By virtue of Monte Carlo integration

The expectation of 4D6-L is roughly 12.24.

I just thought you might like to know.

UPDATE:

Okay, so I realized I'm an idiot for using random integration of a function by sampling it millions of times when it has only 1296 discrete states. So yeah, the expectation is 15869/1296, or 12.2445987654321.

Enjoy!