Yeah, I think that's right. The hypothesis was that on average, one in a million cards is a hit. That implies that if you scratch a million cards, you have a 50:50 chance of a hit.
That the author got this basic thing wrong doesn't inspire much confidence in the rest of his reasoning.
Well, I guess in real life blockchains it’s like the latter case. You have a block and look for a nonce. There is an effectively infinite stream of nonces (“lottery tickets”). You have no guarantee that even one works, other than statistical hope. So then if probability of a match is 1 in X, you expect to have to do X attempts.
I have other issues with the article but this bit seems ok.
I'm not clear how "expected no. of attempts for X" is related to the probability of X. And I seem to be struggling to recall what little I used to know about probability.
I'd welcome a (link to a) clear unpacking of this scenario. I'm feeling rather stupid, as if I've had a stroke and lost a mental faculty. It seems to be a straightforward and obvious scenario, but I've lost confidence in my reasoning about it.
If you have an effectively infinite stream of tickets and each have a 1 in X probability of winning, you will indeed go through X on average.