Tom is correct that generally speaking, a mobile game will not cost that much to initially develop - a healthy feature set with a good amount of polish will probably only run to around $1-2 million and can certainly be done for much less if you're clever about it. If you intend to build a game and throw it onto the market as a premium title, or a title that relies on a simple set of IAPs with limited post release support (i.e no content updates or additions, no customer analysis and adjustment), then your budget will probably not run significantly higher than this figure.
The question though, was a game like Clash of Clans - this falls into a slightly different tier, as they have more post release support and continually iterate on the product. The success of a free-to-play game like this relies on the ability to gauge how players are interacting with the game and in particular the monetisation system. This is complicated stuff and can be quite unpredictable - as a result you want three things:
1) An extensive database encompassing and continuously tracking significant player behaviours within your game environment and your monetary environment.
2) Specialist people who can analyse this database and understand why people are doing things and how to adapt the game so you continue to get the most out of it. The relationship between players and an IAP based system is not as easy to understand as you might think!
3) The ability to apply updates and adapt the title as player behaviour adapts.
This is the most expensive part of the project - we'll go back to the figure of $1 per player per day for your infrastructure. This adds up very quickly, and when you first launch, it will be enormously difficult to anticipate just how many players you need to be able to scale to support. If you don't offer enough, your game will have serious issues that prevent people from paying, and this will cost you money (and possibly your game), but if you offer too much, you're wasting money on infrastructure you're not using.
Clash of Clans is a big title, so I assumed anticipating a big audience - 200k players for the first three months of running the project could cost $16.8 million - 3/4 or more the development cost of the game itself.
If you are only expecting 5,000 - 10,000 players (a more realistic figure for an unknown indie developer) you can get away with much less, about $0.5 million to $1 million. If the game suddenly takes off however, you will need to have the money in the bank to expand your back-end infrastructure to cope with the demand, and this will have to happen before you can get the return from those players.
Hope that helps you understand my lines of thinking when addressing the question!
Edited by ambershee, 06 December 2013 - 05:07 AM.