...n a parallel chain containing an alternate version of his transaction.

The recipient waits until the transaction has been added to a block and z blocks have been linked after it. He 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...

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block explorer
The recipient waits until the transaction has been added to a block and z blocks have been linked after it. He 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...