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
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1-(1-1/1,000,000)^500,000 ≈ 39%
So every day they have a roughly 39% chance of success at 125,000 accounts.
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At a million accounts:
1-(1-1/1,000,000)^(4×1,000,000) ≈ 98%
Pretty close to 1 account per day
Off by a factor of 4 but the concept stands.
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And 125k accounts will be close to guaranteed to getting you one each week:
1-(1-1/1,000,000)^(7×4×125,000) ≈ 97%
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 per day
Off by a factor of 4 but the concept stands.
---
And 125k accounts will be close to guaranteed to getting you one each week:
1-(1-1/1,000,000)^(7×4×125,000) ≈ 97%