For most producers, a pre-Broadway run of a new play is a necessity. Out-of-town tryouts or non-profit engagements allow a show extended time for fine-tuning — and for development away from the often harsh focus of the New York limelight.

But Terrence McNally’s “Deuce,” starring Angela Lansbury and Marian Seldes, hit Broadway cold when it began previews April 11 for a May 6 opening. The play is the third world preem to bow directly on the Rialto this season from producer Scott Rudin, following “The Vertical Hour” and “The Year of Magical Thinking.”

Rudin dismisses the idea that the process of developing a new piece on Broadway is more exposed than the same process elsewhere. “If you’ve got a new play by Terrence McNally, directed by Michael Blakemore and starring Angela Lansbury, people are going to go wherever it is,” he says.

Artistically, McNally doesn’t feel the strain — or at least, not any more than usual. “There’s kind of a misconception that the stakes are lower Off Broadway,” he says. “For me, the stakes are always high wherever we do our work.”

“I don’t think it makes a difference to us in the rehearsal process,” agrees helmer Blakemore (“Kiss Me Kate,” “Copenhagen”). “But there is the pressure of publicity and expectation.”

The glare of publicity around “Deuce” has been amped up primarily by the casting of Lansbury, a much-loved Broadway legend and four-time Tony winner, who, aside from special events, has been absent from a major New York stage since the 1983 “Mame” revival.

“Certainly in the past I’ve always gone out of town,” Lansbury says. “It’s a difficult proposition to do it under the beady eye of an audience.”

Which is to say that when early previews were a little rocky and initial buzz on “Deuce” was less than favorable, the entire Gotham legit world knew about it instantly.

Not that the uncertain start has hurt sales much. According to Rudin, the play has racked up an advance of more than $3 million — a strong showing for a non-musical, especially in a spring season crowded with straight-play competish.

Much of the pre-opening sales draw can be attributed to the appeal of Lansbury. It was her attachment to the project, originally slated as the final offering of the Primary Stages season at Off Broadway’s 59E59 Theater, that upped the ante to Broadway. The anticipated clamor to see Lansbury in a rare stage appearance prompted the move.

McNally first wrote “Deuce” — about two former tennis rivals, now in their 70s, in the stands at a tennis match — as a short play for a benefit for MCC Theater in February 2006. That incarnation was read by Zoe Caldwell and Seldes.

Lansbury and McNally have known each other for years, and the actress had planned to star in a slated Broadway run of the tuner “The Visit,” with music by Kander and Ebb and book by McNally. But that production fell apart when Lansbury pulled out to care for her ill husband. The actress also knew Rudin, having worked with him on the 1982 telepic “Little Gloria… Happy at Last.”

“You get your sea legs back,” says Lansbury of returning to the boards. But she also sees some changes in the biz since she was last a Broadway regular.

“The essence is still intact, the thrill of ‘putting on a show,’ but the economics of Broadway have changed,” she says. “Money used to be spent rather loosely in the old days. Theater today is a dollars-and-cents proposition.”

It is, and that’s one of the things keeping “Deuce” on the radar of Rialto insiders.

“Opening on Broadway means there’s a lot of attention on us,” Blakemore says. “At least the drum is being beaten.”