I predict about 300 150 million paid downloads lifetime - that includes the eventual Android release. About 40 25 million paid downloads the first month.
Total downloads - including non-paid ones will top over 1 billion the first year.
For reference, Pokemon Go has already exceeded 500 million downloads. Many other big smartphone franchises like Angry Birds and Clash of Clans have surpassed 1 billion downloads for individual entries.
Factors to consider:
-Multiple devices, multiple accounts in multiple households
-Apple store marketing
-Previously untapped markets for Nintendo (Asia, South America)
-Holiday. Massive gift-carding
-A fairly large audience of lapsed Nintendo fans (e.g. casuals, older gamers)
-The 60 million people who bought a 3DS are pretty likely to buy this game too
-Generalized mass hysteria of a Mario game on Smartphones
Edit:
Even with everyone's name-calling, I get everyone's point. I was *extra extra* bold on the attach ratio when I first wrote this.
I will revise my prediction to something like 150 million paid downloads. I still think that's big enough to be bold. And not only that, it vastly outperforms most 'free' apps in app-purchases/paid upgrades. Overall, I'm unchanged in my opinion that Super Mario Run will exceed the kind of performance many of you expect of it in the App Store.
I would have thought since I was right about Pokemon Go's download count you'd listen to me. oh well...
I predict NX launches in 2017 - not 2016