If the difference between "best case" and "worst case" ranges from 5--15, then that's the average best-worst difference. So the range is (x-2.5, x+2.5) to (x-7.5, x+7.5). Given it's a "lottery," the average person would expect x and could improve to x+2.5--x+7.5.

But I'm certainly not a psychologist.