Just to be on the safe side this question is NOT about predicting winning numbers in a lottery etc.
I just wonder (since there are people that think that xyz lottery company does not reward jackpots at random etc) is there a way to prove that a specific lottery company indeed has a honest number picking scheme that is truly random by using data from past results (lets assume that we have a sample of 2000 past results)?
Or to put this in an other way suppose that a certain lottery company is indeed fraudulent and cherry picks a winner out of the database of participating tickets -by unknown to us criteria e.g they would like to pick a ticket that has a unique number combination which no other ticket has so that the jackpot never gets shared by more than 1 winner- by rigging the machine that outputs the numbered balls to result in a specific (and different each time) combination of numbers.
In the long run would any patterns emerge (by using 2000 previous drawing results) that would suggest that the resulting numbers are not truly random ?
Or is the sample too small to make such inference?
If it is possible to make such inference how exactly would you solve that problem?
Let's assume a powerball like lottery ticket scheme where you have to pick 5 numbers from 1 to 45 and additionally pick one number from 1 to 20.
so 5 (out of a group of 45) balls are drawn and then 1 (out of a separate group of 20) is drawn and in order for a ticket to win the jackpot it has to have all 5+1 numbers.