gsb@CompuPick.com wrote: [...] > OK, I need these: > > x 0 50 100 > > f(x) oo 0 -oo (I switched the signs) > > Here's what I'm trying to do: I'm trying to measure "luck." > If someone has a 25% chance of doing something (1/4 tries) and > they succeed they should get rating R. If they have a 12.5% > chance of succeeding (1/8 tries) then their rating should be > 2R, double because it will only happen half as often. Likewise, > something with a 6.25% chance would be 4R. I realized my > previous table didn't work because a 16.67% event's R should be > twice a 33.33% event's R and that didn't happen.
Up 'til now it sounds like R should be the number of expected trials until success.
> A 50% event > requires no luck at all and is therefore zero.
This however doesn't fit. It would mean R=0 in the above.
> There should be symmetry about (50, 0) and the function should > be continuous. I know it will resemble sinh(), but that's when > my brain started hurting. [...] Gary S. Best gsb@CompuPick.com
You should probably pick R to be the number of expected trials until success. This gives you a function like: f(0) = \infinity f(.5) = 2 f(1) = 1 Or, if p is the probability of success, let f(p) = 1/p. This function has the multiplicative property that you wanted. -- Eric Gindrup ! email@example.com