#Inside the original Rat Pack and its members’ Las Vegas legacy

In February 1960, crooner Frank Sinatra had an Oscar for “From Here to Eternity” and hit records under his belt. But he feared cultural irrelevancy. Elvis Presley was everywhere. Cool kids danced to “The Twist,” and The Beatles had just formed in Liverpool.

“Frank 100 percent knew that his window was closing. He needed something big,” Richard A. Lertzman, co-author of the new book “Deconstructing the Rat Pack” (Prestige Press), told The Post.

Sinatra’s next move would create the legend of the Rat Pack — and cement the Las Vegas Strip as an international party destination. “Before the Rat Pack’s arrival, Vegas was all Jimmy Durante and Cyd Charisse — old hat,” said Lertzman.

Sinatra was bopping through town in ’59, mulling a big payday while his elite status still held. Meanwhile, Sands casino publicist Al Freeman was looking to take Vegas beyond its status as a cow town with some diversions.

“Al wanted a mega-act to put Vegas on the map,” Lertzman said. “Frank loved the idea and started assembling a group. He had done the movie ‘Some Came Running’ with Dean Martin and thought it would be good to work with him again. Sammy Davis Jr. had just lost an eye in a car accident and Frank wanted to back him. Then he needed a journeyman comic who would not suck air out of the room: In came Joey Bishop. Peter Lawford was married to Patricia Kennedy, and Sinatra was drawn to the Kennedy family’s power.”

So Lawford — characterized by Lertzman as “a little gossip who told Ava Gardner about [her husband] Frank f–king around” -— was improbably in as well. Lawford also came with a gift: a script for a heist movie called “Ocean’s 11” that had been slipped to him by George Clayton Johnson, a Malibu gas-station attendant and aspiring writer.

Sinatra swung a deal where they would shoot “Ocean’s 11” in the casino by day and do two shows a night for February, an event called “The Summit.” It was an instant hit, said Lertzman: “The Sands had 2,800 rooms and 35,000 requests for reservations in February.”

Picking up on a term coined by Lauren Bacall to describe husband Humphrey Bogart and his Hollywood retinue (including Sinatra), the press called the guys the “Rat Pack.” Sinatra despised the name.

Brimming with seemingly improvised gags about liquor and womanizing, The Summit was actually tightly scripted by TV writer Don Sherman (whose daughter Amy Sherman-Palladino would go on to create “Gilmore Girls” and “The Marvelous Mrs. Maisel”).

“This was strictly business. Dean [who had a boozy reputation] drank apple juice on stage, and every show was identical. These were middle-aged men, working hard,” said Lertzman. “Frank made $3- to $4-million. The other guys made six figures.”

And it wasn’t even like they were truly pals: “Joey was being used, and Sinatra hated Lawford’s f–king guts.” But he loved proximity to Massachusetts Sen. John F. Kennedy, who showed up — as did ­Marilyn Monroe and Judy Garland — at a few performances.

Kennedy had recently announced his presidential run, and associating with the Rat Pack made him appear cool. It also helped to fund JFK’s campaign.

“Joe Kennedy [JFK’s father] promised the mob guys who ran Vegas that John would protect them in exchange for a $1 million contribution,” said Lertzman. “A satchel with $1 million was left in the suite of Carl Cohen [a mobster who was president of the Sands] for John to pick up and hand off to Joe. JFK was the bag man! Lawford brought Sammy to see [the bag]. Sammy started telling everybody.”

Over the next year, the Rat Pack played Miami, supported Kennedy at the Democratic National Convention and were to headline his inauguration party. Bishop hosted and Sinatra sang, but Davis was barred because Joe Kennedy feared racist blowback from Davis’ engagement to Swedish actress May Britt. Martin bailed, which created bad blood between him and Sinatra.

Bishop was frozen out after he was asked to fill in for Sinatra at a gig and tried strong-arming Sinatra for $50,000. Then, Joe Kennedy put the kibosh on his son visiting Sinatra at the singer’s Palm Springs home — where a heliport had been built especially for the president — due to Sinatra’s increasingly public mob associations. Lawford was forced to break the bad news, which pretty much killed off the already hobbled Rat Pack.

“JFK flew, instead, to Bing Crosby’s place in Palm Springs,” said Lertzman. Sinatra was furious. “He grabbed a mallet and started wrecking things in his house. He cut Lawford from [his film] ‘Robin and the Seven Hoods’ and tried to blackball him in Hollywood.”

Despite the Rat Pack’s brief shelf life, the legend of their ring-a-ding Vegas good times persists. Marveled Lertzman: “People just love the world that those guys represented.”