First came a poll showing Board of Supervisors President London Breed holding a 2-to-1 lead in San Francisco’s mayoral race. Now there’s a new survey that shows the contest as a statistical dead heat.

This one, however, was commissioned by former state Sen. Mark Leno’s mayoral campaign — so take it for what you will. It shows Leno at 20 percent of first-place votes in the ranked-choice election, just behind Breed and her 21 percent. The poll has Supervisor Jane Kim at 13 percent and former Supervisor Angela Alioto at 8 percent.

More than a third of the 312 voters surveyed by phone from Jan. 20-23 were undecided. The survey’s margin of error was 5.5 percentage points.

The poll’s ranked-choice simulation showed Leno picking up enough support from other candidates’ voters to nose out Breed at the end. However, as pollster David Binder noted, there’s no way to guess how all those undecided respondents would affect the final count.

Oddly enough, Binder was the same pollster who did a survey a few days earlier for the Chamber of Commerce that showed Breed way ahead. He explained that the chamber poll question was a toss-in on a broader survey geared toward the November election, when more young and minority Breed voters would be likely to turn out than in June.

Binder also said Breed appeared to be receiving a significant bounce as acting mayor when that poll was taken — a bounce she won’t be getting now that she’s back to being a full-time Board of Supervisors president.

San Francisco Chronicle columnists Phillip Matier and Andrew Ross appear Sundays, Mondays and Wednesdays. Matier can be seen on the KPIX TV morning and evening news. He can also be heard on KCBS radio Monday through Friday at 7:50 a.m. and 5:50 p.m. Got a tip? Call (415) 777-8815, or email matierandross@sfchronicle.com. Twitter: @matierandross