Can you increase your chances to win big in the National Lottery
This was the question which I asked myself many years ago when I decided to play on a regular basis the nation’s favourite game of flutter. My numbers won’t be selected. But, I can increase my chances that my chosen numbers will be selected. However, I would like to have a greater chance of not sharing any of my winnings. The numbers that come out the machine are random but the numbers that people choose (unless selected with the Lucky Dip option) are not random. Can I play the opposing player if the machine is not available?
Many academic papers have been written about this topic. Additionally, businesses have been set up to sell information on players to prevent them from sharing their winnings. There are plenty of examples, such as the January 14th 1995 win by 133 winners who shared the PS16million jackpot and each won about PS122,500. This should be enough to get people interested in this topic.
Official statistics about the National Lottery numbers that were selected were available in the beginning of the game. However, they are not published anymore. It is possible to find information on player preferences by looking at two subsets, those in which there has been a winner, and those that were not.
From its launch on November 19th 1993 to October 31st 2012 there were 1,398 Lottery winners and 361 without a winner. I examined these subsets separately and compared their frequency with what was expected by probability. I took care to eliminate any sampling bias that might have been introduced by the randomness of the draws. This would help to avoid, for example a scenario in which a number drawn much higher than was predicted across all draws appears more than expected in any subset due solely to random selection bias.
If conscious selection does exist, it is reasonable to expect that unpopular numbers will be less common than expected in the jackpot subset. However, the same would hold true for the roll-over subset. This approach disregards the fact that numbers are selected in a group with six. Therefore, a number chosen randomly could be considered as a combination of a popular and unpopular number. The effect should be less noticeable as the sample sizes increase. However, it is possible to explain the results and they are not always spurious.
Combining the outputs of the analyses of both subsets to create one metric reveals that there is evident conscious selection. The graphic below shows 49 possible numbers. The higher the column, the greater is the popularity. The probability of the occurrence is shown by the red line.
There are certain patterns that are worth noting.
The well-known ‘birthday bias’, in which players use the birthdays of their loved ones as a basis to select numbers, is easily seen. In the graphic, we can clearly see that smaller numbers tend to be more popular than those with larger numbers.
However, 31 appears to be more common than 29 and 30 despite the fact 31 is less likely to be a birthday than the 29th and 30th. This may be due the playlip’s numbers.
13 is unpopular in the birthday bias’ area. This is understandable considering its cultural dislike. Its neighbour 14, however, is not as popular. This may be because 13 was skipped along with 14 when casual selectors scan the board from the left to the right.
The number 7 is the most favored, with 3. being second. This finding is in line with what we already know about public attraction to these numbers. For example, the “choose one number between 1–10” question.
It is becoming increasingly popular to use lower numbers, such 7s or 17s instead of 27.
Future plans include additional analysis to see how the geometry on the selection board affects numbers’ popularity. I will also investigate the popularity and combinations of numbers.
In the meantime, to play an opponent it’s best to select the numbers that are less popular (those shown in the graphic with smaller columns), to reduce the possibility of another player having the exact same numbers. The effectiveness of the combination 32 to 34, 39, 41, 40, 46, 48 and 48 is now reduced by publishing this analysis. This combination may not be worth your time, so I recommend that you avoid sharing any potential jackpots with the Understanding Uncertainty community. TIPS TO IMPROVE YOUR CHANCES OF WINNING USING LOTTO MACHINES