This is a rather fundamental question. Mathematically, 10^6 or 10^7 looks like a close figures. But there is a great difference if one thinks about 3 tons or 30 tons of silver.
There are some estimates how many strikes could serve a die. A figure I remember is about 10,000.
This yields (on the basis of your estimate for the total number of dies) the total 10M coins.
Now let us suppose that only a single coin from thousand survived. How many Othos's
denarii does exists now? The coinsarchive gives
400 entries. Extrapolating, one may estimate that there are several thousand
denarii in
collections. So, the total number of
denarii issued during 3 months of Otho's reign should be several millions.
One can think also about a salary of soldiers. Newly elected emperor could give an advanced payment, probably, for a couple of months -
to ensure support of the army. Say, 50
denarii par capita. Of course, the
denarii should be newly minted with
his effigee.
Counting about 100K soldiers, the figure could be 5M coins, as a lower bound. Of course, coins should be sent to provinces to show that the emperor is a strong guy and the things are goind smoothly. So, minting sufficient number of coins was vital for a newly elected emperor.
On the other hand, Dr. Andrew
Burnett estimates the maximal total year issue for
Domitian only in 2.6M. OK, it was a stationary regime, with coins of
his previous years. Also coins of
his father and brother
still in circulation. But this figure seems to be miserable with respect to the population of the empire believed to be 50M.