So you have to multiply this number by the number of pools, as they also calculated hashed, but that work was lost as someone found the nonce first
This is wrong in so many ways, I can't even
I think I get what bitmover was trying to say.
The question was how many hashes have all the miners calculated in bitcoin history.
Just because the miner didn't find a block, this doesn't mean that this miner didn't calculate anything. He was not asking cumulative chainwork (although it is the best anwser)
Is it possible to somehow calculate how many SHA-256 hashes have all the miners calculated for the entire history of Bitcoin?
Here is a simple example: suppose you have a group of people, each rolling a 6-sided die as fast as they can, and in order to win a round a 1 has to be rolled. Because the probability of rolling a 1 is 1/6, we know that it takes an average of 6 rolls to roll a 1. It doesn't matter who is rolling their die, or how fast they are rolling it. It will take an average of 6 rolls. Sometimes it takes more and sometimes it takes less, but the expected number of rolls is 6 for each round.
This a nice example.