  Kontsevich's formula is a recursion that calculates the number of rational
degree $d$ curves in $\mathbb{P}_{\mathbb{C}}^2$ passing through $3d-1$ general
positioned points. Kontsevich proved it by considering curves that satisfy
extra conditions besides the given point conditions. These crucial extra
conditions are two line conditions and a condition called cross-ratio.
  This paper addresses the question whether there is a general Kontsevich's
formula which holds for more than one cross-ratio. Using tropical geometry, we
obtain such a recursive formula. For that we use a correspondence theorem
arXiv:1509.07453 that relates the algebro-geometric numbers in question to
tropical ones. It turns out that the general tropical Kontsevich's formula we
obtain is capable of not only computing the algebro-geometric numbers we are
looking for, but also of computing further tropical numbers for which there is
no correspondence theorem yet.
  We show that our recursive general Kontsevich's formula implies the original
Kontsevich's formula and that the initial values are the numbers Kontsevich's
fomula provides and purely combinatorial numbers, so-called cross-ratio
multiplicities.
