How many RAM on VPS server I need setup, that my facebook game will be supporting 1000 online users?

Ultimately the only way to be sure is to start up a large number of (simulated) clients and see how the server responds.

Typically server performance graphs have a sharp turn. They perform quite well for lower numbers, then when you add someone you hit the turn and suddenly performance becomes terrible. You will want to know where that line is long before players ever hit it.

Between one mb of ram and infinity.

That is the broad answer for your broad question.

You know how AAA games can have all that great graphics and over a hundred enemies on screen running at 60fps on your PC, then a indie game with only one enemy and bad graphics runs on the same PC at 12fps?

This is the same thing.

How much RAM you need depends on so many factors that there is no way of knowing, your skill as a programmer will greatly influence the amount needed.

The last server I used had 1GB RAM, it hosted for 14 players and 17 bots(Spam bots) with no signs of significant loss of ram and was stable at 316 mb - 342 mb and most of this wasn't the players, it was just the game running. Spikes reached as high as 602 mb not even lasting 10 milliseconds.

I think it was 17 bots, although the freelance programmer I hired to write the defense said it was more like two or three, with the same bot spamming different products.

About this much

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Line not to scale!