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With less than two weeks until the midterm elections, the Democrats’ chances of retaining the Senate keep hovering around 33 percent. Within this 33 percent — and the complementary 67 percent chance for Republicans — are ever-shifting combinations of states that would put one party or the other in control of the Senate.

Here we lay out the five most likely paths to a majority for each party.

Democrats have been the underdogs in this contest for almost the entire year. As David Leonhardt discussed last week, 33 percent does not equate to a Republican victory, but being the underdog means that the Democratic margin for error is thin. Democrats can afford few of what you might call unforced errors — losing a Solid or Likely Democratic seat like those in Michigan or Minnesota. A loss in a single one of those seats would drop Democratic chances of holding the Senate to 6 percent.

In addition to these seats, each of the five most likely paths to a Democratic majority requires wins in Kansas, North Carolina and New Hampshire. We’ll talk more about Kansas and the complicating factor of Greg Orman below, but North Carolina and New Hampshire are both leaning Democratic — each at 81 percent in the Upshot’s latest forecast — and Democrats should be able to win both.

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With a Kansas victory, that would leave them needing just two more seats to bring them to 50, which, along with Vice President Joe Biden’s tiebreaking vote, would allow them to retain control of the Senate.

The path of least resistance to 50 means winning at least two seats among Colorado, Georgia and Iowa — three races that lean Republican to a varying degree but that are still within easy reach for the Democratic candidate. Win two or more of these three, and Democrats’ chances of controlling the Senate rise to 75 percent. The different permutations of these states constitute the four most likely roads to a Democratic Senate. In the fifth most likely scenario, Democrats lose in both Colorado and Iowa yet secure upset victories in Arkansas and Georgia, where Michelle Nunn appears to be narrowing the lead of the Republican David Perdue.

Republicans are playing from a better position and have more room to maneuver (you’ll note that the chances of their majority scenarios are far higher than those for the Democrats). Each of their five likeliest scenarios involves taking the 17 seats that the Upshot model categorizes as Likely or Solid Republican, which — along with their 30 continuing seats — brings them to 47. They then tack on wins in Alaska, Arkansas and Colorado to bring their total to 50.

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At this point, the G.O.P. would need only one more seat to bring it to a majority (which assures the addition of the next senator from Kansas to its caucus as well, regardless of whether that senator is Pat Roberts or Greg Orman). To surpass 50 seats, the top three scenarios involve winning Georgia or Iowa (or both).

The two next likeliest scenarios are what some might describe as “Republican wave” elections: Republicans take both Georgia and Iowa in addition to unseating either Senator Kay Hagan in North Carolina or Senator Jeanne Shaheen in New Hampshire, leaving the G.O.P. with 54 seats and a solid majority.

By now, you may have noticed that Kansas is the common thread running through these possibilities. In all five likeliest scenarios for both parties, the majority party caucus includes the senator from Kansas. To some extent, this is a result of the way we framed the question. Because Greg Orman, the independent candidate, has specified that he would caucus with the majority party, an Orman win (the Upshot forecast model puts his odds at 48 percent) entails that Kansas will go to the majority.

For the Republicans, this guarantees that every combination of states leading to a Republican majority will include Kansas by definition. (If Mr. Roberts wins, the seat goes Republican, and if Mr. Orman wins, since Republicans have a majority, the seat also goes Republican.)

But note: Four of the five likeliest scenarios for Democrats involve relying on Mr. Orman to bring them to 50 seats. The Upshot model, named Leo, assumes that if Mr. Orman is faced with a Senate composed of 49 Democrats and 50 Republicans — with the question of majority control falling to him — he will caucus with the Democrats. But this seems like a thin reed upon which to rest their Senate hopes. What if we’re more ambivalent about what Mr. Orman would do if Senate control came down to him, and we assign Mr. Orman to either party at random instead?

We did a special run of Leo to test this theory, and even after randomizing Mr. Orman’s caucusing decision, four of the five likeliest Democratic paths to a majority still go through Kansas. The state hasn’t elected a Democrat to the Senate since 1932 — the longest streak of any state by far. Yet this year, the Democrats may very well find themselves owing their Senate majority — or lack thereof — to the outcome of the race in Kansas.