Instant-reaction polls following Monday night’s debate in Boca Raton, Fla., judged President Obama to be the winner.

A CBS News poll of undecided voters who watched the debate found 53 percent giving it to Mr. Obama, 23 percent to Mitt Romney and 24 percent declaring it a tie.

Mr. Obama’s margin of victory in the poll was slightly wider than Mr. Romney’s following the first presidential debate in Denver, which a similar CBS News poll gave to Mr. Romney at 46 percent to 22 percent.

Other polls, conducted among a broader group of voters rather than just undecided ones, suggested a smaller margin for the president.

A Public Policy Polling survey of voters in 11 swing states who watched the debate found them giving it to Mr. Obama, 53 percent to 42 percent.

A CNN poll of registered voters who watched the debate put Mr. Obama ahead, 48 percent to 40 percent. That was similar to Mr. Obama’s 46-39 margin in a CNN poll of the second debate, and much smaller than Mr. Romney’s 67-25 advantage in the first one.

An online poll by Google Consumer Surveys had Mr. Obama winning, 45.1 percent to 35.3 percent. His roughly 10-percentage-point margin in the poll is smaller than in a Google poll after the second debate, which gave it to Mr. Obama by 17 percentage points, or Mr. Romney’s after the first, which he won by 22 points.

There is, obviously, some disagreement on the magnitude of Mr. Obama’s advantage — the polls surveyed different types of voters and applied different methods to do so.

But averaging the results from the CBS News, CNN and Google polls, which conducted surveys after all three presidential debates along with the one between the vice-presidential candidates, puts Mr. Obama’s margin at 16 percentage points.

That compares favorably to Mr. Obama’s average 10-percentage-point margin after the second debate, and Vice President Joseph R. Biden’s 6-point margin against Representative Paul Ryan, but is smaller than Mr. Romney’s average 29-point win in Denver.

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The first presidential debate produced roughly a 4-percentage-point bounce in head-to-head polls toward Mr. Romney, while the second presidential debate brought no appreciable bounce toward Mr. Obama.

It is tempting to split the difference, and assume that Mr. Obama might get a 1- or 2-point bounce in the polls, but there are some mitigating factors. The pace of the debate was slow, and it was competing against professional baseball and football games, which may have kept viewership down.

Voters have more information about the candidates than they did before the first debate, which means that their additional impressions of the candidates could make less difference at the margin. Historically, the bounces following the third presidential debate, in the years when one was held, were smaller than after the first two.

Finally, the subject of the debate, foreign policy, is not as important to most voters as economic policy, although some voters may have judged the candidates on style regardless of the substance of the conversation, which did end up including a fair amount of domestic policy as well.

Still, with the contest being so tight, any potential gain for Mr. Obama could matter.

Mr. Obama was roughly a 70 percent Electoral College favorite in the FiveThirtyEight forecast in advance of the debate, largely because he has remained slightly ahead in polls of the most important swing states.

If Mr. Obama’s head-to-head polling were 2 percentage points higher right now, he would be a considerably clearer favorite in the forecast, about 85 percent. A 1-point bounce would bring him to 80 percent, and even a half-point bounce would advance his position to being a 75 percent favorite in the forecast.

Still, Mr. Obama should not take even that for granted. There have been some past debates when the instant-reaction polls judged one candidate to be the winner, but the head-to-head polls eventually moved in the opposite direction.