You won't find them advertised, and you may not even find them -- but, as Claude Rains once observed in mock amazement, it is shocking to "discover that there's gambling going on."

In Cairo, rounding up the usual suspects is relatively easy. There are three legal casinos: the Nile Hilton, the Sheraton and the new Marriott. The existence of the gaming rooms is not advertised -- that's against the law -- and they operate not only as a courtesy to foreigners but also because the Egyptian government gets half the house's take.

But forget everything you know about casinos. Cairo's differ greatly in style and clientele from casinos anywhere else in the world, and that is their charm. In a country where the prevailing religion forbids gambling, they represent a curious, low-key gambling mecca in the desert. Perhaps as a result, you won't find loud, Las Vegas types crowding the tables of Cairo. Pinky rings are hardly ever seen, no blue-haired women work slot machines, and no buxom blonds in slit cocktail dresses proffer free drinks.

Instead, there are turbans, burnooses and occasional designer blue jeans. The gamblers are so reserved and the casinos so small, one can hear the ivory ball skimming around the roulette wheel from across the room. When someone wins a tough hand at the blackjack table, there is little celebration; the winner quietly acknowledges his victory with a nod, bets are placed again, and another hand is dealt.

The games of preference are roulette, blackjack and -- upon demand -- baccarat. At the Sheraton, a craps table gathers dust in a corner, and in each casino a few slot machines stand silent sentry along the walls. Along with Americans seeking betting action, Cairo's gamblers come from the Persian Gulf states and Lebanon, and more than a sprinkling are Saudis who have escaped Riyadh or Jiddah long enough to enjoy the forbidden pleasures of gambling and drinking.

Bring your American dollars to Cairo's casinos -- Egyptian pounds aren't accepted for play. Which brings up the delicate subject of the overall usefulness of Egyptian pounds. Incoming travelers are required to buy $150 in local currency at airport banks before passing through customs, though enforcement is spotty. Visitors are also told to keep their exchange receipts if they hope to convert their extra pounds back into dollars at the end of their trip.

But there's an Egyptian Catch-22. In small print or (in some cases) in no print at all, is the regulation that requires vistors to spend at least $30 worth of Egyptian pounds for every day they're in the country -- and, sorry, credit-card purchases don't count. All too often, departing Americans who've overlooked the fine print make the painful discovery at the Cairo airport that they can't exchange their Egyptian pounds, that their receipt is meaningless and that their pounds have suddenly become an unexpected souvenir of their trip.

Still, there is a burgeoning and quite over-the-counter black market in currency. The official rate of exchange at all banks (and the airport) is about 80 piasters to the dollar. On the black market, however, it tends to be half again as much. And so many people in Cairo seem to be successful, illegal money-changers -- especially the shopkeepers at the Khan el Khalili, the old city of Cairo's legendary Oriental bazaar.

The moral: If you need Egyptian pounds, change your dollars on the street, but don't change any more than absolutely necessary or the edge you gain on the black market will be wiped out if you're forced to stuff the money in your pocket at the airport.

Just as you won't find anyone buying chips with Egyptian pounds at Cairo's casinos, you won't find any Egyptians playing next to you, either. The law forbids them to patronize casinos, though they may work as dealers. The management, however, is likely to be from the United States or Europe.

Alice Nash, an American, runs the Nile Hilton's casino, drawing on experience managing casinos in the Caribbean, Morocco and Yugoslavia. Looking more like a petite librarian, with blond hair and wire-rim glasses, Nash and her aptly-named partner, Silver Rich, operate a bit differently than their counterparts in, say, Las Vegas.

To begin with, the house extends no credit to players.

"I don't believe," says Nash, "that a man should gamble more than he has."

More than that, Nash knows it's difficult, at best, to collect on IOUs drawn on banks in other Arab countries. But she doesn't rule out big players; almost once a day, says Nash, a high roller drops in to put $25,000 or more into play.

At the Nile Hilton casino -- 300 square meters of playing floor offering a handful of blackjack tables and a few roulette wheels -- there's no such thing as a free drink. That's because the casino doesn't own the bar that serves the players, unlike at the Sheraton and Marriott where the drinks are gratis. And since Egyptian law offers no tax write-offs to businesses that extend complimentary food, drink or rooms to players, there's no incentive to "comp" a high roller the way other casinos of the world do.

You'll find the cards well-worn at Cairo's casinos. Another Egyptian Catch-22: Officially, it's illegal to import playing cards into the country, so the casinos knowingly violate the rule and pay 100 percent duty and a 500 percent penalty to bring cards into Egypt. But they are used sparingly -- decks are changed every four days, instead of every four hours as in some American casinos. Further, it's legal to have slot machines in a casino, but illegal to import them. Nash smiles and admits friends brought them in -- by suitcase.

Other touches of gambling, Cairo-style: Roulette wheels, unlike those in Europe but like those in America, have two double zeros, giving the house an additional advantage against players. At the Nile Hilton, dealers routinely ask players if they would like to split 10s, a statistically disastrous maneuver but one that Middle Easterners seem fond of making. But there are none of the varying, confusing rules Las Vegas boasts to attract players.

"Gambling here is straightforward, not gimmicky," says Jack Myers, whose ABP Casino Suppliers in London provide gaming equipment for casinos around the world. Myers happened to be in Cairo inspecting one of his assets -- he is a partner in the Nile Hilton casino. "There aren't any money wheels, and slots aren't big business. To the best of my knowledge, the craps table at the Sheraton has never been used."

At the Sheraton, across the Nile from the Hilton, you almost have to know somebody to find the casino. The place is tucked into a corner of the second floor. Casino patrons find it (without benefit of signs) by walking over aging, bumpy carpets that cover a sagging plywood floor.

Of the three casinos, the Sheraton's is the funkiest. Rose petals float aimlessly in a small cement fountain that greets visitors at the casino's dimly-lit entranceway. The motif is faded turquoise, from the carpet to the curtains. The cashier's cage resembles a Belgravian railroad ticket window. An enclosed baccarat area -- one table with a backdrop of rust-colored, crushed velvet curtains -- sits unattended, as does Cairo's single craps table. In one corner of the room are 42 slot machines, mostly idle.

The real action here is blackjack, and the casino's eight tables (the betting limit is a reasonable $200) are almost never empty. Cigarette ashes and ring marks from sweating glasses on the felt tables are brushed away sporadically by dealers using pink terry-cloth towels.

The Marriott's casino, by contrast, is spiffy because it's not yet a year old and hasn't taken on the worn appearance that marks not only Cairo's casinos, but the city itself. It is the 17th casino British-born Gerald Kushler has opened, and casino director Kushler says most of his players are Americans, reflecting the guest list at the Marriott.

There is talk of opening another casino in Cairo, this one in the new, 840-room Intercontinental Hotel, originally scheduled to open this summer but now delayed until 1987. Since there are only three casino licenses to be had in Cairo -- and they are closely held -- the betting is that the Nile Hilton casino will move to the Intercontinental. Alice Nash pleads ignorance, but the new hotel is so certain of obtaining a casino, one is built into its design.

Whatever the outcome, travelers can be certain the casino will be hard to find and the players will be as exotic as North Africa can offer. A final word of advice: No matter what the dealer suggests at blackjack, never split your 10s. Gambling in Cairo may be different, but the odds don't change with the time zones.