Is there public information available to show if UK National lottery winning tickets were pre chosen by the customer or were Lucky Dip. Are records kept? Which is more profitable?

Best reply by John W:

If it’s anything like the US, the majority of the winners will be quick picks but not because there’s an innate advantage but simply because more tickets purchased are quickpicks.

From a theoretical view, if you allow the machine to pick the numbers for you, it could purchase overlapping numbers, perhaps even the same number combination twice hence you have slightly better odds choosing the numbers yourself to guarantee that you get the chances that you’ve paid for. For example two tickets with the numbers 1 2 3 4 5 6 and 2 3 4 5 6 7 represent fewer chances to win than two tickets with the numbers 1 2 3 4 5 6 and 7 8 9 10 11 12. There is a down side, non overlapping tickets are exclusive, if you got a 3 number match on one ticket, you know that none of the others will do any better as none of the others will have that three number combination.

If p is the probability of winning and N is the number of tickets purchased then the quickpick approach will give you the chance of (1 – ( 1 – p)^N) of having one or more wins while choosing non-overlapping tickets gives you N * p chance of having one and only one win. With the quickpick approach, it’s possible to buy an infinite amount of tickets and still not win while with the non-overlapping approach, you could theoretically but not practically purchase every single combination and hence be guaranteed a win but you would still loose your shirt.

Mathematically, the differences are so slight it would take thousands of years of playing for any advantage to be realized. Only the lottery commissions profit from the lotteries.

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In the UK lottery: What are you better likely to profit on the Lucky Dip or when you pick your own numbers?