"I find it interesting because people would argue whether buying two tickets cuts the odds is half.
When there were a few states with two plays for a dollar the game odds were given as half that of a lottery with one dollar plays without a whole lot of explanation as to why."
That's basic probability theory. You buy two combinations your odds are 2:(whatever it was)
If a lottery has a pool of numbers just: 1, 2, 3
and if two numbers get drawn then all possible combinations are:
1,2
1,3
2,3
Which means that the odds of winning this lottery are 1:3 since there are 3 possible combinations to buy. If you buy 2 of them your odds are 2:3 (66.6%) and if you buy all 3 combinations your odds are 3:3 (100%).
Even if you use a filter and say that the first combination (1,2) won't happen and you only play by buying one of the remaining two combinations, your odds of winning don't change.
Even if you filter by numbers and not by combinations you get no help. If you filter out number 1 or 2 or 3 you are left with the same number of remaining combinations in each of the three cases. In each of the three cases you are left with just 1 combination in this case after filtering. So the odds are 1:3. Just like they were before we even talked about filters.
Now you increase the number of balls in the pool and the number of ball that get drawn so all the numbers increase, but all steps remain the same. So filtering changes nothing.