THE ASSISTANT CRUISE director, Ronnie Reskseit, strolls the sun deck with a bright yellow T-shirt emblazoned on the front with "White Star Line, Titanic, Maiden Voyage." On the back, in large black lettering, is "April 14, 1912," the date the Titanic struck an iceberg and sank.

Ronnie walks to the largest of four swimming pools on the sun deck and asks four bikini-clad young women to jump into the pool. He tosses in maybe 500 ping pong balls.

"Okay, ladies," Ronnie bellows over a loudspeakers, "the winner is the girl who can stuff the most ping pong balls into her bikini top in two minutes. The loser gets the boobie prize."

Later that night, in the ship's elaborate gambling casino, a woman passenger bets the limit - $200 - on the crap table. She loses. But the pit boss, Raymond Hernandez, a natural born extrovert with a blue tuxedo, pushes back half her chips.

"Hate to see a customer lose too much at once," chuckles Hernandez to the utter bewilderment of veteran gamblers.

It's no-holds-barred and absolutely sacred on the 27,250-ton cruise ship TSS Carnivale. The TSS stands for "Turbine Steam Ship.") The Carnivale and her sister ship, the Mardi Gras, are billed as the "fun ships" by the Carnival Cruise Lines. They operate out of Miami, dumping around 2,000 passengers a week into Caribbean ports where they swoop up Cutty Sark and J&B Scotch for $2.75 a bottle, Beefeater's Gin for $2.95 and imported cigarettes for $2.75 a carton.

Perfume is also a top buy at "duty-free" St. Thomas. Seiko wrist watches and Yashica and Konica cameras may bring savings of from 10 per cent to perhaps one-third. But potential buyers of cameras, watches, field glasses and tape recorders should check prices at their hometown stores first to make sure they are getting a genuine bargain.

The Carnivale sails from Dodge Island in Miami ever Saturday for a seven-day cruise to San Juan, Puerto Rico; St. Thomas, U.S. Virgin Islands; and St. Martin, an island in the Antilles controlled jointly by the Dutch and French. The Mardi Gras leaves each Sunday for a seven-day cruise to San Juan, Nassau and St. Thomas.

When my wife, Rosemary, son Rudy, 12, and I sailed on the Carnivale this summer we became part of a mushrooming trend that has turned Miami into the No. 1 cruise port in the world.

Douglas Gillett, marketing and promotion director for Port of Miami, said around 90,000 passengers sail out of Dodge Island each month on six different cruise lines. In 1976, Gillett said, Miami became the first port in the world to handle 1 million cruise passengers in single year - the total was 1,026,875. The growth has been dramatic: 1950, 61,000 passengers; 1960, 136,275; 1970, 569,366.

"We expect to hit the million mark again this year," Gillett said. "The trend is definitely upward." One major reason for the boom is the proximity of Miami to Caribbean ports, allowing travelers to reach calm, warm water quicker - a special bonus in winter cruising.

At the same time, as a public affairs officer for the Port Authority of New York and New Jersey confirmed, the number of passengers going through the modernized New York City Passenger Ship Terminal has dropped. The passenger count for persons sailing either in or out, whether on cruises or straight destination voyages, totaled 626,368 in 1973 and was down 374,387 in 1976.

He said the reason for the decline is that many lines that formerly operated cruises out of New York - such as the French Line and Italian Line - have stopped using the port. And many vessels have been taken out of service entirely.

Another New York port spokesman reported "some resurgence this year," crediting aggressive promotion by travel agents who have offered packages combining a few days in New York City with the cruise. The continuing crisis in New York, however, may have a negative effect on cruising from that port, counteracting the positive note struck there in May when Princess Grace of Monaco christened Cunard's new liner, the Princess.

Cruise lines now operating out of Miami Gillett said, include the Carnival Lines, Commodore Lines, Royal Caribbean Lines, Norwegian Caribbean Cruise Lines, Eastern Steamship Lines and Monarch Cruise Lines. In the winter, Holland America Lines sends in the statendam.

There are an average of 15 sailings each week. The vessels cruise for periods ranging from three days to two weeks. A three-day trip by the Eastern Steamship Lines "SS Emerald Seas" will take you to Nassau for fares ranging from $165 to $295 in the "off" season. A four-day trip on the same vessel going to Nassau and Freeport will run $200 to $375, in season, and $180 to $355 at other times.

The Royal Caribbean Lines has three ships, two of which - the Nordic Prince and Sun Viking - make two-week cruises. The Sun Viking, for example, will visit San Juan, St. Thomas, St. Lucia, Barbados, Grenada, LaGuaira, Curacao and Port au Prince.

Gillett said between six and eight vessels leave for a cruise each Saturday; two on Sunday, three on Monday, and three on Friday. Marketing surveys show many passengers drive their cars to Florida and combine their cruises with trips to Orlando to see Disney World, Circus World, and other local attractions.

On our one-week trip on the Carnivale in July, we found the port facilities operating efficiently. We parked on the dock for $2 per day, payable in advance. Our tickets were picked up at dockside in four or five minutes. Boarding the ship took another 10 minutes as we waited in lines to record our preference of eating at either the first or second sitting.

The Carnivale, formely the "Empress of Britain," was built in 1956, converted in 1966, and completely refurbished in 1976. Cruising at 21 knots, it has a capacity of 1,350 passengers but normally carries about 1,000, plus a crew of about 500. The Mardi Gras, the same tonnage and speed as the Carnivale, was built in 1961 and converted and refurbished in 1973. Its full capacity is 1,240 passengers, with a normal load of 900 to 1,000.

Fares on both vessels start at $395 off season and $425 in season, based on double occupancy. They escalate to $950 and $980 for a verandah suite. All cabins have full facilities.

We had a lovely outside cabin with a porthole and a reproduction of an Italian painting. There were two lower bunks with two upper bunks that folded down - only one of which we used. Rudy would climb into the upper late each night announcing. "Here I go into the eagle's nest."

It was to be eight days and seven nights of escapism. Seven days to be kooky, gamble all night, grow fatter eating as many as eight meals a day, and take part in such crazy feats as beer-drinking contests, body-feeling (to see if you can wear blindfold and pick out your husband's or wife body from among other men or women), and pillow fights where you get knocked off giant horses into foam rubber mattresses.

For 50 cents per shell you could take a 16-gauge shotgun and go skeet-shooting off the stern of the 640-foot, red, white and blue ship, or hit golf balls off the stern. They had a dance band, comedian, puppeteer, male and female vocalists, bingo every night, a movie theater and a discotheque open to 3 a.m. For the rare rainy days, there was an indoor swimming pool. We had been on a number of ships before but had never seen one with five swimming pools.

The first evening on board we were introduced to the entire cruise staff, which included a young woman who announced that she was the ship's masseuse and appointments for a massage could be made at the purser's office.

There were also such standard passenger ship facilities as a boutique, beauty salon, barber shop, health club, sauna room, photo gallery, libarary, children's playroom, Ping-pong and shuffleboard. If anyone ever went to bed it wasn't through boredom. When the last band stopped 3 a.m., and the casino closed, passengers would go to the top deck and drop coins into a juke box and continue dancing and drinking to sunrise.

The Carnivale, like many of the cruise ships sailing out of Miami, is a gambler's paradise. Many of the ships now rely on the gambling as a major source of revenue. The Carnivale had two crap tables, six blackjack tables, a roulette table, wheel of fortune, and 60 slot machines.

My family has cruised aboard the American President Lines, Matson Lines, P&O Lines and others, and thus we could make comparisons. In general, we found the food and service on the Carnivale quite good. A number of the waiters and bus boys were Italian, but all had a good command of English.

There seemed to be no definite age group for the passengers - the median would probably be between 35 and 40.