Tired of betting against Tom Brady in the Super Bowl?

Try tossing some cash on President Trump, who is slated to give a pregame interview to CBS. Will he speak from the White House Map Room, the Treaty Room or the Roosevelt Room? There are odds on each.

BetDSI Sportsbook, a licensed sportsbook in Costa Rica, also offers chances to bet on whether Mr. Trump will pick the Patriots or the Rams, whether he will discuss the national anthem controversy or whether he will call out his “Make America Great Again” campaign slogan.

Although sports betting still dominates, bookies are increasingly eager to get into the political betting market and salivating over the prospect of taking odds on how many times Mr. Trump calls Sen. Elizabeth Warren “Pocahontas” or mentions her infamous ancestry test in a hypothetical 2020 presidential debate.

Dave Mason, the BetOnline.ag sportsbook brand manager, said the market has been growing over the years. Election Day 2016 attracted 15 times more action than the 2012 contest.

“I am not a big political guy, but it was probably one of the most memorable days I had working in this business,” he said.

Scott Cooley, a spokesman for BetDSI, said the presidential election surpassed the Super Bowl that year.

And like so many other areas of modern life, Mr. Trump has made it more interesting.

James Murphy — an international gambling specialist, head of the SportsInsider website and oddsmaker who has set numbers on the outcome of the Lingerie Football League and how many people would get “whacked” on the season premiere of HBO’s “The Sopranos” — described the president as “the Elvis and Beatles of political betting.”

He said that also accounts for why betting on American politics is so big in places like England.

“Whatever you think of Trump and Hillary Clinton, they were kind of the perfect storm of ugly Americanism in Europe,” Mr. Murphy said.

It also doesn’t hurt that gambling in, say, England doesn’t have the stigma that it often has in the U.S.

While political gambling for money is generally illegal in the U.S., that hasn’t always been the case.

A century ago, Mr. Murphy said, gambling was considered a good way to figure out where the political winds were blowing — similar to opinion polling today.

“The big difference between polling and betting is you have skin in the game with the bet,” he said. That can make oddsmakers more accurate than polls in some cases.

There are ways to put money on politics legally. Futures market websites such as PredictIt allows “traders” to buy shares on “yes” or “no” questions such as whether Mr. Trump would build his border wall by the end of his first year in office.

For the most part, though, elected officials in the U.S. have effectively banned political gambling.

“For some reason, they think it undermines the political process, which is funny because the political process is doing a good job of that itself,” Mr. Murphy said.

That means foreign markets are in a dominant position. They get to bet on, among other things, how many times Mr. Trump would refer to the “wall,” “crooked Hillary” or “small hands” in debates.

“His actions make it easy to create newsworthy prop bets and futures markets,” Mr. Cooley said. “We’ve offered props anywhere from which member of his administration will be fired next to sports teams visiting the White House.”

November’s midterm elections also were heavily wagered, and Mr. Cooley said he expects the 2020 Democratic presidential race to be “the most wagered-on political event in betting history.”

The latest 2020 odds from BetOnline show odds of Mr. Trump winning a second term at 2-1, followed by Sen. Kamala D. Harris of California at 6-1, former Rep. Beto O’Rourke at 8-1 and former Vice President Joseph R. Biden at 14-1.

Those looking to get the biggest bang for their buck could put their money behind LaVar Ball, the father of three basketball players who rounds out the list at 250-1. Wagers also can be had next week when Mr. Trump delivers the State of the Union address, including on the color of the president’s tie, the number of times he says “crisis” and the length of the speech.

“There is not a lot of scientific data [on political betting], where the Super Bowl spread is tried and tested,” Mr. Mason said. “It is more coming up with stuff, throwing it against the wall and seeing what sticks.”

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