I don't understand this logic. The US has the Powerball lottery.
So far it has been won 403 times[1] what seems around 20 year time span. With a US population of around 360 million. So not sure why 25 winners would require a population of 1 billion.
I was using some state odds. Ok so 1 in 1m for Powerball, yet HN is ~3m, so we have 1 in 100k on HN. Already an order of magnitude difference. Then, of course, not even 1 in 100 here are actually giving a startup a serious go. So comparing successful startups to the lottery is easily 1000x off.