So, as a lark I have been working on software for this, using Python and OpenCv:

It's not nearly as simple as it may seem, but lots of interesting machine vision issues to deal with.. I've learned more about the Stroke Width Transform and binary thresholding than I ever though possible.
The heart of the problem is getting something fully automatic and reliable, that does not need any human tuning based on the color of dice, etc., and dealing with different kinds of dice (pips, numbers, custom art).
Sometimes the difference between a 6 and a 9 is a tiny little dot present at the baseline.. otherwise known in machine vision as "noise"...
I have not spent much time thinking about the hardware.. that will come after.. I'm thinking Raspberry Pi with a nice touchscreen.
The two challenges with regard to the hardware are how to create a dice jumbler that can sufficiently randomize a die while looking like a nice piece of art, and the second is creating a sufficiently predictable background for the die (that is, ideally i'd like a die pretty well centered on a plain colored background with no shadows).
One can consider two kinds of basic designs: Camera looking down vs camera from underneath. Both have their own sets of difficulties, both in terms of hardware implementation and in terms of software vision processing.