> If a node can present a lottery ticket of rarity one-in-a-million, the network can conclude the node did about a million lottery tickets’ worth of work, on average. This is not true. You will have scratched far fewer tickets on average than one million. If you have one million tickets, one of them guaranteed to be a winner, you will on average scratch exactly half of them (500 000) before finding the winning ticket…
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.