## Mathematicians and the Lottery

Do mathematicians play the lottery, it’s a difficult question as I suspect many would be hesitant to admit it. Although ly one thing is certain, mathematicians do get asked how they should play the lottery. Even though you don’t usually see an endless parade of maths professors walking off with the jackpot.

However although a guaranteed win strategy is unlikely, most forms of gambling have sensible tactics which can at least maximize your chances of winning (although minimizing losses is probably nearer the mark). So can you use statistics to predict which numbers to choose? Again unfortunately this is unlikely and any essay entitled how to win the lottery should be treated with a large amount of caution.

The safest mathematical response to the question of how to increase your chances of winning is this – buy more tickets. No-one can dispute that the more tickets you have the greater your chance of walking away with the jackpot. Although these lotteries are never meant to be a proper gambling choice, the chance of winning is so remote that you would have to buy an awful lot of tickets to be in with even a reasonable chance. The ticket is more a chance to dream than a realistic one of winning having said that over 1500 people have won more than a million pounds in the UK lottery for instance.

The UK lottery requires you to pick 6 numbers from a choice of 1 to 49. You win a prize if you match three of those numbers, the more numbers you match the more you will win. The jackpot is normally paid out for all six numbers although this will be shared by anyone else also picking these numbers. There is an additional bonus number which can be used if you get the first 5 which also is likely to pay out a big prize.

We can assume that most national lotteries are completely fair and random, after all there is no incentive to cheat as all the money is paid out. Most of the European countries have lotteries and most you can play online, you may need to change your IP address like this to an Italian, Spanish or French one though to get access.

Of course with the lottery we are plainly in the field of probability and statistics, because it’s ultimately all about chance. However if you’re aim is to maximise your chance of winning a large jackpot (rather than just picking the correct numbers), then there’s an important fact to remember.

The amount of the jackpot a winning ticket will benefit from depends on how many people picked those numbers. Here there is a fundamental fact that will help you narrow down your choices slightly. To maximise your chances of ‘not sharing’ then you need to avoid a certain group of numbers as much as possible. The reason is that many millions of people base their numbers on birthdays, so the numbers 1-31 will be much more likely to selected than those of 32-49.

John Jones

Author of Watching BBC Abroad in 2017

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