People in Saint Peter's Square watch a live television screen showing cardinals entering the Sistine Chapel to begin the conclave (Reuters/Stefano Rellandini)

When the new pope is chosen, he'll select a papal name. And oddsmakers are betting his choice will be Leo -- though Gregory, Pius and Peter also sound like good picks.

That's according to the oft-quoted, the Irish gambling site that has placed more than $450,000 in papal bets. But the guesses aren't exactly wild conjecture. Papal naming dates back to 533, when Mercurius switched out his name for the more Biblical John I, and Vatican-watchers say the pope's name choice reflects the issues and philosophy of his time.

"They’re thinking about something when they choose this name," William Portier, the chair of Catholic theology at the University of Dayton, told Canada's CTV. "It’s not just something that they think sounds good -- they consider it to be a weighty thing.”

For instance, picking Leo -- current odds, 47 percent -- would pay tribute to the late 19th-century Pope Leo XIII, who wrote extensively on social justice issues and tried to calibrate the church with the modern world. A Leo XIV would theoretically be "a modern social-justice pope," Michael Dougherty theorizes at Slate.

But picking Pius -- current odds, 18 percent -- would be "kind of scary to me," said Portier, the Catholic theologian. Pius XI, who led the church during Napoleon's reign, made his mark as a traditionalist defying secular states.

Both names have been popular with past popes, according to a pretty amazing chart by The Economist that shows the frequency with which certain names have been used.

Aside from frontrunners like Leo and Pius, the pope can choose from roughly 80 names that have been used by his predecessors, though some of the more ancient options (Zephyrinus, Anacletus) seem unlikely.

Benedict XVI chose his name to emulate Benedict XV, who worked for peace during World War I. John Paul II honored his immediate predecessor John Paul I, who died a month into his term.

Peter is also a long shot, given a long-standing tradition of deference to the first pope. The name's solid odds on Paddy Power might reflect the sudden resurgence of a 12th-century prophecy, which claims the 112th pope will be a Peter. The prediction also says that the world will end with his reign, though, so spend those winnings quickly.

Update: This post originally used the incorrect Roman numerals for the 18th-century Pope Leo XIII and a theoretical future Leo XIV. It has been updated with the correct numerals.