The system that you describe in no way resembles the lottery system as it exists today: it's so far from reality that I'm not quite sure why you're even bringing up this fantasy representation of a lottery.
The real lottery abuse - particularly scratch-offs, which are what is being abused here - is not a match-up between "high probability of not winning" and "unable to cheat". It is between "high probability of not winning" and "multiple fairly obvious avenues for cheating". Among them are the two mentioned prominently in the article: Micro-scratching and taking winning tickets and telling customers that they were losers, then claiming it for yourself. Both of which are avenues easily available to the clerks who have suddenly found themselves to be in this "miraculous" state of repeated wins at very low participation rates.
Why are you bringing up some fantasy straw man version of the lottery to defend it?
Because this is HN and people here are interested in exactly such generalizations.
It's mildly interesting to consider the ways in which scratch-offs can be gamed. One can collude with a shop owner to peer behind the scratch-off material with a machine, for instance. It is about as interesting as figuring out how a biometric ID can be gamed by a simple replay attack, storing all the aspects of your fingerprint and replaying it later.
What's MORE interesting is if the lottery was far far harder to game. The general principle is fascinating. We think we can KNOW the truth but using simple math we can SHOW that when evidence on both sides piles up and yet contradicts the other, you cannot recover and somehow come to KNOW the truth.
Thus you see the situation today when people confidently assert one side or the other, but each side has really strong arguments for its side.
Each side will say the other's arguments are bunk, but rarely actually engages with them in depth.
The real lottery abuse - particularly scratch-offs, which are what is being abused here - is not a match-up between "high probability of not winning" and "unable to cheat". It is between "high probability of not winning" and "multiple fairly obvious avenues for cheating". Among them are the two mentioned prominently in the article: Micro-scratching and taking winning tickets and telling customers that they were losers, then claiming it for yourself. Both of which are avenues easily available to the clerks who have suddenly found themselves to be in this "miraculous" state of repeated wins at very low participation rates.
Why are you bringing up some fantasy straw man version of the lottery to defend it?