This is a great thread.

As others have pointed out, if the lottery isn't 'fixed' in some way then a 'lucky dip' entry of random numbers has exactly the same odds as any player selected set of numbers.

If a person believes the game is fixed, it's hard to understand why they would play it...

If it's a big win that you want it's probably better to use the random numbers of a lucky dip as the number of people playing makes it likely that any 'system' is being used by multiple players.

To illustrate that point, two people have told me that they enter with the numbers 1 to 6 'because they are as likely to come up as any other numbers but nobody else will think of this'.

My suspicion is that if (when?) 1 to 6 come up there will be tens of thousands of people sharing the jackpot.

Players also like to use birthday numbers to enter, which means that 1 to 31 are used more than the higher numbers with 1 to 12 being hammered. Whether biasing entries towards higher numbers is a good idea is a moot point however as I'm not the only person who knows about the birthday numbers issue.