Since the days of American Prohibition in the 1920s, the Bahamas have been a favourite getaway for those looking to kick back, relax and have some offshore fun, far from heavy-handed US laws.

These days, this often means gambling the night away at one of the glittering casinos found on the small island of Grand Bahama or in the capital of Nassau on the island of New Providence. Or, if you really want to amp up the action, take yourself on an island- and casino-hopping tour of the region that leaves directly from US shores.

Start your sailing adventure on Celebration Cruise lines’ one-night Bahamas Cruise, which departs from Palm Beach, Florida every other day with a casino full of craps, roulette and 127 slot machines. As you roll the dice, get in a tropical mood with a fruity Bahama Mama (dark and light rum, plus a liquor cabinet’s worth of fruit juices and liqueurs).

The next morning, hop ship in Freeport, Grand Bahama’s main city instead of returning to Palm Beach. In the 1950s, this was the go-to destination for Rat Pack party boys like Frank Sinatra and Sammy Davis Jr, who turned the town into their own private playground of jazz, cigars and card games.

Today, most of the action is in the seaside settlement of Lucaya, a tropical-coloured village of hotels, bars, boutiques and – most importantly – the Treasure Bay Casino at the enormous Grand Lucayan Resort; get there by taxi from the cruise boat harbour west of town. The casino features some 3,250sqm of slot machines, craps tables, blackjack, roulette, poker and more. You can even catch a Vegas-style dinner show on Thursday nights, or hang out in the cabaret lounge with the other high rollers. Once you are done at the tables, slip out back for a bowl of tangy conch salad at Billy Joe’s on the Beach, eaten at a waterfront picnic table while digging your toes in the sand and sipping a cold local Kalik beer. Spend the night in one of the hotel’s luxe guest rooms.

From Freeport, a 45-minute morning flight will get you to Nassau, the Bahamas’ fast-living capital, in time for breakfast at Café Skans, a local favourite (order the fish stew and johnny cake, a sort of corn bread, if you want to eat like a Bahamian). Grab a taxi to the Crystal Palace Casino in the retro-futuristic Wyndham Nassau Resort; the black-and-gold decorated casino rings with the sound of lucky slot machines morning and night. Play the ponies, try your hand at roulette or bet it all on blackjack. If you get tired – or, heaven forbid, run out of cash – head out back to lie in the powdery sand of Cable Beach.

If you win big, take your bounty to the duty-free shops on Bay Street in downtown Nassau.  An island-made batik shirt – or perhaps an emerald ring -- could make for a fitting souvenir. When hunger strikes, head directly to Arawak Cay (known locally as “the fish fry”), a colourful outdoor village of painted shacks where tourists and locals alike mix it up over plates of hot “cracked” (deep-fried) conch and plastic cups of “sky juice”, a high-octane mix of gin, coconut water and nutmeg.

For the grand finale, hop a five-minute water taxi across the bay to Paradise Island, home to the Atlantis Resort, a massive hotel, casino, restaurant and entertainment complex that looks like a cross between Disney World and Ancient Rome. Inside the resort's signature-pink 23-storey Royal Towers, the vast casino on the ground floor is the beating heart of the entire Atlantis operation. All 80 game tables and 850 slot machines form a kind of orbit around a multi-story glass sun by American artist Dale Chihuly, around which swarm scantily-clad resort guests, crisply-attired croupiers and more than a few celebrities (rumoured recent sightings include Kim Kardashian and Justin Bieber). Repair to the Baccarat Lounge for a round (or 20), or, if poker is more your flavour, choose between the Let It Ride and Caribbean Stud tables. Giant international tournaments are held here, so keep your eyes peeled for your favourite poker geniuses. This being the Bahamas, you can go as casual or as glam as you like – James Bond style tuxes and Hawaiian shirts mingle at the blackjack tables 24 hours a day.

At Atlantis, there is just as much action outside the casino as in. When dinnertime rolls around, head to one of the resort’s ultra-styled celebrity chef restaurants. For southwestern on speed, try Bobby Flay’s Mesa Grill, complete with cow hide chairs and a stadium-sized open kitchen dishing up spice-rubbed pork or ancho chilli-glazed salmon. Or hit up Nobu, one of the many outposts of the famed sushi dynasty, where Russian models and Armani-clad businessmen dine on slabs of rich fatty tuna sashimi at a long stone bar. Afterward, the resort’s much-hyped Aura nightclub is the place to see, be seen and drink expensive vodka. On high season weekends it can be almost impossible to get in – look out for special promotional deals on slightly less busy weekdays.

Oh, and when you have hit the jackpot, book yourself into Atlantis’s $25,000 a night Bridge Suite, in the sky-high archway connecting the two towers. May luck be a lady for you!