How can the national lottery make large numbers of sensible players pick similar numbers? These are the players who use some form of random number generator to pick their numbers.
No one sensible trusts electronic voting systems as they are currently exist. However numerous other algorithms are enforced by computers that are not even open in the sense that we know how they should work. For example the quick pick in the lotto.
This algorithm is supposed to pick a random set of six numbers that have not been already picked. No one can guarantee randomness so the lotto terms and conditions must say “we are not to blame if our random number generator turns out to be faulty”.
Large sets of numbers are picked every week by the same people. If you know that a certain set of numbers is always bought on a Saturday you can generate it as a “random” quick pick on the Friday. Should the numbers be a winner you have not generated an already existing number so it is difficult to prove that the lottery is giving falsely random quick picks.
It is hard to tell that the numbers generated by the quick pick genuinely are random. Many lists of numbers look random to people if they include less sequential numbers then they should and if they cluster numbers around a low value.
The lottery could generate pseudo random numbers that appear random and unless large samples of these quick pick numbers are available non randomness is difficult to prove.
I do not believe that either of these schemes are practical. The lottery makes too much money to risk losing their licence to an out and out fraud like this. Too many people would have to be involved and they do not have the plausible deniability of schemes to con the foolish.
Also an independent observer observes the lottery draw itself, the national lottery would have to be complete chuckle monkeys if they did not also have an observer ensuring the correct operation of other aspects of the draw such as the selection of quick picks.
So in order to cheat the sensible a lottery could bias the selection of quick pick tickets. This would be a bad idea but users of the lottery should insist on an independent analysis
of the quick pick system as errors in pseudo random number generators are common.