When the initial conditions, like mass, chemical composition, and rotation are the same, for the vast majority of stars there are no intrinsic variations in their development. Of course, statistical variations exist, like convection. But those act on too small scales in order to influence the star’s development, in particular its core.
Intrinsic large scale variations happen in some stars. A famous example is Betelgeuse whose dramatic change in luminosity is speculated to be caused by very large scale convection processes. But I doubt it will influence the development of the core.
Maybe rotation has the potential to induce large scale statistical processes that may lead to different outcome for otherwise identical initial condition, i.e. fixed initial rotation rate. Another process may be statistical variations during the supernova explosion.
There are several physical parameters in the modeling that strongly influence the development of stars, like nuclear reaction rates, opacity, convection and rotation models. But as long as you keep those parameters fixed, the outcome of the model calculation will be the same.
I don’t think there exists an equation for calculating the remnant mass that is justified by physical insight. But of course you can apply some fitting curve to the outcome of thousands of model calculations and use that as equation.