The odds of winning the Lotto jackpot have increased from one in two million in 1988 to one in eight million today, writes Dr Patrick Murphy.
Wednesday's lottery jackpot of €13.3 million was the largest since the launch of the National Lottery in 1988. The jackpot was last won on the 16th of June and has rolled over a record 11 times since then.
Following the last rollover on Wednesday, it is expected that tonight's jackpot will exceed €16 million, inducing lottery fever in even the most risk averse individual. Many are surprised about the fact that there has been no winner for such a long time.
Has the lottery become as erratic as our summer weather?
In fact, the current behaviour of the lottery is not at all unusual; actually it is the direct result of the introduction last November of new rules for the main Lotto game. The reader may recall that prior to November 2006, the lottery consisted of 42 numbers of which the player chose 6.
In November, to great fanfare the National Lottery presented players with three new numbers to choose from: 43, 44 and 45. At a stroke they increased the chances of a large jackpot by decreasing the chances of a winner for any given draw.
This is not the first time this has happened, indeed when the National Lottery began its Lotto game (known as 6-36) there were only 36 numbers in the game of which players chose 6 numbers.
In 1992, the game changed from 6-36 to 6-39, and soon after in 1994 the game changed again to 6-42.
What have been the consequences of these changes to the game? Under the 6-36 game the probability of winning the jackpot on each play stood at 1 in 1,947,792. With the introduction of each successive new set of three numbers the probability of winning the jackpot decreased: first to 1 in 3,262,623, then 1 in 5,245,786 and presently it stands at 1 in 8,145,060.
By reducing the chances of winning the National Lottery were themselves taking a gamble. Would players see the reduction in their chances of winning as a reason to stop playing?
The company figured that people would not be so aware of this reduced probability of winning. Instead more people would be drawn to play by virtue of the larger jackpots that would inevitably follow their decision to change the rules.
If the current lottery fever that is gripping the country is anything to go by, then that gamble taken has surely paid off.
Why do people still play the lottery? The attraction of the becoming a millionaire is undoubtedly a large reason. But as we have seen, this is an extremely unlikely event. Indeed, an individual has now a statistically greater chance of being struck by lightning than they have of winning the lottery. Since its inception in 1988, 315 people have become millionaires by playing the lottery, significantly less than have become property millionaires in that same period.
It is my opinion that the real reason people play the lottery is that most people just do not understand what a probability of 1 in 8 million means. Yes, we all can see that there is a small chance of winning, but just how small is it really? A better way to view the game is to consider how long on average we might expect to wait before we would win a prize. Let's suppose that you decided to spend the current minimum of €3 every Wednesday and every Saturday so that in each draw you have two sets of 6 numbers. You would, on average, have to wait three years and three months in order to match four numbers, to match five numbers you would have to wait 163 years and two months. To win the jackpot your expected waiting time is a phenomenal 39,159 years.
Dr Patrick Murphy is of the school of mathematical sciences in UCD