NEW YORK — Trading in U.S. stocks was quiet on Tuesday but betting on the U.S. presidential race reached fever pitch, with most online gambling sites giving President Barack Obama favorable odds to win.

With the first polls set to close at 7 p.m. ET in a handful of states, gamblers were still frantically placing final bets on the outcome of the election between Obama and Republican challenger Mitt Romney.

At InTrade, a website that allows users to play events like the election for a monthly fee, 3.8 million "shares" traded in Obama and about 3.1 million Romney shares traded on Tuesday.

In late October, each candidate typically saw between 50,000 and 60,000 shares of daily volume, according to Carl Wolfenden, exchange operations manager at InTrade, which is based in Dublin, Ireland.

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The site operates like a futures exchange, with users betting on the odds of an event occurring. Currently, shares in Obama are going for $6.89, indicating he has a 68.9 percent chance of being reelected. If Obama wins, each contract will close out at $10, netting investors a profit of $3.11 a share. If he loses, contracts will close at $0.

On PaddyPower.com, another online betting site based in Dublin, the odds heavily favor the president. Romney is a four-to-one underdog to win, where Obama is a one-to-six favorite, meaning a $6 bet on Obama would pay out $1.

Obama's edge on the site mirrors the expectations of many polling strategists who see the president with a small lead in national polls and an edge in key swing states like Ohio and Virginia. The final Reuters/Ipsos tracking poll showed the incumbent up two points nationally against Romney, at 48 percent to 46 percent.

The level of trading on the site Tuesday counters a prominent criticism of such online markets, which is that limited use allows for the contracts to be pushed around, rendering them inaccurate reflections of the odds of an event occurring.

On October 23, a rash of bets favoring Romney caused the odds for the former governor of Massachusetts to spike suddenly and then evaporate. Wolfenden estimated that there were a mere 40 Romney buyers that morning and only five sellers.

That kind of limited play continued in some of InTrade's smaller contracts. Romney is expected to win the state of Alabama in a landslide, but the mere nine contracts traded over the state suggests he only has a 60 percent chance of winning. That puts the state in InTrade's "leaning Republican" column.

To compare, a competitive state like Ohio is seeing a great deal more interest, with almost 26,000 shares traded in Obama and another 19,000 in Romney.

For those inclined to skip the heated trading in this race, Paddypower already has odds on the winner of the 2016 Presidential election, with Romney currently standing with 9-to-2 odds and Secretary of State Hilary Clinton at 8-to-1 odds.

Those who prefer to bet on long-shots could consider a play on Donald Trump, who carries 100-to-1 odds on occupying the White House in four years.

More election coverage from NBCNews.com:

• Obama, Romney campaigns play the waiting game
• What to watch for when the results roll in
• GOP faces difficult climb to Senate control
• Republicans in driver's seat to protect House majority
• In 11 governor races, it's about jobs and taxes
• Voting in areas hit by Sandy is 'first step toward recovery'
• GOP leaders draw line on taxes ahead of results

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