Calculate reward value based on percentage non-linearly?

Question

I am programming a gambling type game where the rewards need to get bigger as the chance gets less.

For example here are the target max rewards for the following chance percentages:

100% = 1
50% = 250
0.01% (or 0%) = 2000

What formula can I use to calculate a reward given just the percentage value that would conform with the values above?

Answer 1

There are lots of formulas. You can just fit a quadratic through your three points: $$1=a1^2+b1+c\\250=a(1/2)^2+b(1/2)+c \\ 2000=c\\a+b=-1999\\a/4+b/2=-1750\\a/2=1501\\a=750.5\\b=-1248.5$$ so if the percentage is $p$ (expressed as a decimal, between $0$ and $1$) you award $750.5p^2-1248.5p+2000$ points.