Dear Cecil:

The perception that some number combinations appear more frequently than others in the various state lotteries leads me to wonder: do all number combinations have equal probability, or is there some mathematical quirk that would allow certain number combinations to appear more often than others?

Illustration by Slug Signorino

Cecil replies:

What you want, Doug, is what is known as a system. I know of only one system that’s a sure thing: (1) dream up some cockamamie lottery-beating scheme of your own, preferably involving a personal computer (hey, it’s the 90s), and (2) sell it to 50,000 guppies at $29.95 a pop. Dozens of entrepreneurs have already done just that, and it’s a safe bet they’re better off financially than the people who buy their dubious wares.

In some games of chance, of course, systems do work. Card counting in blackjack, for instance. That’s because every card played in blackjack is a card that can’t be played again. If you keep track of which cards are left, your ability to bet shrewdly improves. In the typical card-counting system you count the 10-point cards (10, jack, queen, king) and bet more heavily when an unusually large number of them remain in a dwindling deck, since they mean trouble for the dealer.

Not so in lotteries, where the game begins afresh with every drawing. If the numbers are drawn at random — a big if, as we shall see — all the number combinations are equally probable. Occasionally you may notice what seem to be suspicious patterns among the winning numbers, but these mean nothing. One of the hallmarks of random numbers is that pseudopatterns occasionally arise — the million-monkeys-with-a-million-typewriters syndrome in action.

Still, gamblers looking for an edge will grasp at anything. There are two main “scientific” approaches to picking lottery numbers — hot numbers and due numbers. Hot numbers are ones that have been coming up a lot lately, while due numbers *haven’t* come up and supposedly are overdue.

Statisticians say the due number system is strictly for the birds. Number-generating systems are either biased or they’re not. If they’re biased, obviously you want to go with whatever numbers the bias favors. If they’re not biased, all the numbers have equal probability and there’s no point using a system.

Hot number systems are a little more interesting. Generating truly random numbers is tougher than you might think. It’s quite possible for the machines used in lottery drawings to have some minor mechanical peculiarity that causes certain numbers to come up slightly more often than others. Purveyors of hot number systems say their programs will detect those subtle biases and use them to your advantage.

Trouble is, lottery officials are as hip to bias as the wiseguys who write computer programs. They know if their drawings do show bias, the betting public will eventually discover it and start betting heavily on the hot numbers. That means more winners dividing up every pot, lower average payouts, and less interest (and fewer bets) on the part of gamblers. So the people in charge do all in their power to ensure that the winning numbers are as random as human ingenuity can make them.

One common type of state lottery uses a machine that blows numbered balls around in a glass bowl until eventually the winning numbers drop into a chute. Normally there are several machines and several sets of balls. Before each day’s drawing, a preliminary lottery is held to determine which machine and which ball set to use. The public is not told which machine/ball set combo is used on any given day and in any case the ball sets are replaced periodically. So it’s impossible to develop the kind of track record a bias-detecting program requires.

The one feature a number-picking program can offer that might actually do you some good is a feature that selects numbers at random — or, equally usefully, avoids numbers that are picked often — e.g., 31 and below, heavily bet by those who insist on picking their birthdays. The idea is that if you do win, you’ll have to share the loot with fewer co-winners. A reasonable notion, perhaps. But divvying the boodle is not a major problem for most people who play.

Send questions to Cecil via cecil@straightdope.com.