The odds of winning the lottery without ever buying a ticket are definitely zero. The odds of cashing a winning ticket (say, because, you found a lost ticket, or stole one, or received the ticket as a gift) are low, but they are definitely not zero.
I think when most people talk about winning the lottery they mean collecting the prize not claiming the abstract victory.
But since you can’t divide by zero the correct calculation becomes:
Say there are 1,000,000 tickets.
You buy one. Your chance of not winning is 99.9999%.
I don’t buy one. My chance of not winning is 100.0000%.
So your chance of not winning is 99.9999% of my chance of not winning. So you have increased your chances of winning by 0.0001% by buying a ticket.
It’s a very popular trick in health stats. You pick something that very few people die of, say 1 in 100,000 and then find that people who eat, say pork, have a death rate of 2 in 100,000. Instant headlines - “Pork Doubles Death Rate.” Not really, either way it isn’t your biggest risk.
Of course, I’d probably be in the wrong universe then.
And honestly, if I could build that machine, do you think I’d be wasting my time composing elaborate hypotheticals on the internet to while away a dreary Sunday afternoon? I’d be waterskiing in the Mediterranean, on skis made of solid gold, on my shoulders a human pyramid consisting of the members of the Swedish national Bikini championship team (I’ll just keep quantum-offing myself until I find a universe in which there is one, 'cause really, as I’ve just now realised, there’s no point in existing in a universe in which there isn’t, even if you’re rich).
…In a vanishingly small subset of worlds, that is. In yours, I’d probably just be dead.
Glad you enjoyed it. 