I can think of two faster ways:
1) If you don't "trust" math, you just run a few thousand virtual test runs with your dice and note the average result. This will be accuracte enough for almost any use case, for example to calculate your average income with these dice ;-)
2) Use math. A good book on stochastics should have the formulas that tell you the exact number if you give the average result of the die (at least if the values are not too different and smaller than the target sum). I think the relevant calculation you need has to do with a gaussian curve.
