And Mr. Bloomberg has said in his ads that by self-financing his campaign, he is not doing the bidding of any donors — playing to voters who worry about politicians beholden to special-interest groups.

What viewers may see from Mr. Bloomberg

When he first ran for mayor, in 2001, Mr. Bloomberg looked bored, rolling his eyes and sighing as his opponent spoke at one of two debates in the general election. In his 2005 and 2009 debates, Mr. Bloomberg kept those gestures to a minimum.

How Mr. Bloomberg may explain his past

Mr. Bloomberg recently apologized for comments he made in 2015 about stop-and-frisk, the policing strategy that was found to be unconstitutional in the way it was practiced in New York City during his tenure.

He will be asked about those comments and other remarks he’s made over the years.

In a 2001 debate, Mr. Bloomberg was asked about quotes attributed to him, including one that characterized domestic violence as a quality-of-life crime. Mr. Bloomberg, visibly upset, responded by saying the words “were certainly said, but out of context.”

Over the years, he has responded more calmly to such questions. For example, in 2005, he was asked about having said poor people get better health care than rich people. “Do you honestly believe those words?” his debate opponent asked.

Mr. Bloomberg took a breath and gave his original comment a different spin. “What I was saying is I cannot tell you how proud I am of the progress our public hospitals, our 11 public hospitals, have made.”

An early rival of Mr. Bloomberg’s will be watching

The first Democratic politician to debate Mr. Bloomberg — then a Republican — was Mark Green. At the time, he was the New York City public advocate, and they squared off in the 2001 mayoral general election.