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Florida, for instance, has 16 Republicans and nine Democrats. That means the delegation would (almost certainly) vote 16-9 for Mr. McCain, while Colorado, with four Democrats and three Republicans, would vote 4-3 for Mr. Obama.

In the current House, Mr. Obama would win - 27 delegations have a majority of Democrats, 21 have a majority of Republicans, and two states, Kansas and Mr. McCain’s home state of Arizona, are evenly split.

But those numbers will change Nov. 4, and Paul Sracic, associate professor in the department of political science Youngstown State University in Ohio, said they could change dramatically. Of the 27 state congressional delegations with a majority of Democrats, 25 of them would switch to deadlocked or Republican control if two or more seats change to Republican.

At least 26 state delegations in the House must agree before the next president can be chosen. But even if Democrats maintain a majority, there would be pressure on Democratic delegations to vote Republican in states where voters chose Mr. McCain.

It took 36 ballots in the House to select Thomas Jefferson as the third president after the 1800 election ended in a 73-73 tie. There was so much animosity after that election that Aaron Burr, elected vice president, faced off in a duel with Alexander Hamilton, who had thrown his support behind Jefferson. Burr shot Hamilton dead in a duel.

The number of electors, 538, is equal to the number of senators - 100 - and representatives - 435 - in the Congress, plus the three electors added in 1961 when the 23rd Amendment gave the District a say in U.S. presidential elections. Thus, there have been 10 presidential elections in which a 269-269 tie was possibly, but it has never occurred.

“The probability of a tie in 2008 is about 1.5 percent, which is slightly higher than we calculated at about the same time back in 2004,” said Mr. Sracic, who enlisted the help of the university’s math department to come up with a possible 1,024 combinations with the current 10 states now considered tossups.

“What really strikes you is how easy it would be for a tie to occur. Take the 2004 map and switch Iowa, New Mexico and Colorado into the Blue column, which is what the poll numbers indicate. Then, take New Hampshire and give it to McCain, which is what two recent polls suggest is going to happen. There is your tie.”