The odds are long. The drawings are random. And the house keeps a much greater share of wagers than other forms of gambling.

In sum: The lottery cannot be beaten.

"There is no system that can improve your chances of winning the lottery, period," says Mike Orkin, a California mathematician who has written extensively about gambling odds.

Yet the quest for an ever-elusive winning lottery strategy is alive and well — and for sale.

On a quiet, dead-end street in Denville stands the headquarters of Double-Red Publishing, purveyors of 90 lottery periodicals. The titles range from "Three Wise Men Dream Book Almanac" — a sort of "Old Farmer's Almanac" for numbers players — to a sloppily hand- drawn leaflet titled "Grandma: What Numerology Means to You."

Company officials won't say how much they make selling advice to the luck-lorn. But a visitor to Double-Red's warehouse can only conclude that the brothers who run the business, Ben and Anthony DeSomma, aren't going broke selling copies of "Professor Hitts Number Secrets" for $3 a pop and "Lucky Number Envelopes" for $5.

File boxes are stuffed with order sheets from thousands of lottery ticket retailers nationwide, many of which ply Double-Red's stock via customized magazine racks next to their lottery ticket displays.

"Sometimes, the books just fly off the shelves too quickly and the retailers don't know what to do," says Anthony DeSomma.

He used to run an electronics repair shop in Montclair, but local TV repairmen are getting squashed by the service departments at big- box retailers, he said. Now, the DeSommas are captains of their industry.

"I have people calling me up just to tell me about a new system they're trying, and how they took one of our books and did this and that," he said. "They track this stuff like crazy. For some of these people, the lottery is like a religion."

Like the lottery itself, the lottery advice business has its niches.

A Star-Ledger analysis of five years of lottery ticket sales and winnings found sales tend to be higher in lower-income neighborhoods than in more affluent areas. And the pattern is even stronger for certain lottery games — lower- income ZIP codes buy far more Pick 3, Pick 4 and scratch-off tickets per capita than areas with higher-income households.

Almost all lottery literature is targeted at Pick 3 aficionados, Ben DeSomma said. "Let me put it this way," he said. "You won't sell a Pick 3 book in Beverly Hills."

Each booklet generally falls into one of two camps: analytical and mythical.

There are ersatz statistical analyses that examine numbers that have come up recently in various state lotteries, and advise playing "hot" or "due" numbers.

"If you would like to see how many times the number '123' hit in New Jersey since the lottery began, our Big Clara's Pix&Hit lottery sheet will tell you this," Ben DeSomma said. "There is a higher probability that the numbers which have hit more are a safer bet to play."

Orkin disputes such claims. In mathematical terms, each drawing is "independent," and what happened the day before is irrelevant. In other words, he said, the numbered balls that pop out of the chute have no memory.

At the other end of the spectrum are mystical tomes that instruct readers how to interpret their dreams in ways that might lead to winning plays.

Some titles have been put out by various publishers for decades.

A century ago, when illegal numbers games were taking hold, underground publishers put out "dream books" for players.

The books were inspired by the African "Hoodoo" tradition, a form of mysticism that attached symbolic significance to numbers and were particularly popular among African-American numbers players, said Catherine Yronwode, who runs an occult products store in Northern California.

"Anglo-Americans tend to see dreams in a Freudian way, about what they say about their lives and their relationships," she said, whereas in the Hoodoo tradition, dreams are windows to the future.

The DeSommas sell a number of dream books. "The Three Wise Men" title has been published since the 1920s, Ben DeSomma said.

Dream about cabbage, for instance, and "The Three Wise Men" advises playing 638 in the Pick 3.

One devoted reader is Ron Jackson, a 52-year-old disabled laborer from Bayonne. He pledges his lottery allegiance to Double- Red's "Black Jack Almanac," which lists suggested plays for every date. Jackson's system: Play the numbers one month ahead of the dates in the book.

On an afternoon earlier this year, he was ensconced in his usual hangout, Pyramid Traders on Broadway at 25th Street, the almanac in hand.

He figures he spends $50 a day playing the lottery. "I live here," he said while waiting in line to make some Pick 3 plays.

Thousands also seek advice online. Todd Northrop, a Somerset County resident, runs "Lottery Post," a Web site with 20,000 registered members. The most popular feature: Forums where members post lottery predictions.

On any given day, he said, a member can pick a state and go through lists of lists — numbers that other members believe will come out on that day. It's a pastime that inspires true devotion.

"Some Lottery Post members literally spend hours each day coming up with the right numbers to play and carefully prepare elaborate forum posts designed to highlight the best numbers," Northrop said.

Both DeSomma and Yronwode also sell an assortment of amulets, charms and potions. In fact, Yronwode has written a book about Hoodoo herb magic and sells 180 herb blends in her shop — including a product called "Lucky 13 Lottery and Bingo Oil."

Yronwode insists this is not snake oil: "We make these and we pray over them for you," she said.

Orkin, who has written several books about gambling odds, is among the unbelievers.

"Millions of dollars are spent by people who run the lottery games to make sure they're random," he said.

In New Jersey, an accounting firm sends two representatives to witness every drawing. And the bottom line: The lottery pays customers just 55 cents back in prizes for every dollar wagered — far less than other forms of legalized gambling.

"There are weird streaks and patterns that are caused by chance alone, but that doesn't mean you can use that to your advantage for future drawings," Orkin said.