This is a quote from the book "Bitcoin: A Peer-to-Peer Electronic Cash System" by Satoshi Nakamoto
... doesn't know the exact amount of progress the attacker has made, but assuming the honest blocks took the average expected time per block, the attacker's potential progress will be a P oisson distribution with expected value:

To get the probability the attacker could still catch up now, we multiply the Poiss
on density for each amount of progress he could have made by the probability he could catch up from that point:

Rearranging ...
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