And Mr. Biden is concluding an eight-day bus tour across Iowa, during which he has said his goal is to win the caucuses, but his supporters privately say they would also be satisfied if Mr. Buttigieg won and denied Ms. Warren a victory.

It may seem a little confusing, but there’s a strategy behind the moves.



Mr. Sanders and Ms. Warren each covet the other’s progressive supporters but are wary about angering them by attacking each other. So Ms. Warren has begun drawing an implicit contrast by emphasizing her gender — a path more available now with Ms. Harris’s exit — and they are both targeting a shared opponent whom many of their fiercest backers disdain: Mr. Buttigieg.

The mayor has soared in heavily white Iowa, but has virtually no support among voters of color. So he started airing commercials in South Carolina spotlighting his faith and took his campaign there and into Alabama this past week — an acknowledgment that Iowans may be uneasy about him if he can’t demonstrate appeal with more diverse voters.

As for Mr. Biden, his supporters think he would effectively end the primary by winning Iowa. But they believe the next best outcome would be if Mr. Buttigieg fends off Ms. Warren there to keep her from sweeping both Iowa and New Hampshire and gaining too much momentum. They are convinced she’s far more of a threat than Mr. Buttigieg to build a multiracial coalition and breach the former vice president’s firewall in Nevada and South Carolina.

Meanwhile, no other hopeful is drawing more chatter in Iowa as a compromise choice among moderates than Senator Amy Klobuchar, who has spent more time in the state than any of the top candidates.

Taken together, the shadowboxing, bank shots and sheer uncertainty of it all reflect what a muddle this race has become. Besides the party’s unifying hunger to defeat Mr. Trump, the only clarity is the rigid divide among voters along generational, ideological and racial lines.