> 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.