Independent U.S. Senate candidate Greg Orman, August 17th. Photograph by Mark Reinstein/Corbis

In national politics, Kansas is considered as Republican as they come: Mitt Romney carried the state in 2012 by twenty-two percentage points, and the last Democratic Presidential candidate to carry Kansas was Lyndon Johnson, in 1964. But this year, the reliability of Sunflower State politics seems to have been upended. With control of the Senate in a tight, uneasy race, Kansas may be a game changer on a national level, thanks to an unusually strong independent candidate.

The Republican incumbent, Pat Roberts, is heartily disliked by Kansas voters: his approval rate is only twenty-seven per cent, even lower than the thirty-three per cent who approve of President Obama’s performance. Roberts, who is in his third term, recently survived a primary challenge by the radiologist Milton Wolf. Dr. Wolf ran under the Tea Party banner and gained attention for posting gruesome X-ray images of gunshot victims on his Facebook page that were accompanied by macabre banter with his friends. Still, Roberts’s margin over Wolf was only forty-eight per cent to forty-one per cent. It seems that Kansas voters will seriously consider just about anyone but Roberts.

Except, maybe, a Democrat. Shawnee County’s district attorney, Chad Taylor, cruised to a relatively easy victory in the state’s Democratic primary, but in recent general-election surveys, Taylor trails Roberts by a median of six percentage points. Kansas has not sent a Democrat to the Senate since Franklin D. Roosevelt was President, and it’s unlikely that it will this year.

The third candidate in the race is the businessman Greg Orman. Orman, who comes from Olathe, a city in the eastern part of the state with about a hundred twenty-five thousand people, has been crisscrossing Kansas by bus, meeting voters and preaching a message of fiscal restraint and social tolerance. A former Democrat, he decried the gridlock and lack of action in Washington, and now declines to identify himself as a member of either major party.

Orman’s formula seems to be working with Kansas voters. Despite the fact that thirty per cent of voters still have not heard of him, a recent Public Policy Polling survey shows that in a one-on-one matchup, Roberts would lose by ten percentage points, forty-three to thirty-three. In contrast, Roberts would survive a one-on-one matchup with Taylor by a margin of four points. So if you’re Roberts, you either want Taylor and Orman to split the vote, or to run against Taylor alone.

This means that, paradoxically, Pat Roberts’s political future may depend on his Democratic opponent staying in the race. And that, in turn, affects the balance of power in the closely contested Senate—by converting a Republican seat into an independent one.

These histograms summarize where control of the Senate stands as of today. They show billions of possibilities and take into account the uncertainties of every Senate race this year. The first chart is the over-all distribution of outcomes if the Kansas contest remains a three-way race. As things stand now, the odds of Democrats retaining control are almost exactly even.

In contrast, the second chart shows the outcomes if Taylor drops out, leaving a two-man race between Orman and Roberts. Currently, there are two independent senators who caucus with Democrats, Bernie Sanders and Angus King. If they and the Democrats win exactly forty-nine seats, Orman would have it in his power to provide—or deny—the critical fiftieth vote to control the chamber. In all the outcomes simulated in my model, this event has an almost thirty per cent probability of happening. Added to the Democrats’ chances of gaining control without Orman, the total probability of combined Democratic and independent control would be eighty-five per cent—a total game-changer.

Two people who would not like this turn of events are the current Majority Leader, Harry Reid, and Mitch McConnell, the Republican who wants to replace him. Orman says that both men “have been too partisan for far too long” to gain his vote of confidence. In this respect, Orman is independent of both parties.

Orman matters, perhaps more than he knows. In the current Senate, Republicans have blocked legislation and dramatically slowed the consideration of judicial nominees. If they attain majority status, the gridlock could worsen. With so much at stake, if the national Republicans were to take a purely Machiavellian perspective, they might find ways to help Taylor to stay in the race. This fall, Taylor may find himself some unexpected allies.