Feature

Lotto's A Chancy Matter

Your chances of winning Lotto are essentially random, but the amount you win depends on how consciously random you can be.

By Vicki Hyde

Lotto has become a part of the New Zealand lifestyle, with hundreds of thousands of people conscientiously selecting their lucky numbers every week in the hope of winning the big one. There are all manner of urban myths associated with lottery numbers, ranging from selecting numbers based on the surface area they cover (means more paint on the balls and so more chance of them dropping through the slot) to picking significant numbers in one's life (birthdates, anniversaries and so forth).

None of these schemes work. By its very nature, Lotto requires a truly random selection of numbers. A great deal of careful mathematics and tested technology makes sure that each and every number has an equal chance of coming up. Any combination of numbers can also occur, as each number is selected independently and has no influence on the following selection. The sequence 1,2,3,4,5,6,7 is just as likely to occur as the apparently more random sequence 18,10,30,19,35,34,6. No matter what numbers you pick, your chances of winning are the same as those of every other punter. So it doesn't matter what numbers you pick? Wrong.

Increase Your Winnings

While your chances of winning are unaltered, the amount you win can definitely be affected by the numbers you select. This is because you are not playing merely against the machine, but also against everyone who has a Lotto ticket. Pick the more "popular" numbers and you'll have to share the prize with more people. Select "uncommon" numbers or "unlikely" sequences and you have a good chance of not having to share the winnings.

David Carr, research analyst with the New Zealand Lotteries Commission, has seen this in action.

"One week when a lot of numbers with 7 in them were drawn, there were more winners than usual," he notes. Seven is commonly considered a lucky number, so when the numbers 7,10,17,23,27,33,37 came up, 21 people shared the first division prize and 80 people took the second division. The average number of winners in the two divisions are 3 and 19 respectively.

Conversely, an "unlikely" sequence such as 15,21,22,24,25,31,32 saw only one winner of the first division prize and eight for the second. Naturally, each winner's payout was considerably higher than those of their more "predictable" counterparts. The number of payouts can also vary depending on how many people enter, the timing of the draw and whether it is a Superdraw or Jackpot. However, even in the early draws where the total pool was low compared to later draws, it paid to pick unlikely sequences.

People assess the value of gambling by looking at the probability of winning and the value of the prize. Mathematicians call this calculating the expectation. However, other factors enter into it. A Jackpot draw may produce a larger prize pool, but more people will enter because of that, potentially reducing the value of the payouts at each division.

Psychological Problems

"The fault lies not in the stars but in ourselves." People have great difficulty in choosing truly random numbers or random sequences. Human psychology tends to demand order. Few people have sufficient grasp of probability mathematics to avoid the temptation to apply spurious rules of chance to number selection.

One of the most common fallacies is that of the "law of averages". Punters believe that those numbers which have yet to come up must somehow have a greater chance of occurring in the next draw. This is not so. Boards at Lotto outlets tend to reinforce this belief, noting how often each number has been in the winning sequence. Some people use this information to make their selections, and err in doing so.

There are a great many factors which affect how people select numbers. By using dates as the basis for numbers, those numbers above 31 tend to be left out, although the data set in Table I didn't show such a tendency. "Lucky" numbers such as 7 or 4 are often picked and double digits, such as 11 or 33, also prove popular.

The very layout of the Lotto card can affect how numbers are chosen. People seem to be reluctant to select numbers in the far left column for some reason, but are keen to have a number in each row to provide a form of "even" distribution. In those standard draws with ten or more sharing the first division prize, there is only one number out of 49 in the left-hand column. Truly random picking would produce about 7 numbers in this column. Of the 42 rows, 41 have numbers in them.

In the draws from Table I where there were few winners in the first division, nine of the winning numbers are in the first column and there are often two or three rows left unfilled. This is apparent when you examine the examples in Table II.

Selecting numbers which are close together is not popular, yet many of the high-paying sequences have such runs, such as 1,20,23,26,28,30,39. For some reason, multiples of 10 appear to be unpopular too, with the low payout selections having only two and the high stakes examples six. Random selection would suggest four or five in this sample.

Computer Conundrums

The numbers in the examples do not follow these "laws" faithfully. The raw data is clouded by the truly random selections made through the Lucky Dip process where people have the computer select the numbers for them.

Carr points out that about half the entries for Lotto are chosen by Lucky Dip. In this procedure, a random number is generated by the Lotto terminal based on an arbitrary "seed" number. Each terminal generates its own set of random numbers independently. The seed number is selected as whatever number happens to be in a piece of hardware called the refresh register at that moment, and this is used to produce a random series of numbers.

Even computerised procedures are not totally foolproof. In Australia, a similar process was used for a number of years to select winning numbers in a lottery. When the computer was upgraded, the new machine was so fast it picked the first division and second division winners using the same seed number. This meant that the hundred winning numbers selected for the first division were repeated at the second division level before the machine had a chance to select a new seed. Naturally this led to a great deal of consternation and the program was quickly changed.

Given the poor strategies that people adopt, would-be Lotto winners may be best served by letting the computer choose their numbers. Of course, if everyone were to follow this strategy, any advantage would be lost. Perhaps the only certainty is that, with only half the money taken in paid out as prizes, for every dollar you spend on Lotto you can expect to receive 50 cents...in the long run...probably.

Vicki Hyde is the editor of New Zealand Science Monthly.