Earlier quoted context omitted.
Why would doing this to 125K accounts give them access to one account per day? The chances of guessing 6-digtis pin code for each account is the same (10^6) regdless of how many accounts your are attacking
It's never truly guaranteed and the numbers aren't quite one account per day at 125k accounts, but: 10^6 digits = 1,000,000 possibilities 125,000 accounts x 4 attempts per account per day = 500,000 attempts per day --- 1-(1-1/1,000,000)^500,000 ≈ 39% So every day they have a roughly 39% chance of success at 125,000 accounts. --- At a million accounts: 1-(1-1/1,000,000)^(4×1,000,000) ≈ 98% Pretty close to 1 account pe…
> 1-(1-1/1,000,000)^(4×1,000,000) ≈ 98%
> Pretty close to 1 account per day
No, this means there is a 98% chance you get _at least_ 1 account.
`1-1/1,000,000` is the probability you fail 1 attempt. That probability to the 4millionth is the probability you fail 4 million times in a row. 1 minus _that_ probability is that the probability that you _don't_ fail 4 million times in a row, aka that you succeed at least once.
The expected number of accounts is still number of attempts times the probability of success for 1 try, or: 4 accounts.