House Speaker John Boehner (R-OH) is telling everyone what most political experts already knew: the odds are in the Republicans’ favor to retain control of the House of Representatives. But Boehner adds a caveat: there’s a reasonable chance Republicans could lose control of the House, too.

Still, the political world exploded when Boehner laid out this stark assessment of conventional wisdom to FOX’s Bill Hemmer in a recorded interview on Monday, scheduled to air on America’s Newsroom at 9 am ET today.

“I’d say there is a two in three chance that we win control of the House again. But there is a one in three chance that we could lose,” Boehner said. “We’ve got a big challenge and we’ve got work to do.”

It’s rare for a Speaker of the House to offer such a candid, on-the-record appraisal about electoral prospects. But let’s take a step back and truly consider what Boehner is saying: there’s a two-thirds chance the GOP holds the House, a one-third chance Republicans lose the House.

This isn’t a newsflash. And those who closely follow House contests know that while it’s more than likely the GOP holds the House, there’s always some scenarios where the Democrats might prevail.

But what’s unique here is that Boehner didn’t stop himself at just saying “there is a two in three chance” that Republicans maintain control of the House. One wonders if there would have been much consternation in the press had Boehner just left it at that and not defaulted to the pessimistic odds. Even though Boehner implied the “one in three” chance immediately after stating the “two in three” possibility, it’s likely that political reporters would have little to chatter about. While obvious under Boehner’s soothsaying, those gloomy odds would remain unsaid – and probably not command much news oxygen. But Boehner completed the syllogism by stating the rest of the handicap. Thus the headline becomes “Boehner says Republicans have a one in three chance of losing the House.”

So why did Boehner bother to complete the premise if the headline implies the possibility of a potentially negative outcome for his party?

It’s simple. Boehner presented the Republican Party with what’s called the “Monty Hall Paradox.”

For the uninitiated, Monty Hall is the legendary game show host of “Let’s Make a Deal.” The program’s touchstone came when Hall would ask a contestant to choose one of three doors. The show’s producers would often park a new car behind one of the three doors. But the show would also outfit the other two doors with booby prizes like goats, wheelbarrows, or faux vacations.

The contestant would choose one of the doors. But before Hall would open the doors to reveal what was behind them, he might inform the contestant that he would eliminate one of the doors from consideration. Now the contestant was down to two doors. Hall would then ask if the contestant wanted to switch from the door he or she originally selected to the remaining door.

And that’s where the Monty Hall paradox kicks in.

When there are three doors, the contestant has an equal chance of picking the winning door: one in three. But if Hall eliminates one of the incorrect doors, then the odds multiply in the contestant’s favor if he or she switches from the door they originally picked. In short, the contestant now has 50-50 odds.

So Boehner pretty much stated the general odds – and expressed concern about Republicans having a lock on the House.

According to Boehner, the odds for the GOP to hold the House are two in three. But like any good political strategist, Boehner sought to increase his party’s odds – by mentioning its deficiency. Unlike Let’s Make a Deal, Boehner couldn’t eliminate one of the doors to bolster Republican opportunities. But he could begin to improve the GOP’s chances by bluntly declaring where problems could creep and refocus attention on those races.

“We have 50 of our members in tough races. 89 freshmen running for their first reelections and we have 32 districts that are in states where there is no presidential campaign going to be run, no big Senate race – and we call these ‘orphan districts,’” Boehner said. “You take 18 of them – California, Illinois and New York, where you know we’re not likely to do well at the top of the ticket – and those districts are frankly pretty vulnerable.”

In fact, that bald statement by Boehner was designed to remind Republicans that holding the House is not going to be a pushover. It won’t be long until everyone is concentrating exclusively on the presidential sweepstakes. Republicans believe they have an excellent shot of capturing the Senate. But by stating the conditions of the House contests, Boehner reminds Republicans that they can’t take control of the House for granted. In this gambit, there’s no Monty Hall to disqualify one of the doors. But Boehner reminds the party faithful that there’s at least a door out there with a donkey lurking behind it.

Perhaps a Democratic donkey.

Democrats are well ahead of their Republican counterparts in fundraising. For instance, the Democratic National Committee has brought in nearly $155 million and the Democratic Congressional Campaign Committee (DCCC) has scored more than $83 million. Meantime, the Republican National Committee has pocketed close to $124 million and the National Republican Congressional Committee (NRCC) has raised $74 million. So, it’s entirely possible that Boehner’s effort might augment GOP fundraising for  House races.

But there’s risk in this.

Boehner’s “one in three” statement could also boost Democratic fundraising as they realize they have a chance to again secure the House of Representatives.

As things stand now, Democrats need to win a net of 26 seats to seize control of the House. DCCC Chairman Rep. Steve Israel (D-NY) told National Journal late last month that Republicans were successful in 2010 at winning seats “they had no business winning.” He says Democrats won seats in 2006 and 2008 “that we had no business winning.” So he’s hoping his party can “reclaim” some of those seats this cycle.

As Boehner said, the odds seem to favor Republicans. There are three doors in the Capitol Hill version of Let’s Make a Deal. Two of them feature the grand prize: control of the House. Boehner’s design is to energize the base and up cash flow.  And like those appearing with Monty Hall, both sides are searching for ways to increase their own odds – and leave the other side with a booby prize.