Would I have a decent chance of a place?

Hi everyone, was wondering if I stand an ok chance of getting into LSE. My profile is:

GCSE: 6.5 A*, Distinction in IT, 3.5 A.
AS: Maths Further Maths Physics Economics all A.
Predictions: A* A* A A* (respectively)

So if my PS and references are good what are the approx chances of a place? Is some of it down to luck too?

Thanks