LAS VEGAS – In a city used to hosting championship boxing matches, President Bush and John Kerry began their final round Thursday.

With the furious punching of three debates over two weeks behind them, the candidates now head into their final 18 days of campaigning essentially tied, looking for any advantage, anywhere.

Scoring the debate round, the campaigns and independent analysts agreed that the three face-offs had allowed Kerry to pull even with Bush. The Republican incumbent steadily improved and, by some measures, fought to a draw in Wednesday’s final debate. But the net effect of the three matchups was clearly in favor of the Democratic challenger.

There was a “fundamental shift of who Kerry is and who Bush is,” said political analyst Stuart Rothenberg. “Without the first debate, I think Bush would still be ahead.”

But Republicans saw openings that they hope to exploit in the last stage of the campaign as well.

“Our very different records are a window into what we believe and what we’ll do in the next four years,” Bush said. “The senator believes in a bigger government; I believe in more freedom and choices for our citizens.”

Strategists suggested that the candidates would be fine-tuning their stump speeches for the final push, but that in many ways the end game will revolve around their television advertising and unprecedented efforts to turn out the vote in a handful of states.

There will be “a lot of hard-hitting campaigning – a lot of dirty ads,” said political scientist Kathleen Hall Jamieson.

The candidates didn’t try to hide that: Both quoted championship boxers in describing their final fight.

Bush continued to smack Kerry with Joe Louis’ line about a slippery opponent – “he can run, but he cannot hide” – while Kerry responded with Muhammad Ali’s pre-knockout taunt of George Foreman: “Is that all you got?”

The battle will be at close quarters: The number of true battleground states probably numbers no more than a dozen.

There’s Florida, of course, the state that decided the 2000 election after a protracted legal and political battle.

There are few other states that some play a similar role this time – the industrial prizes of Ohio, West Virginia and Pennsylvania, as well as three Midwestern states that Bush is trying to reclaim from Democrats: Minnesota, Wisconsin and Iowa.

Bush aides said they would continue to fight for Michigan and Oregon, though Kerry is favored in both states. Colorado, Arizona and Nevada also remain in the mix.

But as Election Day nears, each campaign will shift its advertising and ground forces from one state to another to maximize their impact.

“There’ll be a strong message push, as well as efforts to strengthen the grass-roots,” said Bush campaign manager Ken Mehlman. “You’ll hear the president talk about the war on terror and the economy.”

“We always said it would come down to these two big issues and our focus in the next 2½ weeks will reflect that,” he said.

Another perhaps more important campaign focus: Making sure they get their people to the polls.

Democrats are generally believed to have done a better job on the ground in 2000, spurring Al Gore to victory in the popular vote; Republicans performed better in congressional elections two years later, seizing the Senate back from the Democrats.

It’s not just the campaigns and parties that have organized get out the vote drives. Independent groups such as the Democratic-leaning Americans Coming Together are also trying to enlist new voters and get them to polls.

Tactics for both parties include phone banks, e-mail and face-to-face, door-to-door contacts.

“We have a massive number of volunteers,” Kerry campaign manager Mary Beth Cahill said. And they have but one goal: “To reach as many people possible on the final days.”

While the debates aided Kerry more, Rothenberg said the overall contest is still a toss-up, and there are still a few unexpected “twists and turns” to come, be it a campaign development, a scandal or events on Iraq or Afghanistan.

“Neither of these guys has been able to put the other guy away when they had the opportunity,” Rothenberg said. “And I don’t believe that one of them is going to put the other one away in the next 2½ weeks.

“It’s going to go down to the wire.”