President Obama showcased his comedic side as he formally welcomed British Prime Minister David Cameron and his wife Samantha to the White House this morning.

"It's now been 200 years since the British came here, to the White House - under somewhat different circumstances," the president joked about the British burning of the White House during the War of 1812. "They made quite an impression. They really lit up the place."

The prime minister returned the ribbing. "I am a little embarrassed, as I stand here, to think that 200 years ago my ancestors tried to burn this place down. Now, looking around me, I can see you've got the place a little better defended today," Cameron said as he looked out at the impressive display of members from the U.S. Armed Forces gathered on the South Lawn. "You're clearly not taking any risks with the Brits this time."

While this morning's pomp and circumstance formally marked the start of the prime minister's visit, Obama and Cameron kicked things off Tuesday with an NCAA tournament game in Ohio, where the prime minister said he learned "some new words - alley-oops, brackets, fast breaks."

"Last night, as president, I shared with the prime minister a uniquely American tradition of bracketology. March Madness," Obama boasted. "He's learned to appreciate one of our great national pastimes. His team has told me he has decided to install a hoop at 10 Downing Street."

All joking aside, the president and prime minster have a full day of meetings and a long agenda to cover, including the Afghanistan war strategy, unrest in the Middle East and the global economy.

"Whenever an American president and a British prime minister get together, there is a serious and important agenda to work through. And today is no different. Afghanistan, Iran, the Arab Spring, the need for trade, for growth, for jobs in the world economy, the biggest issues in the world - that is our agenda today," Cameron said.

Stressing the unity of their alliance, the president described the relationship between the two nations as "rock-solid" and "the strongest that it has ever been."

"The reason is simple. We stand together and we work together and we bleed together and we build together, in good times and in bad, because when we do our nations are more secure, our people are more prosperous, and the world is a safer and better and more just place," Obama said.