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%

> 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.