An American military officer who served at the border in 2003 and 2004 recalled Taliban fighters waving their rifles from the Pakistani side to taunt the Americans. “Our rules said we couldn’t follow them and we couldn’t shoot at them unless they shot at us,” the officer said. “But when we saw them over the border, we knew we should expect an attack that night. The only ones who recognized the border were us, with our G.P.S.”

That has been changing all year, however, and it is about to change even more, as the Americans gear up for an intensified war on both sides of the line simultaneously. The dispatch of 30,000 additional Americans to the Afghan side of the border will occur simultaneously with more intensive missile strikes from drone aircraft and Pakistani army offensives on the other side.

Ever since Osama bin Laden escaped American forces in December 2001, crossing the mountains of Tora Bora from Afghanistan into Pakistan, American strategists have spoken of a “hammer and anvil” strategy to crush the militants. Until now, the border has proven so porous, and Pakistani governments so squeamish about a fight, that the American hammer in Afghanistan was pounding Taliban fighters there against a Pakistani pillow, not an anvil.

Image ON PATROL G.I.'s in the Korengal Valley last April had to fight off an attack on their way to meet with tribal elders. Credit... Tyler Hicks/The New York Times

Now, Mr. Obama’s added troops are likely to be concentrated in the Taliban stronghold in Helmand and Kandahar in southern Afghanistan, and near Khost in the east. At the same time, the president has approved a major intensification of drone strikes in Pakistan, even as the Pakistani army continues a campaign against the militants launched this fall in South Waziristan, following on a counterattack that swept militants last spring from the Swat Valley.

“We finally have an opportunity to do a real hammer-and-anvil strategy on the border,” said Michael O’Hanlon, a senior fellow at the Brookings Institution who follows the Afghan war. “We’ve never done it before because we’ve had insufficient strength on both sides of the border or insufficient political will on the Pakistani side.” For years, in fact, Pakistani intelligence has played a double game with Islamist extremists, nurturing them as a force to use against Pakistan’s archrival India in the disputed territory of Kashmir and helping create the Taliban as a buffer against Indian influence in Afghanistan.

But as the mujahedeen who fought the Soviets in Afghanistan in the 1980s later turned on their American benefactors, so some militants in Pakistan have begun attacking the state that once encouraged them. Many in the Pakistani elite were stunned by the emergence in 2007 of the Pakistani Taliban and by the subsequent campaign of terrorist attacks against Pakistan’s power structure, including the assassination of Benazir Bhutto, suicide bombings in cities and an attack on the army headquarters in Rawalpindi in October.