Quite a complicated formula required...

Hi all. I'm making a points rewards system as part of a university project and have hit a bit of a problem..

Basically the project is a tournament system where Z number of users can enter and there exists X number of point paying positions. Y is the total points available for the tournament.

I need to be able to distribute the points across X so that the sum of points awarded is equal to Y and such that

Points awarded to player N > Points awarded to player N+1

(ie. first place gets more points than second place)

The only way i've worked out how to do this so far is halfing the amount of points given to each position each time.. So 1st place wins 1/2 the points, 2nd wins 1/4, 3rd 1/8 etc...

However when I get down to rewarding the 14th user with 1/16384th of the total prize pool they dont really get anything at all.

Can anybody think of a better way of distributing score amongst the players?

Many Thanks in advance

oh just wanted to add, this i say quite a complicated formula as in its quite complicated by my standards! I've not touched maths seriously since a few courses in my first year of university!