The big "bingo machine" used has balls in it that are mixed then one falls out.
The balls were locked in a safe between uses. In a locked room. In a building with security and many cameras. Each door had a door swipe with each user having specific security clearance.
What I found amusing was the balls were cleaned and weighed (yes I made a joke) before every use.
That doesn't even get into the machine itself. I've worked on slot machines so I am sure the bingo machine thing would have security seals on all the EEPROMs. And the EEPROMs would be verified often if not before each draw.
Now imagine the rules and procedures of an underground lottery.
That's what makes it so fascinating. The bingo ball machine concept you describe requires a lot of trust, that's why so much effort has to go into continuous verification. As resiliency goes, this isn't really a feature.
The underground lottery is interesting precisely because it requires comparatively little trust, and the trust it does require is based on reputation and decentralization. For example, as a numbers player, you would be placing your bets with the same banker, one who you know has always paid out in the past, and who has personal ties to you and your neighborhood. The data source and hence the information about whether or not you won is public and hard to fake.
What makes numbers an illegal racket probably has more to do with low payout ratios and the fact that it's not linked in with the tax system (also, it's an unregulated chaos of private persons conducting it).
There are many types and methods of security seal. I've used double-layered stickers that show VOID when peeled off. There are plastic tags that have a heavy wire that you wrap around then seal inside the cap. The wire would have to be cut using a pair of wire cutters. Any type of security seal would have a serial number known to company auditors.
Each participant entered a bingo card of N numbers. Each regular number drawn in the regular Powerball results since the start of the game was marked as "hit". When all N of your numbers become "hit", you win. Then you meet a guy behind a bar at 3 AM, backed up by your beefiest brother-in-law, to receive a sack of cash, which was about 60% of what everyone put in at the start of the game.
The numbers guy tunes N to match game length to buy-in price and jackpot size, while also discouraging ties that would multiply the risk from the cash handoffs.
As far as "illegal" goes, yes numbers games were and are illegal. Nobody cared because the cops got paid off. It's a big part of what made NY what it is. It was so successful that most every state now has a lottery system. The odds of winning in state lotteries are, well, you already know what they are. State lotteries are total rip off designed to fleece the public. State lotteries exist because the pols realized they could make bazillions of dollars running numbers on a large scale and they could chase the competition away, too. So, in a sense, numbers games became legal, but controlled by the usual suspects.
There's also a conflict of interest. The state is responsible for math education while having an interest in people not doing the math.
I normally get a couple of tickets when the Euro lottery gets large - just for fun.
Just for fun, you could take the money you'd spend on a lottery ticket and hand it to the next person you see, just to see how they react.
If you're not just barely scraping together, dropping $25 on a negative EV lottery is not going to make one whit of difference to your finances. But it might change your life.
Dropping $25,000 on a positive EV lottery, on the other hand, is an incredibly dumb move.
Since most poor people will, in fact, miss that $25, the lottery is a really bad idea for them. Yet, they play it a lot more than the middle class do...
Since you'll almost certainly lose, I think the true value is in the fantasy of what you would do with a staggering amount of money. You could do this without buying a ticket, of course, but it feels more real when you have some skin in the game. Mathematically, your odds are still effectively zero, but mentally there's a big difference between effectively zero and actual zero.
Thinking of other consumables in that general price range that provide a short, quick fix of enjoyment (cup of coffee, snack, etc.), $1 for a slightly more vivid dream isn't so crazy to me.
Having said all this, I highly doubt it's the mentality of most lottery players.
Watching peaky blinders Is interesting and I a have a cousin who is an actor who is the direct descendant (and could probably do a better brummie accent)