Shabby Saudi Prince Abdul Aziz bin Fahd spent a fortune renting out the entire Lucky Strike bowling alley on 42nd Street till 3 a.m. on Tuesday night, throwing a wild party rife with wall-to-wall models, bottle service — and Leo DiCaprio.

The prince — who popped up on The Post’s front page last month heading into a Chelsea nightclub in dad jeans, sandals, and carrying a cane and large Slurpee cup with a bendy straw — paid for a lavish private party with 200 of his “closest friends,” including Naomi Campbell, Kardashian pal Jonathan Cheban and Fox Sports analyst and former Giant David Diehl.

The prince, whose fortune is said to be more than $10 billion, filled the venue with young models, who rocked out to a DJ and enjoyed top-shelf bottle service all night on his tab.

But the only person who appeared not to be having a wild time was the wretchedly robed royal himself, who “moped around,” sipping from another Slurpee cup. A source told us, “The prince was wearing sandals, jeans. He had a large 7-Eleven Slurpee cup he was sipping away at. He moped around to each lane with a blank stare.”

The prince turned up around 1 a.m., and “the whole place was [full of] models and hot girls. The door was strict with a lot of security, and there was free bottle service all night, paid for by the prince. This isn’t the first time he’d done this.”

Another attendee added, “The party was insane. He took over the whole bowling alley and there were hundreds of girls. It was better than any club, and the prince walked around saying ‘hello’ to people with a Slurpee cup. He must love the models, as there were lots of them there. Leo and Naomi were there, and she had a cast on.”

The royal comes to New York regularly and spends millions renting private venues for parties and clubbing with his entourage of guys.

He’s often seen sipping from a soda cup. A source tells us, “There have been attempts on his life, so he’s paranoid. He’ll only drink from that cup.” Alcohol is illegal in Saudi Arabia, so its contents remain an international mystery.