It’s betting season in the Republican presidential primaries.

Mitt Romney has proposed a $10,000 wager and Newt Gingrich has put $10 on the table. A safer bet would be to give a combined 10-to-1 odds that no candidate other than Romney or Gingrich will be the nominee. Yet several of these soon-to-be also-rans will play crucial roles in shaping the contest over the next six weeks.

The one certain to remain in the game after the early contests is Texas Representative Ron Paul, who has a fervent following.

If Minnesota Congresswoman Michele Bachmann, Texas Governor Rick Perry or former Pennsylvania Senator Rick Santorum makes a decent showing in the Iowa caucuses in two weeks -- say, fourth place as Senator John McCain did four years ago -- they live to fight on. Former Utah Governor Jon Huntsman, meanwhile, is staking everything on New Hampshire.

The outcome in both of these early states is dicey to predict. New Hampshire has a long history of surges and surprises in the final week.

In Iowa, the Republican faithful -- four years ago, there were 119,000 of them -- will turn out at 7 p.m. on Jan. 3 in 1,774 precincts at churches, schools and other public buildings. After 45 minutes to an hour, where one supporter of each candidate can speak, people vote in private. (Unlike Democrats, who express their support publicly, in a more drawn-out process.)

Paul’s Devotees

Organization -- identifying voters and getting them to the polls on a snowy night -- may be overrated, but it’s more important in Iowa than in the all-day primaries held in other states. That explains the varying predictions about the outcome for Paul. These range from a repeat of his 2008 fifth-place showing, with 10 percent support, to predictions by some analysts who, after last month’s Bloomberg Poll showing him running neck and neck with the leaders, think he might win.

No other candidate matches the intensity factor enjoyed by the Texas congressman who rails against the Federal Reserve, government spending and the wars in Afghanistan and Iraq. The Bloomberg Poll showed he had contacted more voters than any other Republican candidate.

Here’s the biggest uncertainty: the 76-year-old libertarian has surprising appeal among young voters. It’s anyone’s guess how many of them will come out on a cold night, with colleges on winter break. In New Hampshire, most polls show him at about 15 percent.

In Iowa, Bachmann, Perry and Santorum are vying for the social conservative vote, and to peel some off of the support for the front-runner, Gingrich. They bring different assets. Bachmann has a strong backing in the evangelical Christian churches, which are politically active in the state. Santorum has visited all 99 counties and is counting on support from small communities. Perry is spending the most money.

The combined share of the vote of these constituencies could be as much as 35 percent. If most of it goes to one of these candidates, he or she will get momentum. None of them is likely to actively participate in New Hampshire a week later, and instead all three will focus on the Jan. 21 primary in conservative South Carolina.

Huntsman isn’t even participating in Iowa, and New Hampshire is the ballgame for him. He’s banking on the attention that the first-in-the-nation primary state bestows; he has held 125 campaign events there already and is planning to spend the final two weeks leading up to the Jan. 10 vote campaigning full time in the Granite State.

New Hampshire Swing

The former envoy to China runs third or fourth in most polls. New Hampshire, however, has frequently swung late and the possibility that independents and Democrats will re-register as late as Jan. 10 to vote in the Republican primary should be a help for Huntsman.

If Romney, Gingrich, and Paul finish first, second and third in Iowa and New Hampshire, the field will be set. If most of the others try to go on, they will look like that chicken that runs around for a short while even after its head has been cut off.

While Paul has little chance of winning the nomination, he’ll cause problems for the front-runners, especially Gingrich; last week, the Paul campaign released one of the toughest and most polished commercials and it was an attack on the former House speaker as a serial hypocrite.

Another threat to Gingrich would arise if one of the other conservatives emerged from Iowa to fight another day. Bachmann and Santorum, in particular, relish attacking Gingrich’s conservative credentials. If Huntsman wins, places, or probably even shows in New Hampshire and has enough political cachet to run a credible race in the Florida primary on Jan. 31, his efforts likely would cost his fellow Mormon, Romney.

Each scenario would affect the prospects and the strategy of the front-runners. Gingrich’s hubris --- he’s a stranger to humility -- means he tends to brush aside the others as inferior, say people who talk to him and his campaign. He will have to respond to concerted attacks from the political right.

The Romney campaign, on the other hand, has been carefully calculating all the possibilities. First, if Paul wins Iowa, the Romney camp would be happy; it would be viewed, they believe, as a loss for Gingrich. They then envision winning New Hampshire, counting on Huntsman to be an also-ran.

Romney’s strategists believe their candidate has financial and organizational advantages that position him for a protracted fight. The centerpiece of their win-the-nomination scenario is a belief that Gingrich will either self-destruct or be destroyed by revelations about his past.

“We know that Newt will crater,” says a top Romney lieutenant. “What worries us is whether it’ll be in January or not until May.”

(Albert R. Hunt is the executive editor for Washington at Bloomberg News. The opinions expressed are his own.)

To contact the writer of this column: Albert Hunt in Washington at ahunt1@bloomberg.net

To contact the editor responsible for this story: Max Berley at mberley@bloomberg.net.