Brain, I think it's time you begin searching for a Chief Technical Officer for your business. He or she can best advise you on this.

Or you can simply put $10,000 into your preliminary budget for servers, with a footnote that it's a preliminary estimate.

Since it's unlikely that you'll get 2 million users right away, you can simply put off that extra cost until you are ready for second- or third-tier financing. Budget for servers to accommodate only tens of thousands of users for the near term.

I believe Tom was more so trying to say that you should focus on the more immediate and realistic goals. The overhead (cost) of supporting 1.9 million users that you don't have can kill you while you are waiting for the project to sustain itself. Also purchasing top line systems now and taking 3 years before you even need them will cause them to be nearly obsolete by the time that you actually need them and therefor be a complete waste of money.

You would be best to do your research and see what kind of fan base that you have now along with how much interest you have in your game and how easy it is to get people to your website and facebook that are early pitching the idea. If you can't get 1,000 likes on your face book your not likely to get 100 people to play the game and as such you can set your initial budgeting goals much lower. Personally I tend to set my budget goals on a basis of how much I am willing to lose and for how long more so than trying to figure out how much I might need in 2 years from now.

I guess in short what I'm saying is that one fairly modern or better server is a good place to start and will most likely last you a good long while before you will need to worry about adding more or upgrading. It is also much easier to sustain lower costs for a longer period of time ensuring that you have a better chance of actually reaching a sustainable or even profitable age. Not sure if you are looking at how much of you own money it's going to require, how much of an investment to ask for or how much of a loan to take out but it all comes down to the same question...

"What is the cheapest way that I can adequately launch this idea?" The example is that a modern server should be able to support at least a few thousand simultaneous connections of course dependent on your bandwidth requirements (which should be tuned to be as minimal as possible for MMO games anyway). With that being said how many people are going to start playing your game today? None? Well there's your starting point. You have 0 players how many servers do you need to support 150% of them? You have 100 people that are interested and will begin playing immediately? Well how many servers do you need to support 150 players? I think you see the point here, it's more about how many do you expect to have, then judging your requirements a fair amount over that but not astronomically 9/10 MMO games on the internet don't even have 100,000 players let alone 2 million. Maybe some day you will but chances are far more that you won't or at least not any time soon. Why waste you or your investors money for years to find you never hit your goal?

One more thing, if it's for investors they just want to make a return on their investment as quick as possible. They don't care that you think your game will be played by 2 million people. They are quicker to give me some money to sell 1,000 copies if it returns 20% profit on their investment within a year (or is likely to). The more you ask for the longer it's going to take you to get them their money back and then some and the less interested they will be. If it's your money, it's more about how much can you afford to throw away and for how long? If it's for a loan, it's more about what can you afford to pay back? Also note that the price of the computer is not all that is involved with the server, you also need to host it somewhere. Either a few thousand a month to get a nice fast line to your house (and potentially tens of thousands just to get that wire to your office in the first place). Bandwidth costs money, the rack space costs money. All in all too many factors to take in to account, base it on more realistic concepts, being how long can you afford to fail. (Because you will fail for a while before you get the required fan base to sustain the game)

In my experience, unless you have a significant demo-able product already, a significant population interested in your progress or a strong history in profitable games, no investor will touch your idea. Unless you already have one of those things or more, you might want to skip the Business Plan, and focus on marketing for Crowd Funding sites. More investors are interested in hopping on board an already successful operation, than an idea. For instance, start your game small, and start taking in some kind of revenue, however small. Then add one or two features, and track how the finances increase with that. Then present that information to potential investors with an idea showing how the next feature needs some additional capital to create, and based on the history of the game will introduce X percentage increase to profits/customer count.

Investors tend to be experienced enough to recognize the difference between projections based on facts and projects based on guesses. especially with the financial climate the way it is, you'll be hard pressed to get any investor on guesses.

Crowd funding is very different. Typically, you establish goal levels, I.e. at 10,000 the game development will begin. at 50,000, we will contract out to highly professional artists. at 100k, we blah blah blah. then offer things like getting a good feeling about helping the product by giving 5$, getting a free online membership for the first year, for 15, (anticipating 20/year cost), and 100$ for unlimited life time on the server, etc... Check out whats already out there, what worked and what didn't.

In regards to your starting question, Server prices also depend on what your system will need.

I.e. 1x 2ghz 4gram dedicated box with 200g space might go for 40$/mo, including 20G transfer a month free.

But the engine you use may greatly change the need for this. For instance Hero Engine is run in their own cloud, and a development license is 100 for one developer/designer, and 500 for a team of up to 25. Its fully featured, produced lots of great games, easy to work with, and best, is as long as your pulling in anything from customers, the server usage/expansion is all covered, and already built in. You could just consider that you need a 500$ investment to begin with plus any other operating costs for local usage/team needs, and your good to go.

Seriously, check out HeroEngine. There are other services like this, but they are the best I've seen. http://www.heroengine.com

Crowdfunding this should be pretty easy, since its a low investment. If you can't come up with that yourselves.

If i plan to have 2 million users on an online game (like L.O.L) what kind of servers should i need to use and how many

of them? (So i can put the costs of buying the machines on the plan)

I know that the server capacity is defined on active client connections per instance and also we have the network limitations but i am not that good on math.

Here is your chance of to start doing math. No one else can estimete for your.

My question: is a gamer downloads 1 mb or 10 mb just to start the game?

As you can see in both cases ... different servers will be needed.