outspent roughly 3-1 by Romney and Restore Our Future.

With Gingrich unable to come close to duplicating his 21 January victory in South Carolina, his goals are as diminished as his campaign bank account.