Lotteries are random

Of course they are - but however much you tell people that they are, some will doubt it.

Very little is published about the numbers that people have chosen for their lottery tickets, though in the UK (Choose six numbers from forty-nine) the most common combination is known to be 1,2,3,4,5,6.  When the Swiss lottery published some results over a decade ago, there were a lot of tickets which had chosen the previous set of winning numbers plus one - so last week's 5,20,26,29,31,39 would become 6,21,27,30,32,40.

There was mild interest in a rare lottery event in the UK this week.  In last Saturday's draw, the winning numbers were: 15,30,36,39,41,49 and five winners shared the jackpot prize.  Five is unusually high for the number of jackpot winners.  You expect a Poisson distribution, with mean about 0.7, which implies that if people choose randomly, there would be five lottery winners once in about 1000 draws.  But people do not all choose randomly, although I can't see what pattern has been chosen to give this set of numbers.  (There has been some research on how the layout of selection cards affects the choice of numbers - notably on the lottery draw in the UK when over 100 people shared the jackpot!)  This rare number of tickets sharing the jackpot was combined with the rare event of only one ticket winning the next prize, which in the UK is to match five of the six numbers and the so-called BONUS.  This is six times more likely than winning the jackpot.  However on 1st September, only one person won that prize, and as a result, that ticket won 50% more than the tickets that had shared the jackpot.  Coming second was better than coming first.

Is there any pattern to these numbers?

And a spokesperson for the National Lottery said "That's the beauty of the lottery - you never know what's going to happen" ... except that the organisers will make money from people who play, and from time to time there will be surprises.


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