# What's a good algorithm for a random, uneven distribution of a fixed amount of a resource?

### Problem

I have X, a positive integer, of some resource, R.

There are N potential targets.

I want to distribute all of R to the N targets in some "interesting" way.

"Interesting" means:

• Some targets may not get any R.
• It should rarely be near even (with a majority of target getting near X/N of the resource).
• There should be at least a small chance of one target getting all of R.

The naive approach would be to pick a random target and give one R to it and repeat X times. This would result in too even of an approach.

The next idea is to pick a random number between 1 and X and give it to a random target. This results in too large of a number (at least X/2 on average) being given to one target.

### Question

This algorithm will be used frequently and I want the distribution to be interesting and uneven so that the surprise doesn't wear off for users.

Is there a good algorithm for something in between these two approaches, that fits the definition of interesting above?

• Is it possible that this question fits better with gamedev.stackexchange.com ? Apr 4, 2012 at 23:44
• @MyrddinEmrys: Why? Apr 6, 2012 at 18:41
• Mostly because the description, though it never mentions a game, sounds very much like a game. Distributing unspecified 'resources' to 'targets' in an 'interesting' way. It's the phrase 'interesting'; people solving problems want even distributions or a specific pattern of distribution. But when you are creating problems (as in, a game) then you want it to be interesting. Of course I could be wrong, but this certainly sounds like game design to me. Even if its not, I wouldn't be surprised if he'd find a better mix of answers from game developers. Apr 6, 2012 at 19:29